Schilling, Robert J. : Clarkson University

Harris, Sandra L. : Clarkson University

This book provides a comprehensive discussion of numerical computing techniques with an emphasis on practical applications in the fields of civil, chemical, electrical, and mechanical engineering. It features two software libraries that implement the algorithms developed in the text - a MATLAB© toolbox, and an ANSI C library. This book is written in an engaging, informal style that is accessible to all readers. Each chapter includes detailed case study examples from the four engineering fields with complete solutions provided in both MATLAB© and C; detailed objectives, numerous worked-out examples and illustrations, and summaries comparing the numerical techniques. Chapter problems are divided into separate analysis and computation sections. Documentation for the software is provided in text appendices that also include a helpful review of vectors and matrices. The Instructor's Manual includes a disk with software documentation and complete solutions to both problems and examples in the book.

• Comprehensive coverage of topics, including chapters on optimization (Chapter 6) and digital signal processing (Chapter 10).
• Two complete software libraries with source code and built-in documentation that implement the algorithms developed in the text. A GUI-driven MATLAB toolbox and a comprehensive ANSI C library are provided on an accompanying CD-ROM bound into the text.
• 38 detailed case studies apply techniques to problems in civil, mechanical, chemical and electrical engineering, with solutions in both MATLAB and C.
• Clear, engaging writing style with motivational problems at the start of each chapter, and numerous worked-out examples and illustrations.
• Detailed objectives and summaries for each chapter.

1. NUMERICAL COMPUTATION.

Motivation and Objectives.
Number Representation.
Machine Precision.
Round-Off Error.
Truncation Error.
Random Number Generation.
Numerical Software.
Applications.
Chapter Summary.
Problems.

2. LINEAR ALGEBRAIC SYSTEMS.

Motivation and Objectives.
Gauss-Jordan Elimination.
Gaussian Elimination.
LU Decomposition.
Ill-Conditioned Systems.
Iterative Methods.
Applications.
Chapter Summary.
Problems.

3. EIGENVALUES AND EIGENVECTORS.

Motivation and Objectives.
The Characteristic Polynomial.
Power Methods.
Jacobi's Method.
Householder Transformation.
QR Method.
Danilevsky's Method.
Polynomial Roots.
Applications.
Chapter Summary.
Problems.

4. CURVE FITTING.

Motivation and Objectives.
Interpolation.
Newton's Difference Formula.
Cubic Splines.
Least Square.
Two-Dimensional Interpolation.
Applications.
Chapter Summary.
Problems.

5. ROOT FINDING.

Motivation and Objects.
Bracketing Methods.
Contraction Mapping Method.
Secant Method.
Muller's Method.
Newton's Method.
Polynomial Roots.
Nonlinear Systems of Equations.
Applications.
Chapter Summary.
Problems.

6. OPTIMIZATION.

Motivation and Objectives.
Local and Global Minima.
Line Searches.
Steepest Descent Method.
Conjugate-Gradient Method.
Quasi-Newton Methods.
Penalty Functions.
Simulated Annealing.
Applications.
Chapter Summary.
Problems.

7. DIFFERENTIATION AND INTEGRATION.

Motivation and Objectives.
Numerical Differentiation.
Noise-Corrupted Data.
Newton-Cotes Integration Formulas.
Romberg.
Gauss Quadrature.
Improper Integrals.
Multiple Integrals.
Applications.
Chapter Summary.
Problems.

8. ORDINARY DIFFERENTIAL EQUATIONS.

Motivation and Objectives.
Euler's Method.
Runge-Kutta Methods.
Step Size Control.
Multi-Step Methods.
Bulirsch-Stoer Extrapolation Methods.
Stiff Differential Equations.
Boundary Value Problems.
Applications.
Chapter Summary.
Problems.

9. PARTIAL DIFFERENTIAL EQUATIONS.

Motivation and Objectives.
Elliptic Equations.
One-Dimensional Parabolic Equations.
Two-Dimensional Parabolic Equations.
One-Dimensional Hyperbolic Equations.
Two-Dimensional Parabolic Equations.
Applications.
Chapter Summary.
Problems.

10. DIGITAL SIGNAL PROCESSING.

Motivation and Objectives.
Fourier Transform.
Fast Fourier Transform (FFT).
Correlation.
Convolution Digital Filters.
Two-Dimensional FFT.
System Identification.
Applications.
Chapter Summary.
Problems.

REFERENCES AND FURTHER READING.

APPENDIX 1: NLIB USING MATLAB.

A Numerical Toolbox: NLIB.
Main-Program Support.
Linear Algebraic Systems.
Eigenvalues and Eigenvectors.
Curve Fitting.
Root Finding.
Optimization.
Differentiation and Integration.
Ordinary Differential Equations.
Partial Differential Equations.
Digital Signal Processing.

APPENDIX 2: NLIB USING C.

A Numerical Library: NLIB.
NLIB Data Types. NLIB Core: nlib.c.
Tabular Display: show.c. Graphical Display: draw.c.
Linear Algebraic Systems: linear.c.
Eigenvalues and Eigenvectors: eigen.c.
Curve Fitting: curves.c. Root Finding: roots.c.
Optimization: optim.c.
Differentiation and Integration: integ.c.
Ordinary Differential Equations: ode.c.
Partial Differential Equations: pde.c.
Digital Signal Processing: dsp.c.

APPENDIX 3: VECTORS AND MATRICES.

Vector and Matrix Notation.
Basic Operations. Inverses.
Eigenvalues and Eigenvectors.
Vector Norms.

APPENDIX 4: ANSWERS TO SELECTED PROBLEMS.
INDEX.