Now, ADVANCED ENGINEERING MATHEMATICS features revised examples and problems as well as newly added content that has been fine-tuned throughout to improve the clear flow of ideas. The computer plays a more prominent role than ever in generating computer graphics used to display concepts and problem sets. In this new edition, computational assistance in the form of a self contained Maple Primer has been included to encourage students to make use of such computational tools.

The content has been reorganized into six parts and covers a wide spectrum of topics including Ordinary Differential Equations, Vectors and Linear Algebra, Systems of Differential Equations and Qualitative Methods, Vector Analysis, Fourier Analysis, Orthogonal Expansions, and Wavelets, and much more.

**Part I. Ordinary Differential Equations**

**Chapter 1.** First Order Differential Equations

**Chapter 2.** Linear Second Order Differential Equations

**Chapter 3.** The Laplace Transform

**Chapter 4.** Series Solutions

**Chapter 5.** Numerical Approximation of Solutions

** Part II. Vectors and Linear Algebra **

**Chapter 6.** Vectors and Vector Spaces

**Chapter 7.** Matrices and Systems of Linear Equations

**Chapter 8.** Determinants

**Chapter 9.** Eigenvalues, Diagonalization and Special Matrices

** Part III. Systems of Differential Equations and Qualitative Methods**

**Chapter 10.** Systems of Linear Differential Equations

**Chapter 11.** Qualitative Methods and Systems of Nonlinear Differential Equations

** Part IV. Vector Analysis **

**Chapter 12.** Vector Differential Calculus

**Chapter 13.** Vector Integral Calculus

** Part V. Fourier Analysis, Orthogonal Expansions and Wavelets **

**Chapter 14.** Fourier Series

**Chapter 15.** The Fourier Integral and Fourier Transforms

**Chapter 16.** Special Functions, Orthogonal Expansions and Wavelets

** Part VI. Partial Differential Equations **

**Chapter 17.** The Wave Equation

**Chapter 18.** The Heat Equation

**Chapter 19.** The Potential Equation

** Part VII. Complex Analysis **

**Chapter 20.** Geometry and Arithmetic of Complex Numbers

**Chapter 21.** Complex Functions

**Chapter 22.** Complex Integration

**Chapter 23.** Series Representations of Functions

**Chapter 24.** Singularities and the Residue Theorem

**Chapter 25.** Conformal Mappings

** Part VIII. Probability and Statistics **

**Chapter 26.** Counting and Probability

**Chapter 27.** Statistics

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