In-person lectures (Fall 2022)

The following material corresponds with in-person lectures given by Steve Butler during the Fall 2022 semester. Each session has a scanned copy of the notes ("PDF") and is available in streaming from two different online platforms (either "Vimeo" or "YouTube").

1A -- Introduction to differential equations - Springing into action

1B -- Verifying a differential equation

1C -- Differential equations coming from calculus

2A -- Separable differential equations

2B -- Linear first-order differential equations

2C -- Exact ODEs + Substitution

3A -- Population models

3B -- Autonomous ODEs

4A -- Higher order ODEs + Wronskian

4B -- Euler equations + Strategy for nonhomogeneous

4C -- Order reduction + Constant coefficient (including complex)

5A -- Spring-mass-damper systems

5B -- Method of undetermined coefficients

5C -- Method of variation of parameters

6A -- Review of the first part of the course

7A -- Introduction to systems

7B -- Method of elimination

7C -- Introduction to matrices

8A -- Differential equations and matrices

8B -- Eigenvalue method (+complex)

8C -- Eigenvalue method (complex + missing eigenvectors)

9A -- Fundamental matrix and matrix exponentials

9B -- Matrix exponentials and method of undetermined coefficients

9C -- Method of variation of parameters

10A -- Review of the second part of the course

11A -- Introduction to Laplace transforms; basic functions

11B -- Laplace transforms and unit step function, transforming derivatives

11C -- Solving ODEs with Laplace transforms; partial fractions

12A -- Laplace transform rules for derivatives, integrals, convolution

12B -- Laplace transforms and translations

12C -- Laplace transforms and the delta function

13A -- Introduction to series; combining series together

13B -- Radius of convergence for series solutions

13C -- Ordinary and singular points

14A -- Review of the third part of the course