Virtual Math Learning Center

Related Videos

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

Systems of Two Linear Equations in Two Variables Video 1

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

Making Linear Functions Video 1

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

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

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 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

Definition of a Double-Log Plot

Explaining the definition of logarithmic scale and double-log plots

Double-Log Plot Example 1

Using logarithms to transform a power function into a linear function

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

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 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 36-40

Review of derivatives and tangent lines to functions and vector equations

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 36-40

Derivatives and tangents to curves

MLC WIR 20B M151 week3 #12

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

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

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

Vectors and Derivatives: MATH 171 Problems 1-3

Using the limit definition to find derivatives of functions and vector 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

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

Review of derivatives and tangent lines to functions and vector equations

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

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 36-40

Review of derivatives and tangent lines to functions and vector equations

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 36-40

Review of derivatives and tangent lines to functions and vector equations

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

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

Optimization: MATH 171 Problems 1-3

Optimizing values in word problems

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

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

Linear Forms Video 1

Explaining the main three forms for linear equations

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

Making Linear Functions Video 2

Writing a linear equation of profit from a business word problem

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

Quadratic Equations Video 7

Explaining when a quadratic equation does not have a real solution

Quadratic Form Video 1

Explaining the graph and properties for the parent function of quadratics

Properties of Radical Functions and Expressions Video 1

Explaining the general properties of even and odd root functions

Solving Radical Equations Video 2

Solving equations with even roots and checking the solutions

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

Solving Power and Exponential Equations Video 1

Explaining how to solve equations with power and exponential terms

Properties of Logarithmic Functions and Expressions Video 2

Explaining the basic properties of logarithmic functions

Properties of Rational Functions and Expressions Video 1

Discussing parent functions of rational functions and their properties

MATH 140 WIR2 #8a

Determining the change in y as x increases for a line

MATH 140 WIR2 #8b

Determining the change in x as y decreases for a line

MATH 140 WIR2 #9

Determining the slope of a line given points containing a variable

MATH 140 WIR2 #2

Writing the equation of a line that passes through two points

MATH 140 WIR2 #1

Finding the slope of a line through a pair of points

MATH 140 WIR2 #3

Writing the equation of a line with an undefined slope and a given point

MATH 140 WIR2 #4

Writing the equation of a line with a zero slope given a point

MATH 140 WIR2 #5

Finding the x and y-intercepts for a line

MATH 140 WIR2 #6

Solving for a constant so a line has a particular x-intercept

MATH 140 WIR2 #11

Finding linear functions for the cost, revenue, and profit of a business

MATH 140 WIR2 #12a

Finding the linear cost function for a company

MATH 140 WIR2 #12b

Finding the linear revenue function for a company

MATH 140 WIR2 #12c

Finding the linear profit function for a company

MATH 140 WIR2 #13

Finding a linear demand equation

MATH 140 WIR2 #14

Finding a linear supply function

MATH 140 WIR3 #1

Finding the change in y as x increases for a given line

MATH 140 WIR3 #3

Writing a linear function representing the depreciation of a car

MATH 140 WIR3 #13

Finding the solution to a system of linear equations by graphing

MATH 140 WIR3 #17

Answering questions about a demand and supply word problem

MATH 140 WIR7 #3

Using a graph to find specific values of a function

MATH 140 5.5 #2

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

MATH 140 5.5 #3

Graphing a piecewise function

MATH 140 5.7 #1a

Identifying the parent function and transformations for a given graph

MATH 140 5.7 #1b

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

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

Review of limits, continuity, and differentiability

Calculus Exam Review (Curve Sketching): MATH 142

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

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

Definition of a Semilog Plot

Explaining the logarithmic scale and a semilog plot

Semilog Plot Example 1

Using logarithms to transform an exponential function to a linear function

Semilog Plot Example 2

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

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 V1

Finding the equation of a line through two points

WIR1 20B M150 V2

Finding the equation of a line through two points

WIR1 20B M150 V3

Finding the equations of parallel and perpendicular lines

WIR8 20B M150 V7

Finding the equation of a parallel line

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 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 V19

Graphically verifying if two functions are inverses

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 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

