Weekly Topics Schedule
Below is a tentative list of topics to be covered each week during the semester. Please note that this schedule serves as a guide and may be revised as the term progresses to better suit the needs of the class or unforeseen circumstances.
- Week 1
- What is a differential equation?
- Derivative, Partial derivative
- What is a solution to a differential equation?
- Why do we care about differential equations?
- Week 2
- Classification by type, order, linearity
- Solution in explicit closed form
- Solution in explicit series form
- Solution in implicit form
- Week 3
- Plotting solutions in MATLAB
- How to solve first-order linear ODEs
- Week 4
- How to solve separable ODEs
- How to solve ODEs in MATLAB
- Week 5
- How to solve exact ODEs
- Is it possible to convert an inexact ODE into an exact one?
- Analyzing exact ODEs with MATLAB
- Week 6
- Four fundamental questions
- Existence and uniqueness theorems
- Autonomous ODEs, Stability
- Week 7
- How to convert a higher order ODE into a system of first-order ODEs
- How to find approximate solutions to systems of first-order ODEs in MATLAB
- Week 8
- Theory of second-order linear ODEs
- Method of reduction of order
- Week 9
- Solution method for homogeneous second-order linear ODEs with constant coefficients
- Week 10
- How to find a particular solution: The method of undetermined coefficients
- Week 11
- How to find a particular solution: The method of variation of parameters
- Week 12
- Integral transforms
- The Laplace transform
- Important properties of the Laplace transform
- Week 13
- Solving IVPs by the Lapalce transform
- The convolution property
- Week 14
- Differential equations with discontinuous forcing functions
- Week 15
- Series solutions of linear ODEs