Numerical analysis in engineering

Title:

Personal Author:

Bhat, Rama B.

Publication Information:

New Delhi, India : Alpha Science International Ltd., 2004

ISBN:

9781842651216

Subject Term:

Numerical analysis

Engineering mathematics

Added Author:

Chakraverty, Snehashish

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000004990788	QA297 B42 2004	Open Access Book	Book	Searching... Unknown

This text deals with the methods of obtaining numerical solutions to engineering problems. The topics discussed are those that are normally covered in undergraduate engineering programs. This includes an introduction to digital computers, function representation using Taylor's series, error considerations in iterative type computations, searching for roots of equations in a single variable, solution of simultaneous equations, function approximation and interpolation, numerical integration and differentiation, matrix eigenvalue problems, solution of nonlinear system of equations, and solution of ordinary and partial differential equations.

Author Notes

R B Bhat: Department of Mechanical Engineering, Faculty of Engineering and Computer Science, Concordia University, Montreal, Quebec, Canada
S Chakraverty: Scientist, Computer Centre, Central Building Research Institute, Roorkee, India

Preface	p. v
Chapter 1 Solution of Equations for Engineering Design and Analysis	p. 1
1.1 Introduction	p. 1
1.2 Taylor's Series Expansion of Functions	p. 1
1.3 Digital Computers	p. 3
1.4 Number Representation: Floating Point and Fixed Point	p. 5
1.5 Algorithms and Flowcharts	p. 6
1.6 Error Considerations	p. 8
1.7 Sequences	p. 11
Chapter 2 Numerical Research for Roots of Algebraic and Transcendental Equations	p. 14
2.1 Incremental Search	p. 15
2.2 Bisection Method	p. 18
2.3 Method of False Position	p. 20
2.4 Newton Raphson Method	p. 23
2.5 Modified Newton Raphson Method	p. 26
2.6 Secant Method	p. 28
2.7 Complex Roots of Equations	p. 30
2.8 Practical Application	p. 31
Chapter 3 Methods to Solve Linear Simultaneous Equations	p. 34
3.1 Properties of Matrices	p. 34
3.2 Gaussian Elimination	p. 37
3.3 Pivoting Techniques	p. 42
3.4 Gauss-Jordan Method	p. 49
3.5 Matrix Factorization Techniques	p. 53
3.5.1 Doolittle Method (L*U decomposition)	p. 54
3.5.2 Crout's Method	p. 57
3.6 Cholesky Method (valid only for matrices which are positive definite)	p. 62
3.7 Norms of Vectors and Matrices	p. 69
3.8 Jacobi Method	p. 74
3.9 Gauss-Seidel Method	p. 76
Chapter 4 Function Approximation or Interpolation	p. 78
4.1 Discrete Least Squares Approximation	p. 78
4.2 Least Squares Function Approximation	p. 86
4.3 Interpolation with Divided Differences	p. 90
4.4 Lagrange Polynomials	p. 98
4.5 Cubic Spline Approximation	p. 101
Chapter 5 Numerical Integration	p. 115
5.1 Introduction	p. 115
5.2 Trapezoidal Rule	p. 118
5.3 Simpson's Rule	p. 125
5.4 Newton-Cotes Formulas	p. 128
5.5 Romberg Integration	p. 132
5.6 Gauss Quadrature	p. 139
Chapter 6 Numerical Differentiation	p. 149
6.1 Central Differences	p. 149
6.2 Forward Differences	p. 156
6.3 Backward Differences	p. 163
6.4 Error Considerations	p. 172
Chapter 7 Matrix Eigenvalue Problems	p. 174
7.1 Gerschgorin Circle Theorem	p. 174
7.2 Characteristic Equation	p. 178
7.3 Power Method	p. 182
7.4 Inverse Power Method	p. 187
7.5 Jacobi's Method	p. 195
7.6 Householder--Q, L Method	p. 204
7.7 Householder--Q, R, Method	p. 215
Chapter 8 Solution of Equations for Engineering Design and Analysis	p. 223
8.1 Introduction	p. 223
8.2 Newton's Method	p. 223
Chapter 9 Numerical Solutions of Ordinary Differential Equations	p. 233
9.1 Introduction	p. 233
9.2 Euler's Method	p. 234
9.3 Higher Order Taylor Methods	p. 237
9.4 Runge-Kutta Methods	p. 239
9.5 Two Step Predictor-Corrector Methods	p. 243
9.6 Milne's Predictor-Simpson's Corrector Method	p. 245
9.7 Hamming's Method	p. 248
9.8 Higher Order Differential Equations and System of Differential Equations	p. 249
Chapter 10 Introduction to Partial Differential Equations	p. 254
10.1 Introduction	p. 254
10.2 Elliptic Partial Differential Equations	p. 255
10.3 Parabolic Partial Differential Equations	p. 257
10.4 Hyperbolic Partial Differential Equations	p. 261
Chapter 11 Introduction to the Theory of Linear Vector Spaces	p. 263
11.1 Preliminaries	p. 263
11.2 Construction of Orthogonal Polynomials	p. 270
11.3 Boundary Characteristic Orthogonal Polynomials	p. 274
Chapter 12 Solution of Boundary Value Problems	p. 276
12.1 Preliminaries	p. 276
12.2 Shooting Method	p. 276
12.3 Rayleigh-Ritz Method	p. 283
12.4 Collocation Method	p. 287
12.5 Galerkin's Method	p. 289
Problems	p. 293
References	p. 318
Index	p. 319

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents