This market leading text is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises and self contained subject matter parts for maximum flexibility. The new edition continues with the tradition of providing instructors and students with a comprehensive and up-to-date resource for teaching and learning engineering mathematics, that is, applied mathematics for engineers and physicists, mathematicians and computer scientists, as well as members of other disciplines.

Part A: Ordinary Differential Equations (Ode's).

· First-Order ODE's.

· Second Order Linear ODE's.

· Higher Order Linear ODE's.

· Systems of ODE's Phase Plane, Qualitative Methods.

· Series Solutions of ODE's Special Functions.

· Laplace Transforms.

Part B: Linear Algebra, Vector Calculus.

· Linear Algebra: Matrices, Vectors, Determinants: Linear Systems.

· Linear Algebra: Matrix Eigenvalue Problems.

· Vector Differential Calculus: Grad, Div, Curl.

· Vector Integral Calculus: Integral Theorems.

Part C: Fourier Analysis, Partial Differential Equations.

· Fourier Series, Integrals and Transforms.

· Partial Differential Equations (PDE's).

· Complex Numbers and Functions.

· Complex Integration.

· Power Series, Taylor Series.

· Laurent Series: Residue Integration.

· Conformal Mapping.

· Complex Analysis and Potential Theory.

Part E: Numerical Analysis Software.

· Numerics in General.

· Numerical Linear Algebra.

· Numerics for ODE's and PDE's.

Part F: Optimization, Graphs.

· Unconstrained Optimization: Linear Programming.

· Graphs, Combinatorial Optimization.

Part G: Probability; Statistics.

· Data Analysis: Probability Theory.

· Mathematical Statistics.

Appendix 1: References.

Appendix 2: Answers to Odd-Numbered Problems.

Appendix 3: Auxiliary Material.

Appendix 4: Additional Proofs.

Appendix 5: Tables.

Index.