Advanced Engineering Mathematics

Unlike many engineering mathematics books, the new edition of this comprehensive applications-oriented book uses computer programs and computer generated figures to demonstrate the mathematical concepts under discussion. Designed for engineering students as well as practising engineers and scientists, the book has hundreds of examples with in-text solutions. In terms of content, it covers the entire sequence of mathematical topics needed by the majority of university programs, including geometry, matrices, integrals, ODE, PDE, vector calculus, complex variables, probability/statistics, numerical methods and more. The authors demonstrate how the mathematical concepts will be used in practical applications such as Fractals, Robotics, Circuits, Membrane Simulation, Collision Detection, Ray Tracing, and Signal Processing. A CD-ROM with the source code for the in-text computer programs (written in C) includes calculation routines and simulations. Table Of Contents : 1. Complex Numbers, 2. Theory of Equations and Curve Fitting, 3. Determinants and Matrices, 4. Analytical Solid Geometry, 5. Partial Differentiation, 6. Multiple Integrals, 7. Vector Algebra, 8. Vector Calculus, 9. Infinite Series, 10. Fourier Series, 11. First-Order Differential Equations, 12. Applications of First Order Differential Equations, 13. Linear Differential Equations, 14. Applications of Linear Differential Equations, 15. Special Functions and the Series Solution of Differential Equations, 16. Partial Differential Equations, 17. Applications of Partial Differential Equations, 18. The Laplace Transforms, 19. Functions of a Complex Variable, 20. Integral Transforms, 21. Statistics and Probability, 22. Finite Differences and Numerical Methods, 23. Z-Transforms, 24. The Numerical Solution of Ordinary Differential Equations, 25. The Numerical Solution of Partial Differential Equations, 26. Curvilinear Coordinates, 27. Tensor Analysis, 28. Virtual WorkAppendices