ISE Numerical Methods for Engineers

Steve Chapra is the Emeritus Professor and Emeritus Berger Chair in the Civil and Environmental Engineering Department at Tufts University. His other books include Surface Water-Quality Modeling, Numerical Methods for Engineers, and Applied Numerical Methods with Python. Dr. Chapra received engineering degrees from Manhattan College and the University of Michigan. Before joining Tufts, he worked for the U.S. Environmental Protection Agency and the National Oceanic and Atmospheric Administration, and taught at Texas A&M University, the University of Colorado, and Imperial College London. His general research interests focus on surface water-quality modeling and advanced computer applications in environmental engineering. He is a Fellow and Life Member of the American Society of Civil Engineering (ASCE) and has received many awards for his scholarly and academic contributions, including the Rudolph Hering Medal (ASCE) for his research, and the Meriam-Wiley Distinguished Author Award (American Society for Engineering Education). He has also been recognized as an outstanding teacher and advisor among the engineering faculties at Texas A&M University, the University of Colorado, and Tufts University. As a strong proponent of continuing education, he has also taught over 90 workshops for professionals on numerical methods, computer programming, and environmental modeling.Beyond his professional interests, he enjoys art, music (especially classical music, jazz, and bluegrass), and reading history. Despite unfounded rumors to the contrary, he never has, and never will, voluntarily bungee jump or sky dive. 

Part 1 - Modeling, Computers, and Error Analysis

1) Mathematical Modeling and Engineering Problem Solving

2) Programming and Software

3) Approximations and Round-Off Errors

4) Truncation Errors and the Taylor Series

Part 2 - Roots of Equations

5) Bracketing Methods

6) Open Methods

7) Roots of Polynomials

8) Case Studies: Roots of Equations

Part 3 - Linear Algebraic Equations

9) Gauss Elimination

10) LU Decomposition and Matrix Inversion

11) Special Matrices and Gauss-Seidel

12) Case Studies: Linear Algebraic Equations

Part 4 - Optimization

13) One-Dimensional Unconstrained Optimization

14) Multidimensional Unconstrained Optimization

15) Constrained Optimization

16) Case Studies: Optimization

Part 5 - Curve Fitting

17) Least-Squares Regression

18) Interpolation

19) Fourier Approximation

20) Case Studies: Curve Fitting

Part 6 - Numerical Differentiation and Integration

21) Newton-Cotes Integration Formulas

22) Integration of Equations

23) Numerical Differentiation

24) Case Studies: Numerical Integration and Differentiation

Part 7 - Ordinary Differential Equations

25) Runge-Kutta Methods

26) Stiffness and Multistep Methods

27) Boundary-Value and Eigenvalue Problems

28) Case Studies: Ordinary Differential Equations

Part 8 - Partial Differential Equations

29) Finite Difference: Elliptic Equations

30) Finite Difference: Parabolic Equations

31) Finite-Element Method

32) Case Studies: Partial Differential Equations

Appendix A - The Fourier Series

Appendix B - Getting Started with Matlab

Appendix C - Getting Starte dwith Mathcad

Bibliography

Index