Applied engineering mathematics / Xin-She Yang.

Format:

Book

Author/Creator:

Yang, Xin-She.

Language:

English

Subjects (All):

Engineering mathematics.

Mathematical analysis.

Physical Description:

1 online resource (333 p.)

Place of Publication:

Cambridge, UK : Cambridge International Science Publishing, c2007.

Language Note:

English

Summary:

This book endeavours to strike a balance between mathematical and numerical coverage of a wide range of mathematical methods and numerical techniques. It strives to provide an introduction, especially for undergraduates and graduates, to engineering mathematics and its applications. Topics include advanced calculus, ordinary differential equations, partial differential equations, vector and tensor analysis, calculus of variations, integral equations, the finit difference method, reaction-diffusion system, and probability and statistics. The book also emphasizes the application of important mathematical methods with dozens of worked examples. The applied topics include elasticity, harmonic motion, chaos, kinematics, pattern formation and hypothesis testing. The book can serve as a textbook in engineering mathematics, mathematical modelling and scientific computing.

Contents:

Intro

Preface

Acknowledgements

About the Author

Contents

1. Calculus

1.1 Differentiations

1.2 Integrations

1.3 Partial Differentiation

1.4 Multiple Integrals

1.5 Some Special Integrals

2. Vector Analysis

2.1 Vectors

2.1.1 Dot Product and Norm

2.2 Vector Algebra

2.3 Applications

3. Matrix Algebra

3.1 Matrix

3.2 Determinant

3.3 Inverse

3.4 Matrix Exponential

3.5 Hermitian and Quadratic Forms

3.6 Solution of linear systems

4. Complex Variables

4.1 Complex Numbers and Functions

4.2 Hyperbolic Functions

4.3 Analytic Functions

4.4 Complex Integrals

5. Ordinary Differential Equations

5.1 Introduction

5.2 First Order ODEs

5.3 Higher Order ODEs

5.4 Linear System

5.5 Sturm-Liouville Equation

5.5.1 Bessel Equation

6. Recurrence Equations

6.1 Linear Difference Equations

6.2 Chaos and Dynamical Systems

6.3 Self-similarity and Fractals

7. Vibration and Harmonic Motion

7.1 Undamped Forced Oscillations

7.2 Damped Forced Oscillations

7.3 Normal Modes

7.4 Small Amplitude Oscillations

8. Integral Transforms

8.1 Fourier Transform

8.2 Laplace Transforms

8.3 Wavelet

9. Partial Differential Equations

9.1 First Order PDE

9.2 Classification

9.3 Classic PDEs

10. Techniques for Solving PDEs

10.1 Separation of Variables

10.2 Transform Methods

10.3 Similarity Solution

10.4 Travelling Wave Solution

10.5 Green's Function

10.6 Hybrid Method

11. Integral Equations

11.1 Calculus of Variations

11.2 Integral Equations

11.3 Solution of Integral Equations

12. Tensor Analysis

12.1 Notations

12.2 Tensors

12.3 Tensor Analysis

13. Elasticity

13.1 Hooke's Law and Elasticity

13.2 Maxwell's Reciprocal Theorem

13.3 Equations of Motion

13.4 Airy Stress Functions.

13.5 Euler-Bernoulli Beam Theory

14. Mathematical Models

14.1 Classic Models

14.2 Other PDEs

15. Finite Difference Method

15.1 Integration of ODEs

15.2 Hyperbolic Equations

15.3 Parabolic Equation

15.4 Elliptical Equation

16. Finite Volume Method

16.1 Introduction

16.2 Elliptic Equations

16.3 Parabolic Equations

16.4 Hyperbolic Equations

17. Finite Element Method

17.1 Concept of Elements

17.2 Finite Element Formulation

17.3 Elasticity

17.4 Heat Conduction

17.5 Time-Dependent Problems

18. Reaction Diffusion System

18.1 Heat Conduction Equation

18.2 Nonlinear Equations

18.3 Reaction-Diffusion System

19. Probability and Statistics

19.1 Probability

19.2 Statistics

References

Appendix A Mathematical Formulas

A.1 Differentiations and Integrations

A.2 Vectors and Matrices

A.3 Asymptotics

A.4 Special Integrals

Index.

Notes:

Bibliographic Level Mode of Issuance: Monograph

Includes bibliographical references and index.

ISBN:

1-907343-65-2

OCLC:

503447574