Dr. Abdul-Majid Wazwaz is professor of mathematics at Saint Xavier University, Chicago, Illinois. He received his Ph.D from the University of Illinois at Chicago. He is a member of SIAM and AMS associations. He has authored three textbooks in mathematics and more than 150 papers in mathematics, focusing his work on many branches of applied mathematics. His works on modified Adomian method, compactons, and mathematical physics models are distinguished in their respective fields. More details can be found in the site: http://www.sxu.edu/_ wazwaz.

• 1 Basic Concepts 1.1 Introduction 1. 2 Definitions 2 First Order PDE 2.1 Introduction 2.2 Adomian Decomposition Method 2.3 The Noise Terms Phenomenon 2.4 The Modified Decomposition 2.5 Method of Characteristics 2.6 Systems of Linear PDEs 3 One-Dimensional Heat Flow 3.1 Introduction 3.2 The Decomposition 3.3 of Separation of Variables 4 Higher Dimensional Heat Flow 4.1 Introduction 4.2 Adomian Decomposition 4.3 of Separation of Variables 5 One Dimensional Wave Equation 5.1 Introduction 5.2 Adomian Decomposition Method 5.3 Method of Separation of Variables 6 Higher Dimensional Wave Equation 6.1 Introduction 6.2 Adomian Decomposition Method 6.3 Method of Separation of Variables 7 Laplace's Equation 7.1 Introduction 7.2 Adomian Decomposition Method 7.3 Method of Separation of Variables 7.4 Laplace's Equation in Polar Coordinates 8 Nonlinear Equations 8.1 Introduction 8.2 Adomian Decomposition Method 8.3 Nonlinear Ordinary Equations 8.4 Nonlinear Partial Equations 8.5 Systems of Nonlinear PDEs 9 Physical Models 9.1 Introduction 9.2 The Nonlinear Advection Problem 9.3 The Goursat Problem 9.4 The Klein-Gm·don Equation 9.5 The Burgers' Equation . 9.6 The Telegraph Equation . . . . .. 9. 7 Schrodinger Equation 9.8 Korteweg-deVries Equation 9.9 Fourth Order Parabolic Equation 10 Numerical Applications 10.1 Introduction 10.2 Ordinary Differential Equations 10.3 Partial Differential Equations 10.4 The Pade Approximants 10.5 Boundary Value Problems 11 Solitons and Compactions 11.1 Introduction 11.2 Solutons 11.3 Compactions 11.4 The Defoeusing Braneh of K(n,n) A Indefinite Integrals A.1 Fundamental Forms A.2 Trigonometrie Forms A.3 Inverse Trigonometrie Forms A.4 Exponential and Logarithmie Forms A.5 Hyperbolie Forms A.6 Other Forms B Series B.1 Exponential Functions B.2 Trigonometrie Functions B.3 Inverse Trigonometrie Functions B.4 Hyperbolie Functions B.5 Inverse Hyperbolie Functions C Solutions of Burgers' Equation D Pade Approximants D.1 Exponential Fundions D.2 Trigonometrie Functions D.3 Hyperbolie Functions D.4 Logarithmie Functions E The Error and Ganuna Functions E.1 The Error function E.2 The Gamma function r(:r) ANSWERS.