Virtual Math Learning Center

Related Videos

Solving Power and Exponential Equations Video 2

Solving equations with exponential terms

Solving Power and Exponential Equations Video 3

Solving equations with base e exponential terms

Properties of Power and Exponential Expressions Video 4

Properties of exponential growth and decay functions

Properties of Power and Exponential Expressions Video 5

Properties of the exponential function with base e

Properties of Logarithmic Functions and Expressions Video 2

Explaining the basic properties of logarithmic functions

Solving Logarithmic Equations Video 1

Explaining how to solve logarithmic equations

Solving Logarithmic Equations Video 2

Solving logarithmic equations with a single logarithm term

Solving Logarithmic Equations Video 3

Solving logarithmic equations with multiple logarithm terms

Solving Logarithmic Equations Video 4

Solving logarithmic equations with multiple logarithm terms on both sides

WIR4 20B M150 V21

Solving an equation with logarithmic functions

WIR4 20B M150 V22

Solving an equation with logarithmic functions

WIR4 20B M150 V23

Solving an equation with logarithmic functions

WIR4 20B M150 V24

Solving an equation with logarithmic functions

WIR8 20B M150 V11

Solving an equation with logarithmic functions

Domain of Combinations of Functions Video 4

Finding the domain of a function with a root and a logarithm in the denominator

Solving Radical Equations Video 2

Solving equations with even roots and checking the solutions

Solving Radical Equations Video 3

Solving equations with odd radicals

Semilog Plot Example 1

Using logarithms to transform an exponential function to a linear function

Double-Log Plot Example 1

Using logarithms to transform a power function into a linear function

WIR4 20B M150 V10

Determining the graph of a logarithmic function

WIR4 20B M150 V8

Determining the graph of a logarithmic function

WIR4 20B M150 V19

Solving an equation with an exponential function

WIR4 20B M150 V20

Solving an equation with exponential functions by factoring

Quadratic Form Video 1

Explaining the graph and properties for the parent function of quadratics

Solving Radical Equations Video 4

Solving equations with multiple radicals

Properties of Radical Functions and Expressions Video 1

Explaining the general properties of even and odd root functions

Properties of Radical Functions and Expressions Video 2

How to rewrite radical terms as power terms

Solving Radical Equations Video 1

Explaining how to solve radical equations and then solving example problems

Properties of Power and Exponential Expressions Video 9

Simplifying an expression with both power and exponential functions using properties of exponents

Properties of Power and Exponential Expressions Video 6

Simplifying power and exponential expressions using properties of exponents

Properties of Power and Exponential Expressions Video 1

Properties of exponents applied to power and exponential expressions

Properties of Power and Exponential Expressions Video 2

Properties of multiplying and simplifying power and exponential expressions

Properties of Power and Exponential Expressions Video 3

Properties of exponents applied to power and exponential expressions

Properties of Logarithmic Functions and Expressions Video 1

Explaining the terminology and rules of logarithms

Properties of Logarithmic Functions and Expressions Video 3

Expanding logarithmic expressions using logarithm rules

Properties of Logarithmic Functions and Expressions Video 4

Condensing a logarithmic expression into a single logarithm

Properties of Rational Functions and Expressions Video 1

Discussing parent functions of rational functions and their properties

MATH 140 5.6 #1a

Finding the properties of an exponential function including domain, range, end behavior, and intercepts

MATH 140 5.6 #1b

Finding the properties of an exponential function including domain, range, end behavior, and intercepts

MATH 140 5.6 #1c

Finding the properties of an exponential function including domain, range, end behavior, and intercepts

MATH 140 5.6 #3a

Solving an equation with exponential functions

MATH 140 5.6 #3b

Solving an equation with exponential functions

Calculus Exam Review (Derivatives and Approximate Profit): MATH 142

Examples of finding derivatives and calculating approximate profit

Continuity of Functions: MATH 142

Determining where functions are continuous

Derivatives Involving Exponentials and Logarithms: MATH 142

Examples of differentiating exponential and logarithmic functions

Derivatives of Exponential Functions

Explaining the formulas for the derivatives of exponential functions

Definition of a Double-Log Plot

Explaining the definition of logarithmic scale and double-log plots

Definition of a Semilog Plot

Explaining the logarithmic scale and a semilog plot

Semilog Plot Example 2

Writing a non-linear function to represent the line graphed on a semilog plot

Optimization Example 2

Using the second derivative to find the maximum rate of change in a word problem

WIR8 20B M150 V10

Determining properties of an exponential function

WIR4 20B M150 V1

Determining properties of an exponential function

WIR4 20B M150 V2

Determining properties of an exponential function

WIR4 20B M150 V3

Determining properties of an exponential function

WIR4 20B M150 V4

Identifying the graph of an exponential function

WIR4 20B M150 V7

Determining the properties of a logarithmic function

WIR4 20B M150 V9

Determining the properties of a logarithmic function

WIR4 20B M150 V17

Solving an equation with an exponential function

WIR4 20B M150 V18

Solving an equation with an exponential function

WIR4 20B M150 V25

Modeling a population size with an exponential function

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19

Mean Value Theorem and using derivatives to find the shape of curves

Inverse Trigonometric Functions: MATH 151 Problems 9-12

Properties and derivatives of inverse trigonometric functions

Continuity: MATH 151 Problems 1-6

Continuity of Functions and the Intermediate Value Theorem

Inverse Trigonometric Functions: MATH 151 Problems 9-12

Properties and derivatives of inverse trigonometric functions

Studying the Shape of Curves: MATH 151 Problems 2-7

Using derivatives to find properties of graphs

Studying the Shape of Curves: MATH 151 Problems 2-7

Using derivatives to find properties of graphs

MLC WIR 20B M151 week5 #7a

Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week5 #7b

Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week5 #7c

Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week7 #4g

Evaluating a limit with an indeterminate power using L'Hospital's Rule

MLC WIR 20B M151 week7 #4h

Evaluating a limit with an indeterminant power using L'Hospital's Rule

Volume (the Disk, Washer, and Shell Methods): MATH 152 Problem 1(a-e)

