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.