A long-standing, best-selling, comprehensive textbook covering all the mathematics required on upper level engineering mathematics undergraduate courses.  Its unique approach takes you through all the mathematics you need in a step-by-step fashion with a wealth of examples and exercises. The text demands that you engage with it by asking you to complete steps that you should be able to manage from previous examples or knowledge you have acquired, while carefully introducing new steps. By working with the authors through the examples, you become proficient as you go. By the time you come to trying examples on their own, confidence is high.

Suitable for undergraduates in second and third year courses on engineering and science degrees.  

Hints on Using the Book.- Useful Background Information.- Numerical Solutions of Equations and Interpolation.- Laplace Transforms Part 1.- Laplace Transforms Part 2.- Laplace Transforms Part 3.- Difference Equations and the Z Transform.- Introduction to Invariant Linear Systems.- Fourier Series 1 .- Fourier Series 2.- Introduction to the Fourier Transform.- Power Series Solutions of Ordinary Differential Equations 1.- Power Series Solutions of Ordinary Differential Equations 2.- Power Series Solutions of Ordinary Differential Equations 3.- Numerical Solutions of Ordinary Differential Equations.- Matrix Algebra .- Systems of Ordinary Differential Equations.- Direction Fields.- Phase Plane Analysis.- Non-linear Systems.- Dynamical Systems.- Partial Differentiation.- Partial Differential Equations.- Numerical Solutions of Partial Differential Equations.- Multiple Integration Part 1.- Multiple Integration Part 2.- Integral Functions.- Vector Analysis Part 1.- Vector Analysis Part 2.- Vector Analysis Part 3.- Complex Analysis Part 1.- Complex Analysis Part 2.- Complex Analysis Part 3.- Optimization and Linear Programming.