Using the disk, washer, and shell method to find a volume of revolution

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Review for the Common Exam: MATH 151 Exam 3 Review Problems 8-15

Review of limits and derivatives of inverse trigonometric functions

Review for Common Exam: MATH 151 Exam 3 Review Problems 15-19

Mean Value Theorem and using derivatives to find the shape of curves

Inverse Trigonometric Functions: MATH 151 Problems 9-12

Properties and derivatives of inverse trigonometric functions

Continuity: MATH 151 Problems 1-6

Continuity of Functions and the Intermediate Value Theorem

Inverse Trigonometric Functions: MATH 151 Problems 9-12

Properties and derivatives of inverse trigonometric functions

Derivatives of Logarithmic Functions: MATH 171 Problems 7-9

Proving facts about logarithms and exponentials including the derivative of an exponential with an arbitrary base

Studying the Shape of Curves: MATH 151 Problems 2-7

Using derivatives to find properties of graphs

Studying the Shape of Curves: MATH 151 Problems 2-7

Using derivatives to find properties of graphs

Volume (the Disk, Washer, and Shell Methods): MATH 152 Problem 1(a-e)

Using the disk, washer, and shell method to find a volume of revolution

WIR3 20B M251 V1

Finding and sketching the domain of a function of two variables

Domain Restrictions

Explaining domain restrictions for denominators, even roots, and logarithms

Domain of Logarithmic Functions Video 1

Finding the domain of a logarithmic function

Domain of Combinations of Functions Video 1

Finding the domain of a function with a denominator, square root, and logarithm

Domain of Combinations of Functions Video 2

Finding the domain of a function with a natural logarithm and denominator

Linear Forms Video 2

Discussing properties of linear functions

Linear Graphs Video 1

Discussing the types of linear graphs including horizontal and vertical lines and their properties

Quadratic Form Video 2

Discussing properties of quadratic functions including the vertex, domain, range, and end behavior

Quadratic Equations Video 7

Explaining when a quadratic equation does not have a real solution

Properties of Power and Exponential Expressions Video 7

Simplifying power and exponential expressions using properties of exponents

Properties of Power and Exponential Expressions Video 8

Simplifying power and exponential expressions using properties of exponents

Solving Rational Equations Video 1

Solving equations that contain rational expressions

Solving Rational Equations Video 2

Solving an equation that contains rational expressions

Solving Rational Equations Video 3

Solving an equation that contains rational expressions

Functions of Several Variables Exercise V5

Sketching the level curves for a function of two variables

MATH 140 WIR7 #2a

Determining the domain and range of a relation and if the relation is a function

MATH 140 WIR7 #2b

Determining the domain and range of a relation and if the relation is a function

MATH 140 WIR7 #2c

Determining the domain and range of a relation and if the relation is a function

MATH 140 5.5 #2

Finding the piecewise-defined function for a given graph along with its domain and range

MATH 140 5.6 #2a

Finding the domain of a function that is a fraction containing an exponential and root

MATH 140 5.6 #2b

Finding the domain of a function that is a fraction containing an exponential and root

MATH 140 5.6 #2c

Finding the domain of a function that is a fraction containing exponentials and a square root

MATH 140 5.7 #1b

Identifying the parent function and transformations for a given graph

MATH 140 5.8 Exercise 1

Using properties of logarithms to determine whether a statement is true or false

MATH 140 5.8 Exercise 2

Using properties of logarithms to determine whether a statement is true or false

Calculus Exam Review (Derivative Properties): MATH 142

Derivative examples with logarithms

Derivatives of Exponential Functions Example 2

Calculating a derivative of a quotient with an exponential function

Double-Log Plot Example 2

Writing a non-linear function for the graph containing two points on a double-log plot

WIR2 20B M150 V7

Solving a rational equation and checking the solutions

WIR3 20B M150 V13

Determining the properties of a rational function and graphing it

WIR8 20B M150 V09

Determining the properties of a rational function and graphing it

WIR3 20B M150 V20

Restricting the domain of a function so it is one-to-one and has an inverse

WIR3 20B M150 V21

Determining algebraically the inverse of a function

WIR3 20B M150 V22

Determining algebraically the inverse of a function

WIR3 20B M150 V23

Determining algebraically the inverse of a function

WIR4 20B M150 V5

Solving an equation with an exponential function

WIR4 20B M150 V6

Simplifying logarithmic expressions using the properties of logarithms

WIR4 20B M150 V11

Using the properties of logarithms to expand a logarithmic expression

WIR4 20B M150 V12

Using the properties of logarithms to expand a logarithmic expression

WIR4 20B M150 V13

Using the properties of logarithms to condense the expression as a single logarithm

WIR4 20B M150 V14

Using the properties of logarithms to condense the expression as a single logarithm

WIR4 20B M150 V15

Using the formula to change the base of a logarithm

WIR4 20B M150 V16

Using the formula to change the base of a logarithm

WIR2 20B M150 V11

Using a graph to evaluate a function

Review for the Common Exam: MATH 151 Exam 1 Review Problems 14-25

Review of limits, continuity, and the Intermediate Value Theorem

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7

Derivatives of exponential functions and the exponential model

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Approximations and Exponentials: MATH 151 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Approximations and Exponentials: MATH 151 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Differentiation and Applications: MATH 151 Problems 1-8

Derivatives of exponential and logarithmic functions and the exponential model

Differentiation and Applications: MATH 151 Problems 1-8

Derivatives of exponential and logarithmic functions and the exponential model

L'Hospital's Rule: MATH 151 Problem 1(a-h)

Using L'Hospital's Rule to solve limits

Riemann Sums and Definite Integrals: MATH 151 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Integration by Substitution: MATH 151 Problems 13 & 14

