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Differential Equations

This is an overview of differential equations

Format

  • You should visit the sections below in order starting with Section 1.
  • Each section below has several videos explaining the listed concepts, and then exercises with videos.
  • If you have watched the videos below and want to see more videos to better understand the material, you can see Chapter 2, Section 3.6, and Chapter 7 of our course MATH 308: Differential Equations. Note these MATH 308 videos are outside the scope of this mini-course and not required viewing. 
 

Differential Equations

View Section 1: Integrating Factor
  • Definitions and terminology for ordinary differential equations
  • Using an integrating factor to solve a first-order linear differential equation
View Section 2: Separable Equations
  • Definition of separable differential equations
  • How to solve separable differential equations
View Section 3: Compound Interest
  • Using differential equations to solve problems for compound interest
  • Solving compound interest problems when deposits are made at regular intervals
View Section 4: Variations of Parameters
  • Solving first-order linear equations using the method of variation of parameters
View Section 5: Systems of Ordinary Differential Equations
  • Systems of normal, first-order differential equations
  • Writing systems of first-order linear differential equations in matrix form
Section 6: Matrices
  • Matrix operations
  • Gaussian elimination
  • The inverse of a matrix
Section 7: Systems of Equations, Linear Independence, and Eigenvalues & Eigenvectors
  • Systems of linear equations
  • Linear independence
  • Eigenvalues and eigenvectors
Section 8: Homogeneous Linear Systems with Constant Coefficients
  • Solving a homogeneous first-degree, linear system of differential quations with constant coefficients
Section 9: Complex Eigenvalues
  • Solving systems of linear, first-order differential equations with real and complex roots
  • Finding complex eigenvalues and the corresponding eigenvectors
Section 10: Fundamental Matrices
  • Definition of a fundamental matrix for a system of equations
  • Properties of a fundamental matrix
Section 11: Repeated Eigenvalues
  • Solutions to a system of equations where the coefficient matrix has a repeated eigenvalue
  • Finding a generalized eigenvector
Section 12: Nonhomogeneous Linear Systems
  • Solving a nonhomogeneous system of equations
  • Using the method of Variation of Parameters (Lagrange Method) to find the particular solution