**AMS/MAA Textbooks**

Volume: 43;
2019;
402 pp;
Hardcover

MSC: Primary 34; 35;

**Print ISBN: 978-1-4704-4400-6
Product Code: TEXT/43**

List Price: $75.00

AMS Member Price: $56.25

MAA Member Price: $56.25

**Electronic ISBN: 978-1-4704-5108-0
Product Code: TEXT/43.E**

List Price: $75.00

AMS Member Price: $56.25

MAA Member Price: $56.25

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#### Supplemental Materials

# Differential Equations: From Calculus to Dynamical Systems: Second Edition

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*Virginia W. Noonburg*

MAA Press: An Imprint of the American Mathematical Society

A thoroughly modern textbook for the
sophomore-level differential equations course. The examples and
exercises emphasize modeling not only in engineering and physics but
also in applied mathematics and biology. There is an early
introduction to numerical methods and, throughout, a strong emphasis
on the qualitative viewpoint of dynamical systems. Bifurcations and
analysis of parameter variation is a persistent theme.

Presuming previous exposure to only two semesters of calculus,
necessary linear algebra is developed as needed. The exposition is
very clear and inviting. The book would serve well
for use in a flipped-classroom pedagogical approach or for self-study
for an advanced undergraduate or beginning graduate student.

This second edition of Noonburg's best-selling textbook includes
two new chapters on partial differential equations, making the book
usable for a two-semester sequence in differential equations. It
includes exercises, examples, and extensive student projects taken
from the current mathematical and scientific literature.

There exists a number of author-designed extensive student projects
and a collection of additional exercises on the book's webpage. Click
on "Supplemental Materials" on the lower left of this page to access
them.

An instructor's manual for this title is available
electronically to those instructors who have adopted the textbook for
classroom use. Please send email to textbooks@ams.org for more
information.

#### Readership

Undergraduate students interested in teaching and learning differential equations (both ordinary and PDE).

#### Table of Contents

# Table of Contents

## Differential Equations: From Calculus to Dynamical Systems: Second Edition

- Cover Cover11
- Title page iii4
- Copyright iv5
- Contents v6
- Preface ix10
- Chapter 1. Introduction to Differential Equations 112
- Chapter 2. First-order Differential Equations 1930
- 2.1. Separable First-order Equations 2031
- 2.2. Graphical Methods, the Slope Field 2839
- 2.3. Linear First-order Differential Equations 3647
- 2.4. Existence and Uniqueness of Solutions 4455
- 2.5. More Analytic Methods for Nonlinear First-order Equations 5162
- 2.6. Numerical Methods 5970
- 2.7. Autonomous Equations, the Phase Line 7182

- Chapter 3. Second-order Differential Equations 8192
- 3.1. General Theory of Homogeneous Linear Equations 8293
- 3.2. Homogeneous Linear Equations with Constant Coefficients 8899
- 3.3. The Spring-mass Equation 95106
- 3.4. Nonhomogeneous Linear Equations 102113
- 3.5. The Forced Spring-mass System 114125
- 3.6. Linear Second-order Equations with Nonconstant Coefficients 125136
- 3.7. Autonomous Second-order Differential Equations 135146

- Chapter 4. Linear Systems ofFirst-order Differential Equations 145156
- Chapter 5. Geometry of Autonomous Systems 183194
- Chapter 6. Laplace Transforms 221232
- Chapter 7. Introduction to Partial Differential Equations 261272
- Chapter 8. Solving Second-order Partial Differential Equations 285296
- 8.1. Classification of Linear Second-order Partial Differential Equations 285296
- 8.2. The 1-dimensional Heat Equation 289300
- 8.3. The 1-dimensional Wave Equation 299310
- 8.4. Numerical Solution of Parabolic and Hyperbolic Equations 309320
- 8.5. Laplace’s Equation 318329
- 8.6. Student Project: Harvested Diffusive Logistic Equation 324335

- Appendix 329340
- Appendix A. Answers to Odd-numbered Exercises 331342
- Appendix B. Derivative and Integral Formulas 385396
- Appendix C. Cofactor Method for Determinants 387398
- Appendix D. Cramer’s Rule for Solving Systems of Linear Equations 389400
- Appendix E. The Wronskian 391402
- Appendix F. Table of Laplace Transforms 393404
- Appendix G. Review of Partial Derivatives 395406

- Index 397408
- Back Cover Back Cover1414