Examples of integration by substitution

MLC WIR 20B M151 week6 #1gh

Using the Product and Chain Rules to differentiate functions with logarithms

MLC WIR 20B M151 week6 #1ij

Differentiating functions with logarithmic and inverse trigonometric functions

MLC WIR 20B M151 week6 #4a

Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week6 #4b

Using logarithmic differentiation to find the derivative of a function

MLC WIR 20B M151 week7 #4c

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week8 #5c

Antidifferentiating twice to find a function from its second derivative

MLC WIR 20B M151 week8 #5d

Antidifferentiating to find a function from its derivative

MLC WIR 20B M151 week8 #5e

Antidifferentiating twice to find a function from its second derivative

MLC WIR 20B M151 week8 #5f

Antidifferentiating twice to find a function from its second derivative

MLC WIR 20B M151 week8 #6

Using antidifferentiation to find the height of a cliff from the impact speed of a dropped stone

MLC WIR 20B M151 week9 #8a

Evaluating a limit using logarithm properties

MLC WIR 20B M151 week9 #8c

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week9 #8d

Evaluating a limit with an indeterminant power using L'Hospital's Rule

MLC WIR 20B M151 week10 #8e

Evaluating a limit at infinity by combining logarithms

MLC WIR 20B M151 week10 #9c

Finding a derivative using the Chain Rule and Product Rule

MLC WIR 20B M151 week10 #24c

Evaluating a definite integral with an exponential and sine function

MLC WIR 20B M151 week10 #11

Using logarithmic differentiation to find the derivative of a function

Calculus I Integration Review: MATH 151

Examples reviewing integration techniques from Calculus I

Integration by Substitution: MATH 151 Problems 13 & 14

Examples of integration by substitution

Area Between Curves: MATH 152 Problem 1(a-f)

Examples finding the area bounded by curves

Volume (the Disk, Washer, and Shell Methods): MATH 152 Problems 1(f-i) & 2

Finding volume using using disks, washers and the shell method

Integration by Parts: MATH 152 Problems 10-16

Examples using integration by parts

Improper Integrals: MATH 152 Problems 4 & 5

Determining divergence or convergence of improper integrals

WIR 20B M152 V48

Determining if a sequence is increasing, decreasing, or not monotonic and if it is bounded

WIR 20B M152 V77

Finding a power series representation for a function

MATH 152: Improper Integrals Exercise 6

Solving an improper integral where the upper limit of integration is infinity

Review for the Common Exam: MATH 151 Exam 1 Review Problems 14-25

Review of limits, continuity, and the Intermediate Value Theorem

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 3 Review Problems 1-7

Derivatives of exponential functions and the exponential model

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Inverse Trigonometric Functions: MATH 171 Problems 4-6

Properties of inverse trig functions and the derivative of arctangent

Approximations and Exponentials: MATH 151 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Review for the Common Exam: MATH 151 Exam 1 Review Problems 26-35

Review of the limit definition of a derivative and calculating the derivative

Approximations and Exponentials: MATH 151 Problems 7-14

Approximation and Newton's Method, and limits and derivatives of exponential functions

Inverse Trigonometric Functions: MATH 171 Problems 4-6

Properties of inverse trig functions and the derivative of arctangent

Derivatives of Logarithmic Functions: MATH 171 Problems 1-3

Proving the derivative of ln(x) and the power and product rules using logarithmic differentiation

Differentiation and Applications: MATH 151 Problems 1-8

Derivatives of exponential and logarithmic functions and the exponential model

L'Hospital's Rule: MATH 171 Problems 7-9

Proving L'Hospital's Rule and using it to evaluate limits

L'Hospital's Rule: MATH 151 Problem 1(a-h)

Using L'Hospital's Rule to solve limits

Riemann Sums and Definite Integrals: MATH 151 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Riemann Sums and Definite Integrals: MATH 151 Problems 6-12

Using Reimann sums and the Fundamental Theorem of Calculus

Integration by Substitution: MATH 151 Problems 13 & 14

Examples of integration by substitution

Calculus I Integration Review: MATH 151

Examples reviewing integration techniques from Calculus I

Integration by Substitution: MATH 151 Problems 13 & 14

Examples of integration by substitution

Area Between Curves: MATH 152 Problem 1(a-f)

Examples finding the area bounded by curves

Volume (the Disk, Washer, and Shell Methods): MATH 152 Problems 1(f-i) & 2

Finding volume using using disks, washers and the shell method

Integration by Parts: MATH 152 Problems 10-16

Examples using integration by parts

Improper Integrals: MATH 152 Problems 4 & 5

Determining divergence or convergence of improper integrals

WIR2 20B M251 V6

Determining the domain of a three-dimensional vector function

WIR3 20B M251 V2

Finding and sketching the domain of a function of two variables

WIR5 20B M251 V7

Evaluating a double integral over a given region

WIR5 20B M251 V10

Evaluating a double integral by reversing the order of integration

Numerical Calculations in Python

Performing basic numerical calculations in Python

Domain of Radical Functions Video 1

Finding the domain of even and odd roots

Domain of Radical Functions Video 2

Finding the domain of functions with even and odd roots

Domain of Rational Functions Video 1

Finding the domain of several rational functions

Domain of Rational Functions Video 2

Finding the domain of a rational function

Domain of Rational Functions Video 3

Explaining how to find any holes and vertical asymptotes of a rational function

Domain of Rational Functions Video 4

Finding the domain of a rational function using factoring

Making Linear Functions Video 1

Discussing how to write the equation of a line through two given points

Solving Linear Equations Algebraically Video 1

Solving a linear equation algebraically and showing how this relates to the graph

Solving Linear Equations Algebraically Video 2

Solving a linear equation algebraically

Solving Linear Equations Algebraically Video 3

Solving a linear equation algebraically and showing how this relates to the graph

Systems of Two Linear Equations in Two Variables Video 1

Explaining the format and possible solutions for a system of two linear equations

Systems of Two Linear Equations in Two Variables Video 5

Solving a system of two linear equations using a TI-84 calculator

Systems of Two Linear Equations in Two Variables Video 6

Solving a system of two linear equations using a TI-84 calculator

Quadratic Equations Video 1

Explaining the standard form for a quadratic equation and the possible number of solutions

Quadratic Equations Video 2

Solving quadratic equations with the difference of two squares formula

Quadratic Equations Video 3

Solving quadratic equations by factoring

Quadratic Equations Video 4

Solving a quadratic equation by factoring

Quadratic Equations Video 5

Solving a quadratic equation by factoring

Quadratic Equations Video 6

Solving quadratic equations with the quadratic formula and discussing the number of possible solutions

