MATH 308 WIR22A V20Solving linear differential equations and determining the interval in which the solution exists

MATH 308 WIR22A V10Solving initial value problems by separating the variables and using an integrating factor

MATH 308 WIR22A V9Solving differential equations by separating the variables and using integrating factors

MATH 308 WIR22A V9Solving differential equations by separating the variables and using integrating factors

MATH 308 WIR22A V10Solving initial value problems by separating the variables and using an integrating factor

MATH 308 WIR22A V18Determining an interval in which the solution of a first order, linear initial value problem is certain to exist

MATH 308 WIR22A V19Determining an interval in which the solution of a first order, linear initial value problem is certain to exist

MATH 308 WIR22A V9Solving differential equations by separating the variables and using integrating factors

Linear Differential Equations: MATH 172 Problems 1 & 2Solving first order linear differential equations

MATH 308 WIR22A V2Writing and then solving a differential equation for the temperature of a cup of coffee

MATH 308 WIR22A V8Writing and then solving an initial value problem to determine the stopping time and distance of a stone on a smooth surface

MATH 308 WIR22A V11Solving 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 V13Solving an initial value problem using Newtonâ€™s Law of Cooling to determine the time it takes for a cake to cool to a given temperature

MATH 308 WIR22A V14Solving a separable differential equation to determine how long it takes a population of bacteria to double

MATH 308 WIR22A V15Solving an initial value problem including air resistance for the path of a thrown ball to determine the maximum height it reaches

MATH 308 WIR22A V16Solving an initial value problem using Newtonâ€™s Law of Cooling to determine the temperature of a drink left outside as the outdoor temperature changes

MATH 308 WIR22A V17Solving an initial value problem to determine the amount of pollution in a lake at any time

MATH 308 WIR22A V12Solving an initial value problem to find the amount of salt in a tank with salt water flowing in and out

MATH 308 WIR22A V22Finding the equilibrium solutions and properties for an autonomous differential equation

MATH 308 WIR22A V23Finding the equilibrium solutions and properties for an autonomous differential equation

MATH 308 WIR22A V25Show that a differential equation is not exact but becomes exact when multiplied by a given integrating factor

MATH 308 WIR22A V26Finding an integrating factor to make a differential equation exact and then solving it

MATH 308 WIR22A V28Finding an integrating factor to make a differential equation exact and then solving it

MATH 308 WIR22A V29Finding an integrating factor to make a differential equation exact and then solving it

MATH 308 WIR22A V30Finding an integrating factor to make a differential equation exact and then solving it

MATH 308 WIR22A V33Solving 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 V31Determining if two functions form a fundamental set of solutions for a second order linear differential equation

MATH 308 WIR22A V34Solving a second order linear initial value problem with complex roots to the characteristic equation

MATH 308 WIR22A V36Using the reduction of order technique to find the solution to an initial value problem

MATH 308 WIR22A V35Solving a second order linear initial value problem with a repeated root to the characteristic equation

MATH 308 WIR22A V43Using the method of undetermined coefficients to find the form of a particular solution for a second order linear differential equation

MATH 308 WIR22A V42Using the method of undetermined coefficients to solve second-order linear differential equation

MATH 308 WIR22A V44Using the variation of parameters method to solve a nonhomogeneous second-order linear differential equation

MATH 308 WIR22A V45Solving an initial value problem to find the position of a mass on a vibrating spring

MATH 308 WIR22A V46Solving an initial value problem to find the position of a mass on a vibrating spring with damping

MATH 308 WIR22A V48Solving an initial value problem to find the position of a mass on a vibrating spring with an external force

MATH 308 WIR22A V49Solving an initial value problem to find the position of a mass on a vibrating spring under resonance with an external force

MATH 308 WIR22A V47Solving an initial value problem to find the position of a mass on a vibrating spring with an external force

MATH 308 WIR22A V59Using the Laplace transform to solve an initial value problem with an impulse function

MATH 308 WIR22A V65Using the Laplace transform and the impulse function to write and solve an initial value problem for the motion of a spring

MATH 308 WIR22A V64Solving an initial value problem using the Laplace transform and writing the answer using a convolution integral

MATH 308 WIR22A V74Finding the value of the second and third derivative of a solution at the given point

MATH 308 WIR22A V75Transforming an initial value problem into three first-order equations written in matrix form

MATH 308 WIR22A V66Finding the form of a particular solution for a second-order linear differential equation

MATH 308 WIR22A V67Finding the general solutions of a second-order linear nonhomogeneous differential equation

MATH 308 WIR22A V38Determining where a first-order linear initial value problem has a solution and then solving it

MATH 308 WIR22A V39Solving a first-order linear initial value problem to determine the concentration of salt in a tank

MATH 308 WIR22A V40Finding the equilibrium solutions and properties for an autonomous differential equation

MATH 308 WIR22A V41Using an integrating factor to make a differential equation exact and then solving it

MATH 308 WIR22A V23Finding the equilibrium solutions and properties for an autonomous differential equation

MATH 308 WIR22A V29Finding an integrating factor to make a differential equation exact and then solving it

MATH 308 WIR22A V82Using the method of undetermined coefficients to solve second-order linear differential equation

MATH 308 WIR22A V83Using reduction of order and variation of parameters to solve a second-order linear nonhomogeneous differential equation

MATH 308 WIR22A V74Finding the value of the second and third derivative of a solution at the given point

MATH 308 WIR22A V84Using Laplace transforms to solve initial value problems with step and impulse functions

MATH 308 WIR22A V64Solving an initial value problem using the Laplace transform and writing the answer using a convolution integral

Linear Algebra for Math 308: L7V2Showing how the exponential function is the solution to an initial value problem

Linear Algebra for Math 308: L7V3Using power series to define a matrix exponential function to use in solving differential equations with matrices

Linear Algebra for Math 308: L7V4Calculating a matrix exponential function using a power series and the diagonalization of the matrix

Linear Algebra for Math 308: L7E2Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L7E4Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L5V6Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L7E8Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L8V1Solving for the general solution for a system of first-order linear differential equations

Linear Algebra for Math 308: L8V4Solving a system of first-order linear differential equations where the matrix has complex eigenvalues

Linear Algebra for Math 308: L8V5Deriving the general solution for a system of first-order linear differential equations where the matrix has complex eigenvalues

Linear Algebra for Math 308: L8V6Solving a system of first-order linear differential equations where the matrix has complex eigenvalues

Linear Algebra for Math 308: L8E2Solving a system of first-order linear differential equations where the matrix has complex eigenvalues

Linear Algebra for Math 308: L8E3Solving a system of first-order linear differential equations where a generalized eigenvector is needed

Linear Algebra for Math 308: L8E5Solving a system of first-order linear differential equations when a generalized eigenvector is needed

Power Series as Functions: MATH 172 Problems 4 & 5Examples about the derivative and integral of a power series

Separable Differential Equations: MATH 172 Problems 6 & 7Solving separable differential equations involving Newton's Law of Cooling and orthogonal trajectories

MATH 308 WIR22A V5Showing that a function is the general solution to a differential equation and finding the solution to an initial value probem

MATH 308 WIR22A V53Writing piecewise functions in terms of the unit step function and finding the Laplace transform

MATH 308 WIR22A V62Using the Laplace transform to solve for a function in an equation with a convolution

MATH 308 WIR22A V76Finding a differential equation for which two given vector functions are solutions

MATH 308 WIR22A V77aSolving a system of first-order linear differential equations with real, distinct eigenvalues

MATH 308 WIR22A V77cSolving a system of first-order linear differential equations with complex eigenvalues

MATH 308 WIR22A V78Classifying the type and stability of the equilibrium points of a system of linear differential equations for different values of a parameter

MATH 308 WIR22A V77bSolving a system of first-order linear differential equations with a repeated, real eigenvalue

MATH 308 WIR22A V68Using the definition to find the Laplace transform of a function containing an impulse function

MATH 308 WIR22A V85Solving a system of first-order linear differential equations and determining properties of the solutions

MATH 308 WIR22A V77aSolving a system of first-order linear differential equations with real, distinct eigenvalues

MATH 308 WIR22A V77bSolving a system of first-order linear differential equations with a repeated, real eigenvalue

MATH 308 WIR22A V77cSolving a system of first-order linear differential equations with complex eigenvalues

Linear Algebra for Math 308: L1V1Explaining the definitions of real and complex vectors with examples

Linear Algebra for Math 308: L1V6Explaining the concepts of existence and uniqueness for solutions of systems of equations

Linear Algebra for Math 308: L1V8Explaining two vectors are linearly dependent if and only if they are scalar multiples

Linear Algebra for Math 308: L1V12Using linear independence to show the uniqueness of a vector equation solution

Linear Algebra for Math 308: L2V3Defining multiplication of a matrix and vector and then giving an example

Linear Algebra for Math 308: L2V9Explaining how to find the derivative and integral of matricx and vector functions

Linear Algebra for Math 308: L3V2Solving a system of equations with three equations and three variables

Linear Algebra for Math 308: L3V4Defining elementary row operations and row echelon and reduced row echelon form

Linear Algebra for Math 308: L3V6Explaining the Gauss-Jordan Algorithm for putting a matrix in row echelon form

Linear Algebra for Math 308: L3V8Finding the null space of a matrix and defining basic and free variables

Linear Algebra for Math 308: L3V11Finding the eigenvectors of a matrix associated with the given eigenvalues

Linear Algebra for Math 308: L3E1rrSolving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E2rrSolving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E3rrSolving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E4rrSolving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E5rrSolving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E6rrSolving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L3E7rrSolving a system of equations by using the Gauss-Jordan algorithm to row reduce the augmented matrix

Linear Algebra for Math 308: L4V2Theorem comparing linear independence, the determinant, null space, and a spanning set for a 2x2 matrix

Linear Algebra for Math 308: L4V3Using the determinant to determine when two vectors are linearly independent

Linear Algebra for Math 308: L4V4The 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: L4E3Determining if three vectors are linearly independent using the determinant and row reduction

Linear Algebra for Math 308: L4E4Determining if three vectors are linearly independent using the determinant

Linear Algebra for Math 308: L4E5Determining if three vectors are linearly independent using the determinant and row reduction

Linear Algebra for Math 308: L4E6Determining if four vectors are linearly independent using row reduction and the determinant

Linear Algebra for Math 308: L4E7Determining for which values of the variable two vector functions are linearly independent

Linear Algebra for Math 308: L5V1Defining eigenvectors and eigenvalues of a matrix and the null space of a matrix

Linear Algebra for Math 308: L5V8Finding a basis for the eigenspaces of complex eigenvalues of a matrix

Linear Algebra for Math 308: L6V4Defining the inverse of a matrix and it is both a left and right inverse

Linear Algebra for Math 308: L6V5Explaining how to use row reduction of an augmented matrix to find an inverse

Linear Algebra for Math 308: L6V10Using the eigenvectors and eigenvalues to find a formula for diagonalizing a matrix

Linear Algebra for Math 308: L6E1invSolving a system of equation by writing it as a matrix equation and using the matrix inverse

Linear Algebra for Math 308: L7E7Calculating a matrix exponential function using the diagonalization of the matrix

Linear Algebra for Math 308: L7E5Calculating a matrix exponential function using the diagonalization of the matrix

Linear Algebra for Math 308: L7E3Calculating a matrix exponential function using the diagonalization of the matrix

Linear Algebra for Math 308: L7V6Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L7V7Solving a system of first-order linear differential equations using a matrix exponential function

Linear Algebra for Math 308: L7E1Calculating a matrix exponential function using the diagonalization of the matrix

Linear Algebra for Math 308: L8V1.5Deriving the form of the general solution of a system of first-order linear differential equations

Linear Algebra for Math 308: L8V2Deriving the general solution for a system of first-order linear differential equations

Linear Algebra for Math 308: L8V3Finding the general solution to a system of first order differential equations

Linear Algebra for Math 308: L8V7Deriving the formula for the solution to a system of first-order differential equations when a generalized eigenvector is needed