The content and character of mathematics needed in applications are changing rapidly. Introduces students of engineering, physics, mathematics and computer science to those areas that are vital to address practical problems. The Seventh Edition offers a self-contained treatment of ordinary differential equations, linear algebra, vector calculus, fourier analysis and partial differential equations, complex analysis, numerical methods, optimization and graphs, probability and statistics. New in this edition are: many sections rewritten to increase readability; problems have been revised and more closely related to examples; instructors manual quadrupled in content; improved balance between applications, algorithmic ideas and theory; reorganized differential equations and linear algebra sections; added and improved examples throughout.

ORDINARY DIFFERENTIAL EQUATIONS.

First-Order Differential Equations.

Second-Order Linear Differential Equations.

Higher Order Linear Differential Equations.

Systems of Differential Equations: Phase Plane, Stability.

Series Solutions of Differential Equations: Special Functions.

Laplace Transforms.

LINEAR ALGEBRA, VECTOR CALCULUS.

Linear Algebra: Matrices, Vectors, Determinants.

Vector Differential Calculus: Grad, Div, Curl.

Vector Integral Calculus: Integral Theorems.

FOURIER ANALYSIS AND PARTIAL DIFFERENTIAL EQUATIONS.

Fourier Series, Integrals, and Transforms.

Partial Differential Equations.

COMPLEX ANALYSIS.

Complex Numbers, Complex Analytic Functions.

Complex Integration.

Power Series, Taylor Series, Laurent Series.

Residue Integration Method.

Conformal Mapping.

Complex Analysis Applied to Potential Theory.

NUMERICAL METHODS.

Numerical Methods in General.

Numerical Methods in Linear Algebra.

Numerical Methods for Differential Equations.

OPTIMIZATION, GRAPHS.

Unconstrained Optimization, Linear Programming.

Graphs and Combinatorial Optimization.

PROBABILITY AND STATISTICS.

Probability Theory.

Mathematical Statistics.

Appendices.
Index.