Computational Methods in Engineering
- 1st Edition - December 2, 2013
- Imprint: Academic Press
- Authors: S.P. Venkateshan, Prasanna Swaminathan
- Language: English
- Hardback ISBN:9 7 8 - 0 - 1 2 - 4 1 6 7 0 2 - 5
- eBook ISBN:9 7 8 - 0 - 1 2 - 4 1 6 7 0 3 - 2
Computational Methods in Engineering brings to light the numerous uses of numerical methods in engineering. It clearly explains the application of these methods mathemati… Read more
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Request a sales quoteComputational Methods in Engineering brings to light the numerous uses of numerical methods in engineering. It clearly explains the application of these methods mathematically and practically, emphasizing programming aspects when appropriate. By approaching the cross-disciplinary topic of numerical methods with a flexible approach, Computational Methods in Engineering encourages a well-rounded understanding of the subject.
This book's teaching goes beyond the text—detailed exercises (with solutions), real examples of numerical methods in real engineering practices, flowcharts, and MATLAB codes all help you learn the methods directly in the medium that suits you best.
- Balanced discussion of mathematical principles and engineering applications
- Detailed step-by-step exercises and practical engineering examples to help engineering students and other readers fully grasp the concepts
- Concepts are explained through flowcharts and simple MATLAB codes to help you develop additional programming skills
Graduate engineering students; reference book for teachers, professionals, and anyone else looking to expand their knowledge of computational methods.
Dedication
Preface
Acknowledgements
Chapter 1. Preliminaries
1.1 Introduction
1.2 Mathematical and computational modeling
1.3 A brief introduction to MATLAB
Suggested reading
Module I: System of Equations and Eigenvalues
Module I: System of Equations and Eigenvalues
Chapter 2. Solution of Linear Equations
2.1 Analytical methods of solving a set of linear equations
2.2 Preliminaries
2.3 Gauss elimination method
2.4 Gauss Jordan method of determining the inverse matrix
2.5 LU decomposition or LU factorization
2.6 Tridiagonal matrix algorithm
2.7 QR Factorization
2.8 Iterative methods of solution
CG Method
2.A MATLAB routines related to Chapter 2
2.B Suggested reading
Chapter 3. Computation of Eigenvalues
3.1 Examples of eigenvalues
3.2 Preliminaries on eigenvalues
3.3 Analytical evaluation of eigenvalues and eigenvectors in simple cases
3.4 Power method
3.5 Rayleigh Quotient Iteration
3.6 Eigenvalue eigenvector pair by QR iteration
3.7 Modification of QR iteration for faster convergence
3.A MATLAB routines related to Chapter 3
3.B Suggested reading
Chapter 4. Solution of Algebraic Equations
4.1 Univariate nonlinear equation
4.2 Multivariate non linear equations
4.3 Root finding and optimization
4.4 Multidimensional unconstrained optimization
4.5 Examples from engineering applications
4.A MATLAB routines related to Chapter 4
4.B Suggested reading
Exercise I
I.1 Solution of linear equations
I.2 Evaluation of eigenvalues
I.3 Solution of algebraic equations
Module II: Interpolation, differentiation and integration
Module II: Interpolation, Differentiation and Integration
Chapter 5. Interpolation
5.1 Polynomial interpolation
5.2 Lagrange interpolating (or interpolation) polynomial
5.3 Newton Polynomials
5.4 Error estimates of polynomial approximations
5.5 Polynomial approximation using Chebyshev nodes
5.6 Piecewise polynomial interpolation
5.7 Hermite interpolation
5.8 Spline interpolation and the cubic spline
5.A MATLAB routines related to Chapter 5
references
Chapter 6. Interpolation in Two and Three Dimensions
6.1 Interpolation over a rectangle
6.2 Interpolation over a triangle
6.3 Interpolation in three dimensions
Chapter 7. Regression or Curve Fitting
7.1 Introduction
7.2 Method of least squares for linear regression
7.3 Multi-linear regression
7.4 Polynomial regression
