MTH 240 Lecture Resources

Steve Kifowit, Waubonsee Community College

Section 1.1 - Intro to differential equations

• Objectives
• Lecture slides
• Links to optional videos: Khan Academy

Section 1.2 - Solving equations of the form $dy/dx=f(x)$$dy/dx=f(x)$

• Objectives
• Lecture handout

Section 1.3 - Slope fields and solution curves

• Objectives
• Lecture slides
• For plotting slope fields, try this site or this one. You could also use SageMath as in this example.
• Links to optional videos: Khan Academy
• Euler's method: Handout, Python code
• Modified (or Improved) Euler's method: Python code
• Classic 4th-order Runge-Kutta method: Python code
• Here is a SageMath example using Sage's built-in Runge-Kutta solver.

Section 1.4 - Separable equations

• Objectives
• Lecture slides
• Links to optional videos: Khan Academy

Section 1.5 - 1st-order linear equations

• Objectives
• Lecture slides
• Lecture handout (Solution method)

Section 1.6 - Exact equations and substitutions

• Objectives
• Lecture slides
• Lecture handout (Summary of solution methods)
• Links to optional videos: Khan Academy - Exact eqns, Khan Academy - Homogeneous eqns

Sections 2.1-2.3 - General linear ODE's

• Objectives
• Lecture slides
• Links to optional videos: Khan Academy - 2nd-order linear ODE's, Khan Academy - More 2nd-order, constant-coefficient equations

Section 2.4 - Free mechanical vibrations

• Objectives
• Lecture handout (Summary of solution methods)

Section 2.5 - Nonhomogenous linear ODE's

• Objectives

• Lecture handout (Undetermined coefficients and variation of parameters)

• Section 2.6 - Forced oscillations and resonance

• Objectives
• Lecture notes on forced, damped systems

Section 3.1 - Introduction to power series solutions

• Objectives
• Review of power series
• Properties of power series
• Review of Taylor series
• Common infinite series
• Lecture slides
• Lecture examples: Example 1, Example 2
• Links to videos: $y^{\prime }+2xy=0$$y'+2xy=0$, $y^{\prime }-y=0$$y'-y=0$, $y^{″}+y=0$$y''+y=0$

Section 3.2 - Power series solutions around ordinary points

• Objectives
• Lecture slides
• Lecture examples: Example 1, Example 2

Section 4.1 - Intro to Laplace transforms

• Objectives
• Lecture slides
• Table of transforms
• Links to optional videos: Khan Academy-Intro, Khan Academy-Properties

Section 4.2 - Transformation of initial value problems

• Objectives
• Lecture slides
• Links to optional videos: Khan Academy

Section 4.3 - Translation and partial fractions

• Objectives
• Guidelines for partial fractions | Cover-up Method
• Lecture slides

Section 4.4 - Other properties of Laplace transforms

• Objectives
• Lecture slides
• Links to optional videos: Khan Academy
• Lecture examples: $t{x}^{″}+(3t-1)x^{\prime }+3x=0$$tx''+(3t-1)x'+3x=0$, $y^{″}+2t{y}^{\prime }-4y=1$$y''+2ty'-4y=1$

Section 8.1 - Fourier series

• Objectives
• Lecture slides

Section 8.2 - General Fourier series and convergence

• Objectives
• Lecture slides

Section 8.3 - Fourier sine and cosine series

• Objectives
• Lecture slides

Section 8.5 - The heat equation and separation of variables

• Objectives
• See Theorem 1 (page 593) and Theorem 2 (page 596)

Last updated January 27, 2023

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