Enriched with additional topics to exactly cover syllabus, this version of Advanced Engineering Mathematics by Prof. Erwin Kreyszig, globally the most popular textbook on the subject, is restructured in a concise and easy-to-understand manner. It fulfills the need for a book that not only effectively explains the concepts but also aids in visualizing the underlying geometric interpretation. Every chapter has easy to follow explanation of the theory and numerous step-by-step solved problems and examples.


Table of Contents:
Chapter 1 Differential Equations of First Order 1.1 Introduction 1.2 Some Important Definitions 1.3 Differential Equations of First-Order and First Degree 1.4 Geometric Applications 1.5 Variable Separable Method 1.6 Homogeneous Equation (Reduction to Separable Form) 1.7 Non-Homogeneous Equations Reducible to Homogeneous Form 1.8 Exact Differential Equations 1.9 Differential Equations Reducible to Exact Form (Integrating Factors) 1.10 Linear Ordinary Differential Equations 1.11 Simultaneous First-Order Linear Equations with Constant Coefficients 1.12 Applications of Differential Equations Chapter 2 Linear Differential Equations of Second and Higher Order 2.1 Introduction 2.2 Linear Differential Equations 2.3 Homogeneous Linear Differential Equations of Second Order with Constant Coefficients 2.4 Higher Order Linear Homogeneous Differential Equations 2.5 Non-Homogeneous Linear Differential Equations with Constant Coefficients 2.6 Differential Equations with Variable Coefficients Reducible to DE with Constant Coefficients 2.7 Solution of Second Order Differential Equation 2.8 Method of Variation of Parameters 2.9 Simultaneous Differential Equations of Higher Order 2.10 Application to Bending of Beams 2.11 Application to Electric Circuits 2.12 Simple Harmonic Motion Chapter 3 Series Solution and Special Functions 3.1 Introduction 3.2 Power Series Method 3.3 Frobenius Method 3.4 Legendre’s Equation and Legendre Polynomials Pn(x) 3.5 Bessel’s Equations and Bessel Functions Jn(x) 3.6 Bessel Functions of the Second Kind Ym(x) Chapter 4 Laplace Transforms 4.1 Introduction 4.2 Laplace Transforms: Basic Concepts 4.3 Laplace Transforms of the Form t f (t) and f (t)/t 4.4 Laplace Transform of Derivatives and Integrals 4.5 Initial and Final Value Theorems 4.6 Some Special Functions and Their Laplace Transforms 4.7 Inverse Laplace Transform 4.8 Inverse Transform of Logarithmic and Trigonometric Functions 4.9 Inverse Laplace Transform Using Derivatives and Integrals 4.10 Inverse Laplace Transform Using Change of Scale Property 4.11 Second Shifting Property for Inverse Transform 4.12 The Convolution Theorem 4.13 Applications to Differential Equations: Linear and Simultaneous Differential Equations 4.14 Solution of Integral Equations Chapter 5 Fourier Series 5.1 Introduction 5.2 Limit of a Function 5.3 Continuity 5.4 Periodic Functions 5.5 Fourier Series 5.6 Dirichlet’s Conditions 5.7 Euler’s Formulae 5.8 Jump of a Function 5.9 Fourier Series for Discontinuous Functions 5.10 Even and Odd Functions 5.11 Change of Interval 5.12 Half-Range Series 5.13 Root Mean Square (RMS) Value of a Function 5.14 Complex Form or Exponential Form of Fourier Series 5.15 Practical Harmonic Analysis Chapter 6 Partial Differential Equations and Their Applications 6.1 Introduction 6.2 Formation of Partial Differential Equations 6.3 Solution of Partial Differential Equations of First Order 6.4 Linear Partial Differential Equations with Constant Coefficients 6.5 Non-Linear Partial Differential Equations of First Order 6.6 Classification of Second-Order PDEs 6.7 Method of Separation of Variables 6.8 Solution of One-Dimensional Wave Equation 6.9 Solution to Two-Dimensional Wave Equation 6.10 Solution of One-Dimensional Heat Equation 6.11 Steady Two-Dimensional Heat Problems: Laplace’s Equation 6.12 Solution of Laplace Equation in Two Dimensions 6.13 Equations of a Transmission Line