In conjunction with Erwin Kreyszig's

*Advanced Engineering Mathematics*, this book and

*Mathematica* help students in working out class notes, doing homework and exams, and pursuing self-study. No previous experience with

*Mathematica* or any other software is required, and this edition is fully updated for

*Mathematica* 5.2.

Over 130 worked-out examples are provided--covering ordinary and partial differential equations, linear algebra and vector calculus, Fourier series and integrals, complex analysis and potential theory, numeric analysis, linear programming and combinatorial optimization, and probability theory and statistics--as well as over 400 practice problems.

**Introduction, General Commands** **Part A: Ordinary Differential Equations (ODEs)** First-Order ODEs | Linear ODEs of Second and Higher Order | Systems of ODEs, Phase Plane, Qualitative Methods | Series Solutions of ODEs | Laplace Transform Method for Solving ODEs

**Part B: Linear Algebra, Vector Calculus** Matrices, Vectors, Determinants, Linear Systems of Equations | Matrix Eigenvalue Problems | Vector Differential Calculus,

`Grad`,

`Div`,

`Curl` | Vector Integral Calculus, Integral Theorems

**Part C: Fourier Analysis and Partial Differential Equations (PDEs)** Fourier Series, Integrals, and Transforms | Partial Differential Equations (PDEs)

**Part D: Complex Analysis** Complex Numbers and Functions, Conformal Mapping | Complex Integration | Power Series, Taylor Series | Laurent Series, Residue Integration | Complex Analysis in Potential Theory

**Part E: Numerical Analysis** Numerics in General | Numeric Linear Algebra | Numerics for ODEs and PDEs

**Part F: Optimization, Graphs** Unconstrained Optimization, Linear Programming

**Part G: Probability and Statistics** Data Analysis, Probability Theory | Mathematical Statistics

**Appendices** References | Answers to Odd-Numbered Problems

Algebra,

Applied Mathematics,

Calculus and Analysis,

Differential Equations,

Engineering,

Probability and Statistics