Properties of Rational Functions and Expressions Video 9

Explaining how to multiply and divide rational expressions

Properties of Rational Functions and Expressions Video 10

Performing algebraic operations with rational expressions and simplifying the answer

MATH 152: Sequences Exercise 6

Finding the limit of a sequence using logarithm properties

Functions of Several Variables Exercise V4

Sketching the level curves for a function of two variables

Functions of Several Variables Exercise V1

Evaluating and then finding and sketching the domain of a function of two variables

Functions of Several Variables Exercise V2

Finding and sketching the domain of a function of two variables

Systems of Two Linear Equations in Two Variables Video 1

Explaining the format and possible solutions for a system of two linear equations

MATH 140 WIR2 #7a

Graphing a line without using technology

MATH 140 WIR2 #7b

Graphing a line without using technology

MATH 140 WIR2 #7c

Graphing a line without using technology

MATH 140 WIR2 #10

Writing a function for the value of an item depreciating linearly over time

MATH 140 WIR3 #13

Finding the solution to a system of linear equations by graphing

MATH 140 WIR4 #3

Graphing the solution set of an inequality with two variables

MATH 140 WIR4 #4

Graphing the solution set of an inequality with two variables

MATH 140 WIR4 #5

Graphing the solution set of system of linear inequalities

MATH 140 WIR7 #3

Using a graph to find specific values of a function

MATH 140 WIR7 #6a

Determining the end behavior, real zeros, domain, and y-intercept for a polynomial

MATH 140 WIR7 #6b

Determining the end behavior, real zeros, domain, and y-intercept for a polynomial

MATH 140 WIR7 #6c

Determining the end behavior, real zeros, domain, and y-intercept for a polynomial

MATH 140 WIR7 #6d

Determining the end behavior, real zeros, domain, and y-intercept for a polynomial

MATH 140 WIR7 #6e

Determining the end behavior, real zeros, domain, and y-intercept for a polynomial

MATH 140 WIR7 #7

Identifying quadratic functions and their properties

MATH 140 5.5 #1

Finding the domain of a piecewise function and evaluating it

MATH 140 5.6 #4

Calculating how much to invest with continuously compounded interest

MATH 140 5.7 #1a

Identifying the parent function and transformations for a given graph

MATH 140 5.7 #1c

Identifying the parent function and transformations for a given graph

MATH 140 WIR 8 Pr 1

Finding the domain, intercepts, asymptotes, and holes of a rational function

MATH 140 WIR 8 Pr 2

Finding the domain, intercepts, asymptotes, and holes of a rational function

MATH 140 WIR 8 Pr 3

Finding the domain, intercepts, asymptotes, and holes of a rational function

Calculus Exam Review (Limits and Continuity/Differentiability): MATH 142

Review of limits, continuity, and differentiability

Calculus Exam Review (Limits at Infinity with Exponentials): MATH 142

Examples of calculating infinite limits with exponentials in a rational function

Calculus Exam Review (Application Problems with Integrals): MATH 142

Using integrals to solve application problems

Calculus Exam Review (Curve Sketching): MATH 142

Using the first and second derivative to sketch the graph of the function

Exponential Functions (Limits at Infinity): MATH 142

Limits with exponential functions

Continuity of Functions II: MATH 142

Determining where functions are continuous

Power Rule for Derivatives: MATH 142

Using the power rule to find derivatives

Analyzing Functions IV (Concavity, Inflection Points, Sketching a Graph): MATH 142

Determining concavity and inflection points and sketching the graph

Analyzing Functions (More Curve Sketching): MATH 142

Using Information From the Derivative to Sketch a Graph

Analyzing Functions (Sketching a Graph): MATH 142

Using the Derivative to Sketch the Graph of a Function

More u-Substitution: MATH 142

More examples using u-Substitution

More Application Problems Using Integrals: MATH 142

Solving more application problems using definite integrals

Average Value of a Function: MATH 142

Application problems finding the average value of a function

Area Between Curves: MATH 142

Solving examples finding the area between curves

Intermediate Value Theorem and Bisection Method

Explaining the Intermediate Value Theorem and the Bisection Method

Intermediate Value Theorem and Bisection Method Example

Using the Intermediate Value Theorem and Bisection Method to approximate the solution of an equation

Higher Derivatives Example 1

The definition of higher derivatives and solving an example

Higher Derivatives Example 2

Using derivatives to find the velocity and acceleration functions from the position function

Derivatives of Exponential Functions Example 1

Calculating the derivative of a function with exponentials using the chain and product rule

Exponential Growth and Decay in Discrete Time

Explaining exponential functions in discrete time

Exponential Growth in Discrete Time Example

Solving a population example of exponential growth in discrete time

Recursions Example

Solving a population grown example on recurrence equations

Sandwich Theorem (or Squeeze Theorem)

