Steve Chapra and Raymond Canale collaborated on the 1st edition of NUMERICAL METHODS FOR ENGINEERS published by McGraw-Hill in 1985. Now in its 8th edition, it is the most widely used text of this type by colleges and universities around the world and has been translated into 10 languages.
The eighth edition of Chapra and Canale's Numerical Methods for Engineers retains the instructional techniques that have made the text so successful. The book covers the standard numerical methods employed by both students and practicing engineers. Although relevant theory is covered, the primary emphasis is on how the methods are applied for engineering problem solving. Each part of the book includes a chapter devoted to case studies from the major engineering disciplines.
Numerous new or revised end-of chapter problems and case studies are drawn from actual engineering practice. This edition also includes several new topics including a new formulation for cubic splines, Monte Carlo integration, and supplementary material on hyperbolic partial differential equations.
▶ Hallmark Features of the Text
Theory is included in a practical way
As it provides insights into the strengths and shortcomings of the methods.
Emphasis on trade-offs among methods
This helps students understand that several methods are typically available to solve a particular mathematical problem and that there are trade-offs between methods (e.g., speed versus accuracy).
This book is written for the student, not the instructor. Features supporting this goal are the overall organisation, the use of introductions and epilogues to consolidate major topics, the extensive use of worked examples and case studies from all areas of engineering, and liberal use of figures to graphically illuminate concepts and theory. The authors have also endeavoured to keep our explanations straightforward and practically oriented.
Strong emphasis on both programming and packages
This helps the authorsto apply numerical methods for problem solving. The authors empower students by helping them utilise the numerical problem-solving capabilities of packages like Excel, MATLAB, and Mathcad software. However, students are also shown how to develop simple, well-structured programs to extend the base capabilities of those environments.
Engineering and science examples, case studies, and end-of-chapter problems
Drawing from engineering and scientific problem-solving contexts this enlivens the student experience by
emphasising how the methods will help them in practice.
▶ Overall Changes and New Topics
New and revised problems
Numerous new or revised end-of chapter problems and case studies are drawn from actual
New, improved formulation for cubic splines
Easier to understand than the previous version and compatible with MATLAB algorithm.
Monte Carlo integration
Increasingly used in engineering and science.
Supplementary material on hyperbolic partial differential equations (PDEs)
Together with existing material on Elliptic & Parabolic PDEs, makes the part of the book on PDEs more complete.
▶ For Students & Instructors
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
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 Started with Mathcad