An Introduction to Partial Differential Equations (with Maple)

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The book is designed for undergraduate or beginning level graduate students, and students from interdisciplinary areas including engineers, and others who need to use partial differential equations, Fourier series, Fourier and Laplace transforms. The prerequisite is a basic knowledge of calculus, linear algebra, and ordinary differential equations. The textbook aims to be practical, elementary, and reasonably rigorous; the book is concise in that it describes fundamental solution techniques for first order, second order, linear partial differential equations for general solutions, fundamental solutions, solution to Cauchy (initial value) problems, and boundary value problems for different PDEs in one and two dimensions, and different coordinates systems. Analytic solutions to boundary value problems are based on Sturm–Liouville eigenvalue problems and series solutions. The book is accompanied with enough well tested Maple files and some Matlab codes that are available online. The use of Maple makes the complicated series solution simple, interactive, and visible. These features distinguish the book from other textbooks available in the related area. Sample Chapter(s) Preface Chapter 1: Introduction Chapter 2: First order partial differential equations Request Inspection Copy Contents: Preface Introduction First Order Partial Differential Equations Solution to One-Dimensional Wave Equations Orthogonal Functions & Expansions, and Sturm-Liouville Theory Method of Separation Variables for Solving PDE BVPs in Cartesian Coordinates Various Fourier Series, Properties and Convergence Series Solutions of PDEs of Boundary Value Problems Fourier and Laplace Transforms Numerical Solution Techniques Appendices A: ODE Review and Other Useful Information Appendices B: Introduction to Maple Bibliography Index Readership: Undergraduate, beginning level mathematics/physics graduate students, students from interdisciplinary areas and engineering.

第一本入門 Maple 的必讀寶典：現在，數學可以這樣算！

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1. 認識Maple 2. Maple 的工作環境 3. Maple 的基本運算 4. 二維圖形繪製 5. 三維圖形繪製與進階繪圖應用 6. 圖形化介面的設計 7. 字串、串列與陣列 8. Maple 在微積分上的應用 9. 微分方程式 10. 線性代數的應用 11. 複變數運算 12. 程式設計