Explaining the Sandwich (or Squeeze) Theorem with a graphical example

Sandwich Theorem Example

Solving a limit at infinity using the Sandwich (or Squeeze) Theorem

WIR1 20B M150 V7

Simplifying a fraction using properties of exponents

WIR1 20B M150 V12

Simplifying a fraction containing fractional exponents

WIR8 20B M150 V01

Simplifying a fraction with negative exponents

WIR2 20B M150 V4

Solving an equation using the quadratic formula

WIR2 20B M150 V5

Solving a quadratic equation by completing the square

WIR2 20B M150 V6

Solving a polynomial equation using factoring by grouping

WIR8 20B M150 V05

Solving a quadratic equation using the quadratic formula

WIR2 20B M150 V8

Determining if an equation represents a function

WIR2 20B M150 V10

Finding the domains of functions

WIR8 20B M150 V03

Finding the domains of expressions

WIR2 20B M150 V13

Identifying the parent function and transformations of a function

WIR2 20B M150 V14

Identifying the parent function and transformations of a function

WIR3 20B M150 V19

Graphically verifying if two functions are inverses

WIR5 20B M150 V13

Determining the properties of a sine function and graphing it

WIR5 20B M150 V15

Determining the properties of a cosine function and graphing it

WIR5 20B M150 V17

Writing the equation for a sine function to match a given graph

WIR5 20B M150 V18

Writing the equation for a cosine function to match a given graph

WIR6 20B M150 V10

Solving a trigonometric equation

WIR6 20B M150 V11

Solving a trigonometric equation

WIR6 20B M150 V12

Solving a trigonometric equation by factoring

WIR6 20B M150 V13

Solving a trigonometric equation

WIR6 20B M150 V14

Solving a trigonometric equation

WIR6 20B M150 V15

Solving a trigonometric equation

WIR8 20B M150 V13

Solving a trigonometric equation

WIR7 20B M150 V06

Adding and subtracting vectors graphically

WIR6 20B M150 V01

Finding the properties of a transformed tangent function and graphing it

WIR2 20B M150 V12

Determining if a function is even or odd

WIR6 20B M150 V20

Using a double angle formula to solve a trigonometric equation

WIR6 20B M150 V21

Using a double angle formula to solve a trigonometric equation

WIR6 20B M150 V22

Using a double angle formula to solve a trigonometric equation

WIR6 20B M150 V23

Using double angle formulas to evaluate trigonometric functions

Parametric Curves: MATH 151 Problems 1-5

Cartesian equations and parametric equations of curves

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40

Review of derivatives and tangent lines to functions and vector equations

Review for Common Exam: MATH 151 Exam 3 Review Problems 25-30

Antiderivatives and physics applications

Limits: MATH 151 Problems 6-20

Evaluating limits of functions

Limits: MATH 151 Problems 6-20

Evaluating Limits of Functions

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40

Review of derivatives and tangent lines to functions and vector equations

Differentials and Approximations: MATH 151 Problems 1-6

Differentials, linear approximations and quadratic approximations

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40

Derivatives and tangents to curves

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

Mean Value Theorem and Studying the Shape of Curves: MATH 151 Problems 1-6

Mean Value Theorem and properties of a graph

Mean Value Theorem and Studying the Shape of Curves: MATH 151 Problems 1-6

Mean Value Theorem and properties of a graph

MLC WIR 20B M151 week2 #01

Converting parametric equations into a Cartesian equation and graphing

MLC WIR 20B M151 week3 #04

Finding a Cartesian equation for a parametric equation and graphing it

MLC WIR 20B M151 week3 #12

Find the Cartesian form and sketch the graph for the parametric equation of a line

MLC WIR 20B M151 week3 #17

Using the graph of a function to sketch a graph of its derivative

MLC WIR 20B M151 week4 #1e

Differentiating a function with an exponential function and using the Power Rule

MLC WIR 20B M151 week4 #1f

Using the Product Rule to differentiate a function

MLC WIR 20B M151 week4 #1g

Using the Quotient Rule to differentiate a function

MLC WIR 20B M151 week4 #1j

Using the Product and Quotient Rules to differentiate a function

MLC WIR 20B M151 week4 #2a

Using the Product Rule to find a first and second derivative

MLC WIR 20B M151 week4 #1mn

Using the Chain Rule to differentiate functions with exponential and trigonometric functions

MLC WIR 20B M151 week4 #2b

Using the Chain Rule to find a first and second derivative

MLC WIR 20B M151 week4 #6

Using the Chain Rule to find the pattern for a higher order derivative

MLC WIR 20B M151 week4 #7

Finding the derivatives of compositions of functions from their graphs

MLC WIR 20B M151 week5 #1c

Finding the derivative using implicit differentiation

MLC WIR 20B M151 week5 #4ef

Finding the derivative of a function containing a logarithmic function

MLC WIR 20B M151 week5 #4ghi

Finding the derivatives of functions containing logarithms

MLC WIR 20B M151 week5 #5

Finding the derivative of a function containing a logarithms

MLC WIR 20B M151 week5 #6

Finding the equation of a tangent line to a function containing a logarithm

MLC WIR 20B M151 week6 #1ab

Using the Product and Chain Rule to find several derivatives

MLC WIR 20B M151 week6 #1cd

Using the Product, Quotient and Chain Rules to find several derivatives

MLC WIR 20B M151 week6 #1ef

Using the Quotient and Chain Rules to find several derivatives

MLC WIR 20B M151 week6 #1kl

Differentiating functions with inverse trigonometric functions

MLC WIR 20B M151 week6 #2a

Finding the derivative of an implicit function

MLC WIR 20B M151 week6 #2b

Finding the derivative of an implicit function

MLC WIR 20B M151 week6 #3

Using the chain rule to find a derivative

MLC WIR 20B M151 week7 #2b

Finding a number that satisfies the conclusion of the Mean Value Theorem on an interval

MLC WIR 20B M151 week7 #4d

Evaluating a limit using L'Hospital's Rule

MLC WIR 20B M151 week7 #4e

Evaluating a limit with an indeterminate product using L'Hospital's Rule

MLC WIR 20B M151 week7 #4f

Evaluating a limit with an indeterminant difference using L'Hospital's Rule

MLC WIR 20B M151 week8 #5b

Antidifferentiating twice to find a function from its second derivative

MLC WIR 20B M151 week9 #1

Determining the properties of a function from the graph of its derivative

MLC WIR 20B M151 week9 #8f

Evaluating a limit with an indeterminant product using L'Hospital's Rule

MLC WIR 20B M151 week9 #10d

Finding the antiderivative of a function and using a function value to find the constant

MLC WIR 20B M151 week10 #19b

Using L'Hospital's Rule to solve a limit with an indeterminant product

MLC WIR 20B M151 week10 #19c

Using L'Hospital's Rule to solve a limit with an indeterminant difference

MLC WIR 20B M151 week10 #19d

Using L'Hospital's Rule to solve a limit with an indeterminant power

MLC WIR 20B M151 week10 #23a

Evaluating an indefinite integral by simplifying a fraction to powers of x

MLC WIR 20B M151 week10 #24b

Evaluating a definite integral by first simplifying the integrand

MLC WIR 20B M151 week10 #8c

Evaluating the limit at infinity of a fraction with exponential functions

MLC WIR 20B M151 week10 #8d

Evaluating the limit at negative infinity of a fraction with exponential functions

