1 Numerical Analysis. - 1. 1 The Nature of Numerical Analysis. - 1. 2 Polynomial Interpolation. - 1. 3 Numerical Integration and Differentiation. - 1. 4 Solution of Equations. - 1. 5 Inverse Functions. - 1. 6 Implicit Functions. - 1. 7 Numerical Summation of Infinite Series. - 2 Ordinary Differential Equations of First Order. - 2. 1 The Nature of Differential Equations. - 2. 2 Separable Equations. - 2. 3 Linear First-Order Equations. - 2. 4 Exact Equations. - 2. 5 Applications to Some Second-Order Equations. - 2. 6 The Initial Value Problem. - 2. 7 Numerical Methods for the Initial Value Problem. - 3 Ordinary Differential Equations of Higher Order. - 3. 1 Examples from Engineering and Physics. - 3. 2 Linear Second-Order Equations Structure of Solutions. - 3. 3 Linear Second-Order Equations with Constant Coefficients. - 3. 4 Linear Second-Order Equations with Analytic Coefficients. - 3. 5 Numerical Methods for Second-Order Equations. - 3. 6 Linear Equations of Order n > 2. - 4 The Laplace Transform. - 4. 1 The Nature of the Laplace Transform. - 4. 2 The Laplace Transforms of Some Elementary Functions. - 4. 3 Operational Rules for the Laplace Transform. - 4. 4 Applications to Differential Equations. - 4. 5 Applications to Systems of Differential Equations. - 5 Linear Algebra. - 5. 1 Systems of Linear Equations. - 5. 2 The Gauss Elimination Method. - 5. 3 Vector Spaces. - 5. 4 Matrices and Matrix Algebra. - 5. 5 The Fundamental Theorem of Linear Algebra. - 5. 6 Determinants and Cramer's Rule. - 5. 7 Eigenvalues and Eigenvectors. - 6 Vector Analysis. - 6. 1 Vector Algebra. - 6. 2 Vector Calculus of Curves in Space. - 6. 3 Vector Calculus of Surfaces in Space. - 6. 4 Calculus of Scalar and Vector Fields. - 6. 5 Integral Theorems of Vector Calculus. - 6. 6 X-Ray Diffraction and Crystal Structure. - 7 Partial Differential Equations of MathematicalPhysics. - 7. 1 Vibrating Strings: D'Alembert's Wave Equation. - 7. 2 Heat Diffusion in Rods: Fourier's Heat Equation. - 7. 3 Heat Diffusion in Plates. - 7. 4 Steady-State Heat Diffusion in Plates: The Laplace Equation. - 7. 5 Vibrations of Drums. - 7. 6 Heat Diffusion in Solids. - 7. 7 Steady-State Heat Diffusion in Solids. - 8 Fourier Analysis and Sturm-Liouville Theory. - 1 Fourier Series. - II Fourier Integrals. - III Sturm-Liouville Theory. - 9 Boundary Value Problems of Mathematical Physics. - 9. 1 Heat Diffusion in One Dimension. - 9. 2 Vibration of Strings and Traveling Waves. - 9. 3 Steady-State Diffusion of Heat in Plates. - 9. 4 Transient Diffusion of Heat in Plates. - 9. 5 Vibrations of Drums. - 9. 6 Steady-State Diffusion of Heat in Solids. - 9. 7 The Laplace Transform Method. - Appendix: Answers and Hints to Selected Exercises. - References. Language: English