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MATH 308 WIR22A V15

Solving an initial value problem including air resistance for the path of a thrown ball to determine the maximum height it reaches

MATH 308 WIR22A V16

Solving an initial value problem using Newton’s Law of Cooling to determine the temperature of a drink left outside as the outdoor temperature changes

MATH 308 WIR22A V17

Solving an initial value problem to determine the amount of pollution in a lake at any time

MATH 308 WIR22A V11

Solving a first order linear differential equation with an integrating factor and then finding the initial condition so the solution touches the x-axis

MATH 308 WIR22A V10b

Solving an initial value problems with an integrating factor and finding the interval of validity

MATH 308 WIR22A V38

Determining where a first-order linear initial value problem has a solution and then solving it

MATH 308 WIR22A V39

Solving a first-order linear initial value problem to determine the concentration of salt in a tank

MATH 308 WIR22A V2

Writing and then solving a differential equation for the temperature of a cup of coffee

MATH 308 WIR22A V3

Writing and then solving an initial value problem for the amount of dye in a pool

MATH 308 WIR22A V8

Writing and then solving an initial value problem to determine the stopping time and distance of a stone on a smooth surface

MATH 308 WIR22A V13

Solving an initial value problem using Newton’s Law of Cooling to determine the time it takes for a cake to cool to a given temperature

MATH 308 WIR22A V14

Solving a separable differential equation to determine how long it takes a population of bacteria to double

MATH 308 WIR22A V18

Determining an interval in which the solution of a first order, linear initial value problem is certain to exist

MATH 308 WIR22A V20

Solving linear differential equations and determining the interval in which the solution exists

MATH 308 WIR22A V28

Finding an integrating factor to make a differential equation exact and then solving it

MATH 308 WIR22A V29

Finding an integrating factor to make a differential equation exact and then solving it

MATH 308 WIR22A V30

Finding an integrating factor to make a differential equation exact and then solving it

Integrating Factor Exercise 2

Using an integrating factor to solve a first-order linear differential equation and finding its interval of validity

Linear Differential Equations: MATH 172 Problems 1 & 2

Solving first order linear differential equations

MATH 308 WIR 22A V9a

Solving a linear, first-order differential equation using an integrating factor

MATH 308 WIR 22A V9c

Solving a linear, first-order differential equation using an integrating factor

MATH 308 WIR22A V10a

Finding the solution to a separable initial value problem and its interval of validity

MATH 308 WIR22A V21

Verifying two different functions are both solutions to a differential equation

MATH 308 WIR22A V19

Determining an interval in which the solution of a first order, linear initial value problem is certain to exist

MATH 308 WIR22A V22

Finding the equilibrium solutions and properties for an autonomous differential equation

MATH 308 WIR22A V23

Finding the equilibrium solutions and properties for an autonomous differential equation

MATH 308 WIR22A V27

Solving an exact differential equation with a given initial condition

MATH 308 WIR22A V33

Solving a second order linear initial value problem and then solving for the initial condition so the solution will have a given properties

MATH 308 WIR22A V34

Solving a second order linear initial value problem with complex roots to the characteristic equation

MATH 308 WIR22A V36

Using the reduction of order technique to find the solution to an initial value problem

MATH 308 WIR22A V52

Using Laplace Transforms to solve initial value problems

MATH 308 WIR22A V58

Solving an initial value problem using the Laplace transform

MATH 308 WIR22A V59

Using the Laplace transform to solve an initial value problem with an impulse function

MATH 308 WIR22A V65

Using the Laplace transform and the impulse function to write and solve an initial value problem for the motion of a spring

MATH 308 WIR22A V64

Solving an initial value problem using the Laplace transform and writing the answer using a convolution integral

MATH 308 WIR22A V73

Finding a power series solution to an initial value problem

MATH 308 WIR22A V74

Finding the value of the second and third derivative of a solution at the given point

MATH 308 WIR22A V57

Using Laplace transforms and step functions to solve an initial value problem

MATH 308 WIR22A V80

Solving a second-order linear initial value problem

MATH 308 WIR22A V84

Using Laplace transforms to solve initial value problems with step and impulse functions

Integrating Factor

Using an integrating factor to solve first-order linear differential equations

Integrating Factor Exercise 1

Using an integrating factor to solve a first-order linear differential equation

Separable Differential Equations: MATH 172 Problems 6 & 7

Solving separable differential equations involving Newton's Law of Cooling and orthogonal trajectories

MATH 308 WIR22A V5

Showing that a function is the general solution to a differential equation and finding the solution to an initial value problem

MATH 308 WIR22A V25

Show that a differential equation is not exact but becomes exact when multiplied by a given integrating factor

MATH 308 WIR22A V26

Finding an integrating factor to make a differential equation exact and then solving it

MATH 308 WIR22A V32

Solving for a function given the Wronskian of it and another function

MATH 308 WIR22A V40

Finding the equilibrium solutions and properties for an autonomous differential equation

MATH 308 WIR22A V41

Using an integrating factor to make a differential equation exact and then solving it

Linear Algebra for Math 308: L7E2

Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L7E4

Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L7E6

Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L7E8

Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L8E1

Solving a system of first-order linear differential equations

Linear Algebra for Math 308: L8E2

Solving a system of first-order linear differential equations where the matrix has complex eigenvalues

Linear Algebra for Math 308: L8E4

Solving a system of first-order linear differential equations

Linear Algebra for Math 308: L8E5

Solving a system of first-order linear differential equations when a generalized eigenvector is needed

Linear Algebra for Math 308: L8E6

Solving a system of first-order linear differential equations

Separable Equations Exercise 2

Solving a separable first-order differential equation

Variation of Parameters

How to solve differential equations using variation of paramaters

Variation of Parameters Exercise 1

Solving a first-order, linear, nonhomogeneous differential equation using variation of parameters

Calculus Exam Review (Absolute Extrema and Integration): MATH 142

Examples finding absolute maximums, antiderivatives, and definite integrals

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

Using integrals to solve application problems

Initial Value Problems: MATH 142

Integrating to find a function from its derivative and an initial condition

MATH 308 WIR22A V1

Finding the slope of solutions and the critical points of a differential equation

MATH 308 WIR22A V4

Classifying differential equations as ordinary or partial and linear or nonlinear and finding the order

MATH 308 WIR22A V6

Solving for a constant so that a function is a solution of a differential equation

MATH 308 WIR22A V7

Solving for a constant so that a function is a solution of a differential equation

MATH 308 WIR 22A V9b

Solving a separable differential equation

MATH 308 WIR22A V24

Determining if differential equations are exact and solving the ones that are

MATH 308 WIR22A V37

Using Abel's Theorem to calculate a value of the Wronskian

MATH 308 WIR22A V31

Determining if two functions form a fundamental set of solutions for a second order linear differential equation

MATH 308 WIR22A V35

Solving a second order linear initial value problem with a repeated root to the characteristic equation

MATH 308 WIR22A V43

Using the method of undetermined coefficients to find the form of a particular solution for a second order linear differential equation

MATH 308 WIR22A V42

Using the method of undetermined coefficients to solve second-order linear differential equation

MATH 308 WIR22A V44

Using the variation of parameters method to solve a nonhomogeneous second-order linear differential equation

MATH 308 WIR22A V45

Solving an initial value problem to find the position of a mass on a vibrating spring

MATH 308 WIR22A V46

Solving an initial value problem to find the position of a mass on a vibrating spring with damping

MATH 308 WIR22A V47

Solving an initial value problem to find the position of a mass on a vibrating spring with an external force

MATH 308 WIR22A V48

Solving an initial value problem to find the position of a mass on a vibrating spring with an external force

MATH 308 WIR22A V49

Solving an initial value problem to find the position of a mass on a vibrating spring under resonance with an external force

MATH 308 WIR22A V71

Finding a power series solution to a differential equation

MATH 308 WIR22A V72

Finding a power series solution to a differential equation

MATH 308 WIR22A V75

Transforming an initial value problem into three first-order equations written in matrix form

MATH 308 WIR22A V66

Finding the form of a particular solution for a second-order linear differential equation

MATH 308 WIR22A V67

Finding the general solutions of a second-order linear nonhomogeneous differential equation

MATH 308 WIR22A V82

Using the method of undetermined coefficients to solve second-order linear differential equation

MATH 308 WIR22A V83

Using reduction of order and variation of parameters to solve a second-order linear nonhomogeneous differential equation

Linear Algebra for Math 308: L7V2

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

Linear Algebra for Math 308: L7V3

Using power series to define a matrix exponential function to use in solving differential equations with matrices

Linear Algebra for Math 308: L7V4

Calculating a matrix exponential function using a power series and the diagonalization of the matrix

Linear Algebra for Math 308: L7V6

Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L8V3

Finding the general solution to a system of first order differential equations

Linear Algebra for Math 308: L8V4

Solving a system of first-order linear differential equations where the matrix has complex eigenvalues

Linear Algebra for Math 308: L8V5

Deriving the general solution for a system of first-order linear differential equations where the matrix has complex eigenvalues

Linear Algebra for Math 308: L8V6

Solving a system of first-order linear differential equations where the matrix has complex eigenvalues

Linear Algebra for Math 308: L8V1

Solving for the general solution for a system of first-order linear differential equations

Linear Algebra for Math 308: L8E3

Solving a system of first-order linear differential equations where a generalized eigenvector is needed

Differential Equation Models Exercise 1

Using a differential equation to determine how much salt is in a tank after 60 minutes

Linear Algebra for Math 308: L8V1

Solving for the general solution for a system of first-order linear differential equations

Ordinary Differential Equations Introduction

An introduction to ordinary differential equations along with several examples

Separable Equations

How to solve first-order separable differential equations

Separable Equations Exercise 1

Solving a separable first-order differential equation

Compound Interest Video 2

How to calculate continuously compounded interest with money also being deposited or withdrawn continuously

Compound Interest Exercise 1

Calculating the balance of an IRA when you retire with continuous compounding interest

Systems of Ordinary Differential Equations Exercise 1

Converting a given linear system of ordinary differential equations into matrix form

Systems of Ordinary Differential Equations

An introduction to systems of first-order ordinary differential equations

Calculus Exam Review (Integration): MATH 142

Indefinite integral examples and u-substitution

Application Problems Using Integrals: MATH 142

Solving several application problems using integrals

More Application Problems Using Integrals: MATH 142

Solving more application problems using definite integrals

Average Value of a Function II: MATH 142

Another example finding the average value of a function

WIR4 20B M150 V25

Modeling a population size with an exponential function

MLC WIR 20B M151 week10 #14

Writing an equation for the growth of a population of bacteria

Antiderivatives: MATH 171 Problems 4-6

Proving facts about antiderivatives and a physics application

Power Series as Functions: MATH 172 Problems 4 & 5

Examples about the derivative and integral of a power series

WIR2 20B M251 V12

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

MATH 308 WIR22A V50

Using the definition to find the Laplace transforms of functions

MATH 308 WIR22A V51

Finding the inverse Laplace transforms of functions

MATH 308 WIR22A V53

Writing piecewise functions in terms of the unit step function and finding the Laplace transform

MATH 308 WIR22A V60

Finding the convolution of two functions using the definition

MATH 308 WIR22A V61

Using the Laplace transform to compute the convolution of functions

MATH 308 WIR22A V62

Using the Laplace transform to solve for a function in an equation with a convolution

MATH 308 WIR22A V63

Writing the inverse Laplace transform of a function using a convolution integral

MATH 308 WIR22A V70

Determining the radius of convergence of a power series

MATH 308 WIR22A V76

Finding a differential equation for which two given vector functions are solutions

MATH 308 WIR22A V77a

Solving a system of first-order linear differential equations with real, distinct eigenvalues

MATH 308 WIR22A V77c

Solving a system of first-order linear differential equations with complex eigenvalues

MATH 308 WIR22A V77b

Solving a system of first-order linear differential equations with a repeated, real eigenvalue

MATH 308 WIR22A V78

Classifying the type and stability of the equilibrium points of a system of linear differential equations for different values of a parameter

MATH 308 WIR22A V79

Solving a nonhomogeneous system of linear first order differential equations

MATH 308 WIR22A V54

Using the definition to find the Laplace transform of a function

MATH 308 WIR22A V55

Using Heaviside's unit step functions to find the Laplace transform of a function

MATH 308 WIR22A V56

Finding the inverse Laplace transforms of functions

MATH 308 WIR22A V68

Using the definition to find the Laplace transform of a function containing an impulse function

MATH 308 WIR22A V69

Finding the Laplace transform of functions with a convolution integral

MATH 308 WIR22A V85

Solving a system of first-order linear differential equations and determining properties of the solutions

MATH 308 WIR22A V81

Finding the Wronskian of two functions

Linear Algebra for Math 308: L1V1

Explaining the definitions of real and complex vectors with examples

Linear Algebra for Math 308: L1V9

Determining if two vectors are linearly independent

Linear Algebra for Math 308: L1V2

Defining scalar multiplication and giving an example

Linear Algebra for Math 308: L1V3

Defining vector addition and giving an example

Linear Algebra for Math 308: L1V4

Finding a linear combination of vector functions

Linear Algebra for Math 308: L1V5

Defining linear combinations of vectors and providing an example

Linear Algebra for Math 308: L1V6

Explaining the concepts of existence and uniqueness for solutions of systems of equations

