Differential equations : from calculus to dynamical systems
著者
書誌事項
Differential equations : from calculus to dynamical systems
（AMS/MAA textbooks, v. 43）
MAA Press, an imprint of the American Mathematical Society, c2019
2nd ed
- : pbk
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注記
Includes index
内容説明・目次
内容説明
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.
目次
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
Appendixes: A. Answers to odd-numbered exercises
B. Derivative and integral formulas
C. Cofactor method for determinants
D. Cramer's Rule for solving systems of linear equations
E. The Wronskian
F. Table of Laplace transforms
G. Review of partial derivatives
Index
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