Introduction to Differential Equations 2e
by Mark H. Holmes

Ordering: The ISBN is 9781975077204. It is available from Amazon, as well as directly from the publisher XanEdu Publishing. It costs about \$54, and you get a softcover (full color) spiral bound textbook as well as access to a digital version.

Videos for:

Chapter 3
Chapter 4
Chapter 5
Chapter 7

 Author Information Mark H. Holmes Department of Mathematical Sciences Rensselaer Polytechnic Institute, Troy, NY 12180 USA holmes (@rpi.edu) Page Last Updated: 11/1/2020

Figures From Text

Table 1.1 for Exercise 7 (pg 5)

Figures from Chaps 2-7 (all of them)

Videos for Chapter 3

Below are links to MATLAB generated videos related to the examples in the chapter.

Zipped folder including all Chapter 3 videos.

Section 3.10.2: Linear Oscillator

Example A   for u(0) = 0, u'(0) = 1, k = 4

Example B   for u(0) = 1, u'(0) = 1, k = 4

Example C   for u(0) = 0, u'(0) = -3, k = 4

Example D   for u(0) = 0, u'(0) = 1, k = 16

Section 3.10.3: Damped Oscillator (the damping mechanism is not shown in the videos)

Example A   for u(0) = 0, u'(0) = 1, k = 4, c = 5 (over)

Example B   for u(0) = 0, u'(0) = 1, k = 4, c = 4 (critical)

Example C   for u(0) = 0, u'(0) = 1, k = 4, c = 0.5 (under)

Example D   for u(0) = 0, u'(0) = 1, k = 4, c = 0.01 (weak)

Videos for Chapter 4

Below are links to MATLAB generated videos related to the examples in the chapter.

Zipped folder including all Chapter 4 videos.

Section 4.6: Phase Plane

Two Positive Eigenvalues

One Positive and One Negative Eigenvalue

Complex Eigenvalues

Videos for Chapter 5

Below are links to MATLAB generated videos related to the examples in the chapter.

Section 5.1: Non-Linear Systems

Solution Curves

Videos for Chapter 7

Below are links to MATLAB generated videos related to the examples in the chapter.

Zipped folder including all Chapter 7 videos.

Section 7.3: Diffusion Equation (D = 1)

Example 1   for u(x,0) = 3sin(pi*x)

Example 2   for u(x,0) = 3sin(pi*x/2)-4sin(3*pi*x/2)+5sin(2*pi*x)

Example 3   for u(x,0) = bump

Section 7.4: Fourier Series

Example 3   g(x) = piecewise linear

Example 4   g(x) = step

Example 5   g(x) = step (cosine series)

Example A   g(x) = exp(x)

Example B   g(x) = cos(3pi*x)

Example C   g(x) = x^2

Section 7.5: Wave Equation (c = 1)

Example 1   u(x,0) = 3cos(pi*x)

Example A   u(x,0) = x^2(1-x)^2

Example B   u(x,0) = x^2(1-x)^2(x-0.25)

Example C   u(x,0) = x^2(1-x)^2sin(17x/3)

Example D   u(x,0) = bump