7.5 Non-linear regression
7.A MATLAB routines related to Chapter 7
7. B Suggested reading
Chapter 8. Numerical Differentiation
8.1 Introduction
8.2 Finite difference formulae using Taylor’s series
8.3 Differentiation of Lagrange and Newton polynomials
8.4 Numerical partial differentiation
8.A MATLAB routines related to Chapter 8
Chapter 9. Numerical Integration
9.1 Introduction
9.2 Trapezoidal rule
9.3 Simpson’s rule
9.4 Integration of functions
9.5 Quadrature using Chebyshev nodes
9.6 Gauss quadrature
9.7 Singular integrals
9.8 Integrals with infinite range
9.9 Adaptive quadrature
9.10 Multiple integrals
9.A MATLAB routines related to Chapter 9
9.B Suggested reading
Exercise II
II.1 Interpolation
II.2 Interpolation in two dimensions
II.3 Regression
II.3 Regression
II.4 Numerical differentiation
II.5 Numerical integration
Module III: Ordinary differential equations
Module III: Ordinary differential equations
Chapter 10. Initial Value Problems
10.1 Introduction
10.2 Euler method
10.3 Modified Euler method or Heun method
10.4 Runge Kutta (RK) methods
10.5 Predictor corrector methods
10.6 Set of first order ODEs
10.7 Higher order ODEs
10.8 Stiff equations and backward difference formulae (BDF) based methods
10.B Suggested reading
Chapter 11. Boundary Value Problems (ODE)
11.1 Introduction
11.2 The ‘shooting method’
11.3 Finite difference method
11.4 Collocation method
11.5 Method of weighted residuals
11.6 Finite element method
11.7 Finite volume method
11.A MATLAB routines related to Chapter 11
11.B Suggested reading
Exercise III
III.1 Initial value problems
III.2 Boundary value problems
Module IV: Partial Differential Equations
Module IV: Partial Differential Equations
Chapter 12. Introduction to PDEs
12.1 Preliminaries
12.2 Second order PDE with constant coefficients
12.3 Numerical solution methods for PDEs
12.4 MATLAB functions related to PDE
12. A Suggested reading
Chapter 13. Laplace and Poisson Equations
13.1 Introduction
13.2 Finite difference solution
13.3 Elliptic equations in other coordinate systems
13.4 Elliptic equation over irregular domain
13.5 FEM and FVM applied to elliptic problems
Chapter 14. Advection and Diffusion Equations
14.1 Introduction
14.2 The advection equation
14.3 Parabolic PDE: Transient diffusion equation
14.4 Advection with diffusion
14.5 Advection equation in multi dimensions
14.6 Diffusion equation in multi dimensions
14.A Suggested reading
Chapter 15. Wave Equation
15.1 Introduction
15.2 General solution of the wave equation
15.3 Numerical solution of the one dimensional wave equation
15.4 Waves in a diaphragm
Exercise IV
IV.1 Types of partial differential equations
IV.2 Laplace and Poisson equations
IV.3 Advection and diffusion equations
IV.4 Wave equation
Chapter 16. Beyond the Book – the Way Ahead
16.1 Researchers developing their own code
16.2 Users of commercial codes
16.3 Where does one look for help?
Index
- Edition: 1
- Published: December 2, 2013
- No. of pages (Hardback): 692
- Imprint: Academic Press
- Language: English
- Hardback ISBN: 9780124167025
- eBook ISBN: 9780124167032
SV
S.P. Venkateshan
Professor S. P. Venkateshan received his Ph.D. in Heat Power Engineering from the Indian Institute of Science, Bangalore in 1977. He has taught computational methods in engineering at the Indian Institute of Technology (IIT) Madras for 15 years. Recently, Professor Venkateshan worked as Head of the Department of Mechanical Engineering at IIT Madras.
Affiliations and expertise
S.P. Venkateshan has taught computational methods in engineering at the Indian Institute of Technology (IIT) Madras for 15 years. He has also worked as the Head of the Department of Mechanical Engineering at IIT Madras.PS
Prasanna Swaminathan
Prasanna Swaminathan is a research scholar at the Heat Transfer and Thermal Power Lab at IIT Madras.
Affiliations and expertise
Prasanna Swaminathan is a research scholar at the Heat Transfer and Thermal Power Lab at IIT Madras.Read Computational Methods in Engineering on ScienceDirect