MLC WIR 20B M151 week10 #24e

Using u-substitution to evaluate an indefinite integral

MLC WIR 20B M151 week10 #9d

Finding a derivative using the Quotient Rule

Review for the Common Exam: MATH 152 Exam 3 Review Problem 6

Review of estimating the sum of a series and the remainder

Review for the Common Exam: MATH 152 Exam 3 Review Problems 4 & 5

Review of using tests to determine if a series is absolutely convergent, convergent, and divergent

Review for the Common Exam: MATH 152 Exam 2 Review Problems 8 & 9

Review of improper integrals and the Comparison Theorem

Review for the Common Exam: MATH 152 Exam 3 Review Problems 10-13

Review of power series properties and writing functions as power series

Review for the Common Exam: MATH 152 Exam 3 Review Problems 13-18

Review of Taylor and Maclaurin Series and their properties

Review for the Common Exam: MATH 152 Exam 3 Review Problems 19 & 20

Review of Taylor Polynomials and Taylor's Inequality

Review for the Common Exam: MATH 152 Exam 3 Review Problems 4 & 5

Review of using tests to determine if a series is absolutely convergent, convergent, and divergent

Sequences: MATH 152 Problems 1-3

Determining properties of sequences

Taylor and Maclaurin Series: MATH 152 Problems 4-10

Finding Taylor and Maclaurin Series for functions

Representations of Functions as Power Series: MATH 152 Problems 2 & 3

Finding power series representations for functions and the radius and interval of convergence of the power series

Volume (Disks, Washers, and by Slicing): MATH 152 Problems 2 & 3

Examples finding a volume using disks, washers, and by slicing

Integration by Partial Fractions: MATH 152 Problems 12 & 13

Using the method of partial fractions to integrate rational functions

WIR 20B M152 V1

Integrating an exponential function using u-substitution

WIR 20B M152 V2

Integrating a rational function using u-substitution

WIR 20B M152 V3

Integrating a rational function using u-substitution

WIR 20B M152 V10

Finding the area of a region bounded by curves

WIR 20B M152 V15

Finding the volume of a solid of revolution using the washer method

WIR 20B M152 V17

Finding the volume of a solid of revolution using cylindrical shells

WIR 20B M152 V22

Evaluating an integral using integration by parts

WIR 20B M152 V23

Evaluating an integral using integration by parts

WIR 20B M152 V26

Evaluating an integral using integration by parts

WIR 20B M152 V34

Evaluating an integral using integration by parts

WIR 20B M152 V35

Evaluating an integral using integration by parts

WIR 20B M152 V35.5

Evaluating an integral using integration by parts

WIR 20B M152 V43

Using the comparison test to determine if an improper integral converges or diverges

WIR 20B M152 V45

Determining if a sequence converges or diverges

WIR 20B M152 V53

Determining if a series converges or diverges and find the sum if it converges

WIR 20B M152 V56

Using the comparison test to determine if a series converges or diverges

WIR 20B M152 V57

Using the comparison test to determine if a series converges or diverges

WIR 20B M152 V58

Using the comparison test to determine if a series converges or diverges

WIR 20B M152 V59

Using the limit comparison test to determine if a series converges or diverges

WIR 20B M152 V69

Determining if a series is absolutely convergent, conditionally convergent, or divergent. 

WIR 20B M152 V70

Determining if a series is absolutely convergent, conditionally convergent, or divergent. 

WIR 20B M152 V75

Finding the interval and radius of convergence for a power series

WIR 20B M152 V83

Finding the Taylor polynomial of a function

WIR 20B M152 V84

Converting parametric equations into a Cartesian equation and graphing

WIR 20B M152 V85

Converting parametric equations into a Cartesian equation and graphing

WIR 20B M152 V86

Converting parametric equations into a Cartesian equation and graphing

WIR 20B M152 V87

Converting parametric equations into a Cartesian equation and graphing

WIR 20B M152 V88

Finding the length of a curve given by parametric equations

WIR 20B M152 V96

Finding the area of a region defined using polar coordinates

MATH 152: Area Exercise 1

Finding the area of a region bounded by two curves

MATH 152: Integration by Parts Exercise 1

Solving an indefinite integral with an exponential function using integration by parts

MATH 152: Integration by Parts Exercise 2

Solving a definite integral with an exponential function using integration by parts

MATH 152: Integration by Parts Exercise 4

Solving an indefinite integral with a natural logarithm using integration by parts

MATH 152: Integration by Parts Exercise 5

Solving a definite integral with a natural logarithm using integration by parts

MATH 152: Integration by Parts Exercise 8

Solving an indefinite integral with an exponential function using integration by parts

MATH 152: Integration by Parts Exercise 9

Using integration by parts twice for an integral with sine and an exponential function

MATH 152: u-Substitution Exercise 4

Using u-substitution to evaluate a definite integral with a natural logarithm

MATH 152: u-Substitution Exercise 6

Using u-substitution on an indefinite integral with an exponential function, sine, and cosine

MATH 152: u-Substitution Exercise 8

Using u-substitution to solve an indefinite integral with an exponential function

MATH 152: Improper Integrals Exercise 2

Solving an improper integral where the upper limit of integration is infinity

MATH 152: Improper Integrals Exercise 4

Solving an improper integral where the upper limit of integration is infinity

Vectors: MATH 171 Problems 1 & 2

Proving associative and scalar multiplication properties for vectors

Parametric Curves: MATH 151 Problems 1-5

Cartesian equations and parametric equations of curves

Vectors and Derivatives: MATH 171 Problems 1-3

Using the limit definition to find derivatives of functions and vector functions

Vectors and Derivatives (Product Rule): MATH 171 Problems 1-3

Proving facts about the derivatives of vector functions including the product rule

