A text in Advanced Engineering Mathematics is a compendium of many mathematical topics, all of which are loosely related by the expedient of either being needed or useful in courses and subsequent careers in science and engineering. There is literally no upper bound to the number of topics that could be included in a text such as this. Consequently, this book represents the authors’ opinion of what constitutes “engineering mathematics” i.e. Ordinary Differential Equations, Vectors, Matrices, and Vector Calculus, Systems of Differential, Fourier Series and Partial Differential Equations and Complex Analysis etc. as the authors believe that the backbone of science/engineering-related mathematics is the theory and applications of ordinary and partial differential equations.

Preface / Part 1: Ordinary Differential Equations – Introduction to Differential Equations / First-Order Differential Equations / Higher-Order Differential Equations / The Laplace Transform / Series Solutions of Linear Differential Equations / Numerical Solutions of Ordinary Differential Equations / Part 2: Vectors, Matrices, and Vector Calculus – Vectors / Matrices / Vector Calculus / Part 3: Systems of Differential Equations – Systems of Linear Differential Equations / Systems of Nonlinear Differential Equations / Part 4: Fourier Series and Partial Differential Equations – Orthogonal Functions and Fourier Series / Boundary-value Problems in Rectangular Coordinates / Boundary-value Problems in Other Coordinate Systems / Integral Transform Method / Numerical Solutions of Partial Differential Equations / Part 5: Complex Analysis – Functions of a Complex Variable / Integration in the Complex Plane / Series and Residues / Conformal Mappings / Appendices / Answers for Selected Odd-Numbered Problems / Index.

Undergraduate – Postgraduate Students in Engineering & Mathematics