Linear Algebra for Math 308: L1V7

Defining linear independence and dependence for vectors

Linear Algebra for Math 308: L1V8

Explaining two vectors are linearly dependent if and only if they are scalar multiples

Linear Algebra for Math 308: L1V10

Determining if three vectors are linearly independent

Linear Algebra for Math 308: L1V11

Showing that three vectors are linearly independent

Linear Algebra for Math 308: L1V12

Using linear independence to show the uniqueness of a vector equation solution

Linear Algebra for Math 308: L1V13

Defining a spanning set for a vector space

Linear Algebra for Math 308: L1V14

Determining if vectors form a spanning set and defining a basis

Linear Algebra for Math 308: L2V2

Writing a vector equation using matrix multiplication

Linear Algebra for Math 308: L2V3

Defining multiplication of a matrix and vector and then giving an example

Linear Algebra for Math 308: L2V4

Defining eigenvalues and eigenvectors of a matrix

Linear Algebra for Math 308: L2V5

Defining matrix operations such as addition and multiplication

Linear Algebra for Math 308: L2V6

Algebraic properties of matrix and vector multiplication

Linear Algebra for Math 308: L2V7

Algebraic properties of matrix multiplication and addition

Linear Algebra for Math 308: L2V8

Defining the zero and identity matrices and giving their properties

Linear Algebra for Math 308: L2V9

Explaining how to find the derivative and integral of matrix and vector functions

Linear Algebra for Math 308: L3V2

Solving a system of equations with three equations and three variables

Linear Algebra for Math 308: L3V3

Solving a two systems of equations

Linear Algebra for Math 308: L3V4

Defining elementary row operations and row echelon and reduced row echelon form

Linear Algebra for Math 308: L3V5

Rewriting a system of equations as an augmented matrix

Linear Algebra for Math 308: L3V6

Explaining the Gauss-Jordan Algorithm for putting a matrix in row echelon form

Linear Algebra for Math 308: L3V7

Using the Gauss-Jordan algorithm to solve a system of equations

Linear Algebra for Math 308: L3V8

Finding the null space of a matrix and defining basic and free variables

Linear Algebra for Math 308: L3V9

Solving a system of equations by row reducing the augmented matrix

Linear Algebra for Math 308: L3V10

Finding the null space of a matrix

Linear Algebra for Math 308: L3V11

Finding the eigenvectors of a matrix associated with the given eigenvalues

Linear Algebra for Math 308: L3V12

Determining if three vectors are linearly independent

Linear Algebra for Math 308: L4V1

Using linear independence of matrices to introduce the determinant

Linear Algebra for Math 308: L4V2

Theorem comparing linear independence, the determinant, null space, and a spanning set for a 2x2 matrix

Linear Algebra for Math 308: L4V3

Using the determinant to determine when two vectors are linearly independent

Linear Algebra for Math 308: L4V4

The determinant of 3x3 matrices and a theorem comparing linear independence, the determinant, null space, and a spanning set for those matrices

