Noonburg V.W. Differential Equations: From Calculus to Dynamical Systems

2nd Ed. — Maa Press, 2019. — xi+400 p. — (AMS/MAA Textbooks, Vol. 43). — ISBN: 978-1-4704-5108-0.
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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.Introduction to Differential Equations
First-order Differential Equations
Second-order Differential Equations
Linear Systems of First-order Differential Equations
Geometry of Autonomous Systems
Laplace Transforms
Introduction to Partial Differential Equations
Solving Second-order Partial Differential Equations
Answers to Odd-numbered Exercises
Derivative and Integral Formulas
Cofactor Method for Determinants
Cramer’s Rule for Solving Systems of Linear Equations
The Wronskian
Table of Laplace Transforms
Review of Partial Derivatives