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40

Review of derivatives and tangent lines to functions and vector equations

Review for Common Exam: MATH 151 Exam 3 Review Problems 25-30

Antiderivatives and physics applications

Limits: MATH 151 Problems 6-20

Evaluating limits of functions

Limits: MATH 151 Problems 6-20

Evaluating limits of functions and using the Squeeze Theorem

Continuity: MATH 171 Problems 6 & 7

Proving a piecewise function and a polynomial are continuous

Derivatives and Rates of Change: MATH 171 Problems 1-3

Using the limit definition to find derivatives of functions and vector functions

The Derivative as a Function: MATH 171 Problems 1-3

Using the limit definition to find derivatives of functions and vector functions

The Derivative as a Function: MATH 171 Problems 4 & 5

Using the limit definition to find a derivative and proving the power rule

Differentiation Formulas: MATH 171 Problems 4 & 5

Using the limit definition to find a derivative and proving the power rule

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40

Review of derivatives and tangent lines to functions and vector equations

Differentials and Approximations: MATH 151 Problems 1-6

Differentials, linear approximations, and quadratic approximations

Review for the Common Exam: MATH 151 Exam 1 Review Problems 36-40

Review of derivatives and tangent lines to functions and vector equations

Exponentials and Hyperbolic Trigonometric Functions: MATH 171 Problems 3 & 4

Examples involving the tangent line to an exponential function and finding the derivative of hyperbolic cosine

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

Implicit Differentiation: MATH 171 Problems 6 & 7

Using implicit differentiation to solve a problem and to prove the power rule for rational exponents

Mean Value Theorem and Studying the Shape of Curves: MATH 151 Problems 1-6

Mean Value Theorem and properties of a graph

Studying the Shape of Curves: MATH 171 Problems 1-3

What the derivatives of a function tell us about the shape of its graph

Mean Value Theorem and Studying the Shape of Curves: MATH 151 Problems 1-6

Mean Value Theorem and properties of a graph

Optimization: MATH 171 Problems 1-3

Optimizing values in word problems

Fundamental Theorem of Calculus: MATH 171 Problems 1-3

Proving and then applying the Fundamental Theorem of Calculus

Integration by Substitution: MATH 171 Problems 4-6

Using u substitution to evaluate integrals and prove facts about logarithms and integrals and

Review for the Common Exam: MATH 152 Exam 3 Review Problem 6

Review of estimating the sum of a series and the remainder

Review for the Common Exam: MATH 152 Exam 3 Review Problems 4 & 5

Review of using tests to determine if a series is absolutely convergent, convergent, and divergent

Review for the Common Exam: MATH 152 Exam 2 Review Problems 8 & 9

Review of improper integrals and the Comparison Theorem

Review for the Common Exam: MATH 152 Exam 3 Review Problems 10-13

Review of power series properties and writing functions as power series

Review for the Common Exam: MATH 152 Exam 3 Review Problems 13-18

Review of Taylor and Maclaurin Series and their properties

Review for the Common Exam: MATH 152 Exam 3 Review Problems 19 & 20

Review of Taylor Polynomials and Taylor's Inequality

Review for the Common Exam: MATH 152 Exam 3 Review Problems 4 & 5

Review of using tests to determine if a series is absolutely convergent, convergent, and divergent

Sequences: MATH 152 Problems 1-3

Determining properties of sequences

Taylor and Maclaurin Series: MATH 152 Problems 4-10

Finding Taylor and Maclaurin Series for functions

Representations of Functions as Power Series: MATH 152 Problems 2 & 3

Finding power series representations for functions and the radius and interval of convergence of the power series

Volume (Disks, Washers, and by Slicing): MATH 152 Problems 2 & 3

Examples finding a volume using disks, washers, and by slicing

Integration by Partial Fractions: MATH 152 Problems 12 & 13

Using the method of partial fractions to integrate rational functions

Integration Using Partial Fractions: MATH 172 Problems 8 & 9

Finding a partial fraction decomposition and integrating using partial fractions

WIR1 20B M251 V1

Showing how an equation in three dimensional space represents a plane

WIR2 20B M251 V4

Identifying the equation of a hyperboloid and sketching its graph

WIR2 20B M251 V5

Identifying the equation of a cone in three dimensions and sketching its graph

WIR2 20B M251 V7

Finding the limit of a three-dimensional vector function

WIR2 20B M251 V12

Finding the position vector function given the velocity and an initial position

WIR3 20B M251 V3

Sketching the graph of a function of two variables

WIR3 20B M251 V4

Sketching the graph of a function of two variables

WIR3 20B M251 V5

Sketching the level curves of a function of two variables

WIR3 20B M251 V6

Sketching the level curves of a function of two variables

WIR3 20B M251 V7

Describing the level surfaces of a function of three variables

WIR3 20B M251 V8

Finding the partial derivatives of a function of two variables

WIR3 20B M251 V9

Finding the partial derivatives of a function of two variables

WIR3 20B M251 V11

Finding all second-order partial derivatives of a function of two variables

WIR5 20B M251 V6

Evaluating a double integral over a given region

WIR5 20B M251 V8

Evaluating a double integral and sketching the region of integration

WIR5 20B M251 V9

Changing the order of integration for a double integral

WIR5 20B M251 V11

Setting up double integrals of Type I and II to give the volume of a solid under a surface

WIR6 20B M251 V1

Evaluating a double integral over a circular region by changing to polar coordinates

WIR6 20B M251 V2

Evaluating a double integral by changing to polar coordinates

WIR6 20B M251 V3

Evaluating a double integral by changing to polar coordinates

WIR6 20B M251 V4

Converting a double integral to a double integral in polar coordinates

WIR6 20B M251 V5

Writing an iterated integral in polar coordinates that gives the volume of the solid that lies below a paraboloid

WIR6 20B M251 V6

Writing an iterated integral in polar coordinates that gives the volume of the solid bounded by a cone

WIR6 20B M251 V7

Writing an a triple integral over a given solid as an iterated integral

WIR6 20B M251 V8

Evaluating a triple integral over a solid bounded by given surfaces

WIR6 20B M251 V9

Writing an iterated integral that gives the volume of a solid

WIR7 20B M251 V1

Evaluating a triple integral over a solid bounded by elliptic paraboloids

WIR7 20B M251 V2

Writing a triple integral as an iterated integral in cylindrical coordinates

WIR7 20B M251 V3

Converting an iterated triple integral into cylindrical and spherical coordinates