Linear Algebra for Math 308: L5V1

Defining eigenvectors and eigenvalues of a matrix and the null space of a matrix

Linear Algebra for Math 308: L5V2

Finding a basis for the null space of a matrix

Linear Algebra for Math 308: L5V3

Finding eigenvalues and eigenvectors for a matrix

Linear Algebra for Math 308: L5V4

Finding the eigenvalues of two matrices

Linear Algebra for Math 308: L5V5

Finding the eigenvalues for a matrix

Linear Algebra for Math 308: L5V6

Finding the eigenvectors and basis for the eigenspaces of a matrix

Linear Algebra for Math 308: L5V7

Finding a basis for each eigenspace of a matrix

Linear Algebra for Math 308: L5V8

Finding a basis for the eigenspaces of complex eigenvalues of a matrix

Linear Algebra for Math 308: L5V9

Finding the eigenvalues and associated eigenspaces of a matrix

Linear Algebra for Math 308: L5V10

Finding the eigenvalues and associated eigenspaces of a matrix

Linear Algebra for Math 308: L5V11

Discussing the geometric multiplicity of eigenvalues

Linear Algebra for Math 308: L5V12

Defining algebraic and geometric multiplicity of eigenvalues

Linear Algebra for Math 308: L5V13

Defining generalized eigenvectors for a matrix

Linear Algebra for Math 308: L5V14

Finding the eigenvectors and generalized eigenvectors for a matrix

Linear Algebra for Math 308: L6V3

Explaining how to use a matrix inverse to solve matrix equations

Linear Algebra for Math 308: L6V4

Defining the inverse of a matrix and it is both a left and right inverse

Linear Algebra for Math 308: L6V5

Explaining how to use row reduction of an augmented matrix to find an inverse

Linear Algebra for Math 308: L6V6

Showing when a matrix has an inverse

Linear Algebra for Math 308: L6V8

Finding the inverse of a matrix by row reducing an augmented matrix

Linear Algebra for Math 308: L6V9

Solving a matrix equation using the inverse of the matrix

Linear Algebra for Math 308: L6V10

Using the eigenvectors and eigenvalues to find a formula for diagonalizing a matrix

Linear Algebra for Math 308: L6V11

Diagonalizing a matrix using its eigenvectors and eigenvalues

Linear Algebra for Math 308: L7V7

Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L8V7

Deriving the formula for the solution to a system of first-order differential equations when a generalized eigenvector is needed

Linear Algebra for Math 308: L8V1.5

Deriving the form of the general solution of a system of first-order linear differential equations

Linear Algebra for Math 308: L8V2

Deriving the general solution for a system of first-order linear differential equations

Linear Algebra for Math 308: L3E1rr

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E2rr

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E3rr

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E4rr

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E5rr

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E6rr

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E7rr

Solving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L4E1

Determining if two vectors are linearly independent

Linear Algebra for Math 308: L4E2

Determining if three vectors are linearly independent

Linear Algebra for Math 308: L4E3

Determining if three vectors are linearly independent using the determinant and row reduction

Linear Algebra for Math 308: L4E4

Determining if three vectors are linearly independent using the determinant

Linear Algebra for Math 308: L4E5

Determining if three vectors are linearly independent using the determinant and row reduction

Linear Algebra for Math 308: L4E6

Determining if four vectors are linearly independent using row reduction and the determinant

Linear Algebra for Math 308: L4E7

Determining for which values of the variable two vector functions are linearly independent

Linear Algebra for Math 308: L5E1

Finding the eigenvalues and eigenvectors of a matrix

Linear Algebra for Math 308: L5E2

Finding the eigenvalues and eigenvectors of a matrix

Linear Algebra for Math 308: L5E3

Finding the eigenvalues and eigenvectors of a matrix

Linear Algebra for Math 308: L5E5

Finding the eigenvalues and eigenvectors of a matrix

Linear Algebra for Math 308: L5E6

Finding the eigenvalues and eigenvectors of a matrix

Linear Algebra for Math 308: L6E1inv

Solving a system of equation by writing it as a matrix equation and using the matrix inverse

Linear Algebra for Math 308: L7E7

Calculating a matrix exponential function using the diagonalization of the matrix

Linear Algebra for Math 308: L7E5

Calculating a matrix exponential function using the diagonalization of the matrix

Linear Algebra for Math 308: L7E1

Calculating a matrix exponential function using the diagonalization of the matrix

Linear Algebra for Math 308: L7E3

Calculating a matrix exponential function using the diagonalization of the matrix

Equilibria and Their Stability Exercise 1A

Finding and classifying the equilibria for an autonomous differential equations

Equilibria and Their Stability Exercise 1B

Finding and classifying the equilibria for an autonomous differential equations

Equilibria and Their Stability Exercise 1C

Finding and classifying the equilibria for an autonomous differential equations

Levins' Model of Population Growth Example

Finding and classifying all equilibria in a differential equation using Levins' model of population growth

Drawing Solutions to Linear Systems Example

Finding and drawing the solution curve for a system of first-order linear differential equations

Linear Algebra for Math 308: L8V1.5

Deriving the form of the general solution of a system of first-order linear differential equations

Compount Interest

Explaining compound interest and continuously compounded interest using differential equations

Systems of Ordinary Differential Equations Video 2

Defining a linear system of ordinary differential equations and how to convert it to a vector equation

Matrix Operations

Explaining matrix operations including addition and multiplication

Gaussian Elimination

Explaining the row operations used in gaussian elimination

Eigenvalues and Eigenvectors

Explaining how eigenvalues and eigenvectors can be used to solve a system of first-order linear differential equations