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Introduction to Applied Partial Differential Equations: (English)

Introduction to Applied Partial Differential Equations: (English)

          
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About the Book

Taking a new approach to partial differential equations, Introduction to Applied Partial Differential Equations presents the content with equal parts computational proficiency, visualization, and physical interpretation of the problem at hand.

Table of Contents:
Preface  1 Introduction to PDEs 1.1 ODEs vs. PDEs 1.2 How PDEs Are Born: Conservation Laws, Fluids, and Waves 1.3 Boundary Conditions in One Space Dimension 1.4 ODE Solution Methods 2 Fourier's Method: Separation of Variables 2.1 Linear Algebra Concepts 2.2 The General Solution via Eigenfunctions 2.3 The Coefficients via Orthogonality 2.4 Consequences of Orthogonality 2.5 Robin Boundary Conditions 2.6 Nonzero Boundary Conditions: Steady-States and Transients* 3 Fourier Series Theory 3.1 Fourier Series: Sine, Cosine, and Full 3.2 Fourier Series vs. Taylor Series: Global vs. Local Approximations* 3.3 Error Analysis and Modes of Convergence 3.4 Convergence Theorems 3.5 Basic L2 Theory 3.6 The Gibbs Phenomenon*  4 General Orthogonal Series Expansions 4.1 Regular and Periodic Sturm-Liouville Theory 4.2 Singular Sturm-Liouville Theory 4.3 Orthogonal Expansions: Special Functions 4.4 Computing Bessel Functions: The Method of Frobenius 4.5 The Gram-Schmidt Procedure*  5 PDEs in Higher Dimensions 5.1 Nuggets from Vector Calculus 5.2 Deriving PDEs in Higher Dimensions 5.3 Boundary Conditions in Higher Dimensions 5.4 Well-Posed Problems: Good Models 5.5 Laplace's Equation in 2D 5.6 The 2D Heat and Wave Equations 6 PDEs in Other Coordinate Systems 6.1 Laplace's Equation in Polar Coordinates 6.2 Poisson's Formula and Its Consequences* 6.3 The Wave Equation and Heat Equation in Polar Coordinates 6.4 Laplace's Equation in Cylindrical Coordinates 6.5 Laplace's Equation in Spherical Coordinates 7 PDEs on Unbounded Domains 7.1 The Infinite String: d'Alembert's Solution 7.2 Characteristic Lines 7.3 The Semi-infinite String: The Method of Reflections 7.4 The Infinite Rod: The Method of Fourier Transforms  Appendix Selected Answers Credits Index


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Product Details
  • ISBN-13: 9781429275927
  • Publisher: MacMillan Learning
  • Publisher Imprint: W.H.Freeman & Co Ltd
  • Depth: 25
  • Language: English
  • Returnable: Y
  • Spine Width: 21 mm
  • Width: 185 mm
  • ISBN-10: 1429275928
  • Publisher Date: 06 Jan 2012
  • Binding: Hardback
  • Height: 244 mm
  • No of Pages: 313
  • Series Title: English
  • Weight: 708 gr


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Introduction to Applied Partial Differential Equations: (English)
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