The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.
The Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.
Drawing on his decade of experience teaching the differential equations course ,John Davis offers a refreshing and effective new approach to partial differential equations that is equal parts computational proficiency, visualization, and physical interpretation of the problem at hand.
Table of Contents
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