Volume: 43; 2019; 402 pp; Softcover
MSC: Primary 34; 35;
Print ISBN: 978-1-4704-6329-8
Product Code: TEXT/43.S
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
Share this pageVirginia 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.
Online assignments for this title are available in WebAssign.
WebAssign is a leading provider of online instructional tools
for both faculty and students.
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
- Title page iii3
- Copyright iv4
- Contents v5
- Preface ix9
- Chapter 1. Introduction to Differential Equations 111
- Chapter 2. First-order Differential Equations 1929
- 2.1. Separable First-order Equations 2030
- 2.2. Graphical Methods, the Slope Field 2838
- 2.3. Linear First-order Differential Equations 3646
- 2.4. Existence and Uniqueness of Solutions 4454
- 2.5. More Analytic Methods for Nonlinear First-order Equations 5161
- 2.6. Numerical Methods 5969
- 2.7. Autonomous Equations, the Phase Line 7181
- Chapter 3. Second-order Differential Equations 8191
- 3.1. General Theory of Homogeneous Linear Equations 8292
- 3.2. Homogeneous Linear Equations with Constant Coefficients 8898
- 3.3. The Spring-mass Equation 95105
- 3.4. Nonhomogeneous Linear Equations 102112
- 3.5. The Forced Spring-mass System 114124
- 3.6. Linear Second-order Equations with Nonconstant Coefficients 125135
- 3.7. Autonomous Second-order Differential Equations 135145
- Chapter 4. Linear Systems ofFirst-order Differential Equations 145155
- Chapter 5. Geometry of Autonomous Systems 183193
- Chapter 6. Laplace Transforms 221231
- Chapter 7. Introduction to Partial Differential Equations 261271
- Chapter 8. Solving Second-order Partial Differential Equations 285295
- 8.1. Classification of Linear Second-order Partial Differential Equations 285295
- 8.2. The 1-dimensional Heat Equation 289299
- 8.3. The 1-dimensional Wave Equation 299309
- 8.4. Numerical Solution of Parabolic and Hyperbolic Equations 309319
- 8.5. Laplace’s Equation 318328
- 8.6. Student Project: Harvested Diffusive Logistic Equation 324334
- Appendix 329339
- Appendix A. Answers to Odd-numbered Exercises 331341
- Appendix B. Derivative and Integral Formulas 385395
- Appendix C. Cofactor Method for Determinants 387397
- Appendix D. Cramer’s Rule for Solving Systems of Linear Equations 389399
- Appendix E. The Wronskian 391401
- Appendix F. Table of Laplace Transforms 393403
- Appendix G. Review of Partial Derivatives 395405
- Index 397407