Introduction to Ordinary Differential Equations with Scientific Applications - Tapa dura

Sinopsis

This book discusses introductory ordinary differential equations (ODEs) comprehensively, from first-order/second-order equations, up to series solutions and special functions, with the hope to offer a full learning experience for keen students. It also comes with many scientific applications, particularly in Physics and Earth Sciences, which further help students to make connections between abstract theories and real-world problems. With carefully chosen examples, figures, and exercises, students can understand the material and concepts in this book effectively. This book can also serve as a quick reference and question bank for instructors. Overall, this book is suitable for undergraduate students majoring in Mathematics, Engineering, Physics, and Earth Sciences who already have basic familiarity with Calculus and are taking a first course in ordinary differential equations. Specifically, it is expected that the readers are comfortable with prerequisite knowledge up to Multivariable Calculus (including, but not limited to, integrating by parts and partial derivatives). For US students, this will be equivalent to Calc III.

List of Topics:
- First-order ODEs (Separable, Linear, Exact, Homogeneous/Isobaric, Bernoulli, Riccati)
- Second-order ODEs (Constant-coefficient Homogeneous, Method of Undetermined Coefficients/Variation of Parameters, Euler, Canonical)
- Series/Frobenius Solution (Airy, Hypergeometric)
- Laplace Transform
- Sturm-Liouville Theory (Fourier Series)
- Special Functions (Legendre, Chebyshev, Hermite, Laguerre, Bessel)
- Intro. to PDEs (Heat, Laplace, Wave)
- and some extra topics like matrix ODEs and numerical methods
with a total of 157 Exercises plus Short Solution keys.

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