Introduction to Differential Equations 3ed
by Mark H. Holmes
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Availability: The publisher/printer was switched to Macmillian effective May 1, 2025 and the new ISBN is 978-1-5339-7759-5. As before,
you get a softcover, full color, spiral bound textbook as well as access to the digital version. What Macmillian is
printing is the 3d edition, but with the typos corrected. New to the digital version are embedded videos along with active links to supplementary material.
The book is not available through Amazon, but it is available through the RPI Bookstore.
Older Versions: The 3d edition was originally printed by XanEdu, ISBN 978-1-71147-191-4. The hardcopy text is just fine but the digital version does not work.
Amazon Ratings (of previous editions): 2nd
3d
Preface and table of contents
Chapter 3 snippet
Chapter 4 snippet
Index
Answers
Typos for XanEdu version of text (the Macmillian version fixes these)
Author Information
- Mark H. Holmes
- Department of Mathematical Sciences
- Rensselaer Polytechnic Institute, Troy, NY 12180 USA
- holmes (@rpi.edu)
- HomePage
Page Last Updated: 8/26/2025
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Figures and Tables in Text
Table 1.1 for Exercise 7 on pg 5
Table 4.1 phase plane examples (pg 105)
Table 6.1 Laplace transforms (pg 158)
Figures all (but one) of the figures in text (zip file)
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.
Zipped folder including all Chapter 5 videos.
Section 5.1: Non-Linear Systems
Solution Curves video for Figure 5.2
Section 5.3: Periodic Solutions
Pendulum video for Figure 5.11
Pendulum video for circulating motion
Pendulum video for separatrix motion
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) = 3sin(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
Chapter Extras
Diffusion equation, Einstein, and AI Generated Images
Wave equation and an elastic string