WIR8 20B M150 V10

Determining properties of an exponential function

WIR4 20B M150 V8

Determining the graph of a logarithmic function

WIR4 20B M150 V10

Determining the graph of a logarithmic function

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

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 V11

Using a graph to evaluate a function

WIR2 20B M150 V12

Determining if a function is even or odd

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 10-13

Review of vector functions and parametric equations

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

Review of limits, continuity, and the Intermediate Value Theorem

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

Limits: MATH 151 Problems 6-20

Evaluating limits of functions

Limits: MATH 151 Problems 6-20

Evaluating Limits of Functions

Continuity: MATH 151 Problems 1-6

Continuity of Functions and the Intermediate Value Theorem

Approximations and Exponentials: MATH 151 Problems 7-14

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

Differentials and Approximations: MATH 151 Problems 1-6

Differentials, linear approximations and quadratic approximations

Approximations and Exponentials: MATH 151 Problems 7-14

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

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

Inverse Trigonometric Functions: MATH 151 Problems 9-12

Properties and derivatives of inverse trigonometric functions

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

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 M151 week1 #12

Finding the distance between a point and a line using scalar projection

MLC WIR 20B M151 week2 #01

Converting parametric equations into a Cartesian equation and graphing

MLC WIR 20B M151 week2 #02

Finding a vector equation for the line through two points

MLC WIR 20B M151 week3 #03

Finding a parallel vector through a point

MLC WIR 20B M151 week3 #04

Finding a Cartesian equation for a parametric equation and graphing it

MLC WIR 20B M151 week3 #11

Finding a line perpendicular to a vector and passing through a point

MLC WIR 20B M151 week3 #17

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

MLC WIR 20B M151 week4 #7

Finding the derivatives of compositions of functions from their graphs

MLC WIR 20B M151 week9 #1

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

MLC WIR 20B M151 week10 #4

Finding a vector equation for the line passing through two points

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 Problem 1(a-e)

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

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

Finding volume using using disks, washers and the shell method

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

MATH 152: Area Exercise 1

Finding the area of a region bounded by two curves

Parametric Curves: MATH 151 Problems 1-5

Cartesian equations and parametric equations of curves

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 10-13

Review of vector functions and parametric equations

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

Review of limits, continuity, and the Intermediate Value Theorem

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 171 Problems 4-6

Properties of inverse trig functions and the derivative of arctangent

Inverse Trigonometric Functions: MATH 151 Problems 9-12

Properties and derivatives of inverse trigonometric functions

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

Precise Definition of a Limit: MATH 171 Problems 3 & 4

Proving limits using the epsilon-delta definition

Continuity: MATH 171 Problems 6 & 7

Proving a piecewise function and a polynomial are continuous

Continuity: MATH 151 Problems 1-6

Continuity of Functions and the Intermediate Value Theorem

Approximations and Exponentials: MATH 151 Problems 7-14

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

Differentials: MATH 171 Problems 1 & 2

Proving facts about differentials including a product rule

Differentials and Approximations: MATH 151 Problems 1-6

Differentials, linear approximations, and quadratic approximations

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

Approximations and Exponentials: MATH 151 Problems 7-14

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

Vectors and Derivatives: MATH 151 Problems 1-8

Derivatives and vectors with some physics applications

Inverse Trigonometric Functions: MATH 171 Problems 4-6

Properties of inverse trig functions and the derivative of arctangent

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

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

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

Fundamental Theorem of Calculus: MATH 171 Problems 1-3

Proving and then applying the Fundamental Theorem of Calculus

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 Problem 1(a-e)

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

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

Finding volume using using disks, washers and the shell method

WIR1 20B M251 V1

Showing how an equation in three dimensional space represents a plane

WIR2 20B M251 V2

Finding the point where two lines in three-dimensional space intersect

WIR2 20B M251 V3

Finding an equation of the plane containing two given lines in three-dimensional space

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

WIR3 20B M251 V1

Finding and sketching the domain of a function of two variables

WIR3 20B M251 V2

Finding and sketching the domain of a function of two variables

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

WIR5 20B M251 V6

Evaluating a double integral over a given region

WIR5 20B M251 V7

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 V10

Evaluating a double integral by reversing the order of integration

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 V5

Evaluating a line integral along a curve in space

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

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

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

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 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

Domain of Combinations of Functions Video 3

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

Domain of Combinations of Functions Video 4

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

Domain of Logarithmic Functions Video 1

Finding the domain of a logarithmic function

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

Domain Restrictions

Explaining domain restrictions for denominators, even roots, and logarithms

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

Quadratic Form Video 2

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

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

Solving Radical Equations Video 3

Solving equations with odd radicals

Solving Radical Equations Video 4

Solving equations with multiple radicals

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

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 6

Simplifying power and exponential expressions using properties of exponents

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

Properties of Power and Exponential Expressions Video 9

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

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

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

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

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

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 Conceptual V1

Introducing functions of several variables and level curves

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

Functions of Several Variables Exercise V3

Sketching the level curves for a function of two variables

Functions of Several Variables Exercise V4

Sketching the level curves for a function of two variables

Functions of Several Variables Exercise V5

Sketching the level curves for a function of two variables

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

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

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

The Equation of a Line Perpendicular to a Vector

Finding the equation of a line perpendicular to a vector in \(R^2\)

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