WIR7 20B M251 V4

Using an iterated integral in spherical coordinates to find the volume of a solid

WIR7 20B M251 V5

Evaluating a triple integral for a given solid by writing an iterated integral in spherical coordinates

WIR8 20B M251 V4

Evaluating a line integral along a curve

WIR8 20B M251 V5

Evaluating a line integral along a curve in space

WIR9 20B M251 V5

Finding the curl and divergence of a three dimensional vector field

WIR10 20B M251 V4

Evaluating a surface integral of a vector field

Parametric Plots and Tangents at a Given t-value in Python

Using Python to find the tangent line to a parametric equation and plot the two graphs

Plotting Multiple Expressions in One Graph in Python

Graphing a piecewise function using Python

Word Problems and the Algorithmic Process for Multistep Problem Solving in Python

Solving a multistep word problem in Python and graphing the resulting function

Approximating Definite Integrals with Riemann Sums in Python

Using Python to approximate a definite integral using left endpoint Riemann sums

Finding and Graphing Tangent Lines to a Curve in Python

Using Python to find the equation of the tangent line to a curve and graphing the result

Implicit Plots and Implicit Differentiation in Python

Using Python to plot an implicit curve and find a tangent line using implicit differentiation

List Comprehension and Numerical, Graphical, and Symbolic Limits in Python

Using Python to numerically estimate a limit, graphically estimate a limit, and find the exact limit

Linear Algebra for Math 308: L7V2

Showing how the exponential function is the solution to an initial value problem

Changing Order of Integration for Iterated Integrals

Evaluating iterated integrals over the same region but with different orders of integration

Determining the Iterated Integral for a Given Region

Writing and then solving an iterated integral for a given region

Splitting a Domain Into Two Pieces for a Double Integral

Evaluating a double integral over a given region by splitting it into two double integrals

Using Double Integrals to Compute Mass and Weight

Using double integrals to calculate the weight of a plate given its density and size

Domain of Combinations of Functions Video 3

Finding the domain of a function with a square root in the denominator

Linear Forms Video 1

Explaining the main three forms for linear equations

Systems of Two Linear Equations in Two Variables Video 2

Solving a system of linear equations with two variables

Systems of Two Linear Equations in Two Variables Video 3

Solving a system of two linear equations with two variables using the elimination method

Systems of Two Linear Equations in Two Variables Video 4

Solving a system of two linear equations using a TI-84 calculator

Making Linear Functions Video 2

Writing a linear equation of profit from a business word problem

Properties of Rational Functions and Expressions Video 2

Finding horizontal asymptotes for rational functions

Properties of Rational Functions and Expressions Video 3

Explaining how to do polynomial long division

Properties of Rational Functions and Expressions Video 4

Finding horizontal asymptotes for rational functions

Properties of Rational Functions and Expressions Video 5

Determining the end behavior and horizontal asymptotes for rational functions

Properties of Rational Functions and Expressions Video 6

Explaining basic algebraic operations for fractions

Properties of Rational Functions and Expressions Video 7

How to simplify rational expressions

Properties of Rational Functions and Expressions Video 8

Adding and subtracting rational expressions by finding a common denominator

MATH 152: Sequences Exercise 7

Finding the limit of a sequence

Functions of Several Variables Exercise V3

Sketching the level curves for a function of two variables

Functions of Several Variables Conceptual V1

Introducing functions of several variables and level curves

Euler Circuits Example 10

Determining if a list of vertices in a graph is a path, a circuits, an Euler path, an Euler circuit, or none of the above

What is a Graph?

Explaining that a graph is a collection of vertices and edges

Euler Circuits Example 1

Drawing a graph to depict a bus route

Euler Circuits Example 2

Counting the vertices and edges from a graph

Euler Circuits Example 3

Identifying the adjacent vertices in a graph

Euler Circuits Example 4

Finding two different paths between vertices in a graph

Euler Circuits Example 5

Determining if a list of vertices in a graph is a path, circuit, Euler path, Euler circuit, or none of the above

Euler Circuits Example 6

Determining if a list of vertices in a graph is a path, a circuits, an Euler path, an Euler circuit, or none of the above

Euler Circuits Example 7

Determining if a list of vertices in a graph is a path, a circuits, an Euler path, an Euler circuit, or none of the above

Euler Circuits Example 8

Determining if a list of vertices in a graph is a path, a circuits, an Euler path, an Euler circuit, or none of the above

Euler Circuits Example 9

Determining if a list of vertices in a graph is a path, a circuits, an Euler path, an Euler circuit, or none of the above

Finding Euler Circuits

Explaining Euler's Theorem on when a graph has an Euler path or Euler circuit

Finding Euler Circuits Example 1

Finding the valence of each vertex in a graph

Hamiltonian Circuits

Explaining Hamiltonian Circuits and paths, the Method of Trees to find them, and the number of Hamiltonian circuits for complete graphs

Hamiltonian Circuits Example 1

Determining if a graph has a Hamiltonian path, Hamiltonian Circuit, or neither

Hamiltonian Circuits Example 2

Determining if a graph has a Hamiltonian path, Hamiltonian Circuit, or neither

Hamiltonian Circuits Example 3

Determining if a graph has a Hamiltonian path, Hamiltonian Circuit, or neither

Hamiltonian Circuits Example 4

Determining if a graph has a Hamiltonian path, Hamiltonian Circuit, or neither

Hamiltonian Circuits Example 5

Using the method of trees to find all Hamiltonian circuits of a graph starting at a given vertex

Hamiltonian Circuits Example 8

Determining if a graph is a complete graph

Hamiltonian Circuits Example 9

Determining if a graph is a complete graph

Hamiltonian Circuits Example 10

Determining if a graph is a complete graph

Hamiltonian Circuits Example 11

Determining if a graph is a complete graph

Minimum-Cost Spanning Trees Example 1

Finding two spanning trees for a graph

Functions of Several Variables Conceptual V1

Introducing functions of several variables and level curves

Graphs for Data

Explanation of graphs for data and which are appropriate for categorical or numerical data

Measures of Spread

Finding the range, IQR, standard deviation, and variance for a given set of data