Nguồn ngoài
Introduction to Partial Differential Equations
This is a self-published text book with excellent coverage and solid mathematics and theory to support applications. Each chapter is rich in applications, described in good detail and fine exercises which involve solution techniques, but many applications and variations. There are many applications of second order differential equations with complete and thorough discussion of damping, eigenvalues, and characteristic equation.
- Tác giả
- Russell Herman
- Nhà xuất bản
- University of North Carolina Wilmington
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC-SA
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 104 mục
- 01: First Order Partial Differential Equations
- 1.01: Introduction
- 1.02: Linear Constant Coefficient Equations
- 1.03: Quasilinear Equations- The Method of Characteristics
- 1.04: Applications
- 1.05: Nonlinear Advection Equations
- 1.06: General First Order PDEs
- 1.08: Problems
- 02: Second Order Partial Differential Equations
- 2.01: Introduction
- 2.02: Derivation of Generic 1D Equations
- 2.03: Boundary Value Problems
- 2.04: Separation of Variables
- 2.05: Laplaces Equation in 2D
- 2.06: Classification of Second Order PDEs
- 2.07: dAlemberts Solution of the Wave Equation
- 2.08: Problems
- 03: Trigonometric Fourier Series
- 3.01: Introduction to Fourier Series
- 3.02: Fourier Trigonometric Series
- 3.03: Fourier Series Over Other Intervals
- 3.04: Sine and Cosine Series
- 3.05: Solution of the Heat Equation
- 3.06: Finite Length Strings
- 3.07: The Gibbs Phenomenon
- 3.08: Problems
- 04: Sturm-Liouville Boundary Value Problems
- 4.01: Sturm-Liouville Operators
- 4.02: Properties of Sturm-Liouville Eigenvalue Problems
- 4.03: The Eigenfunction Expansion Method
- 4.04: Appendix- The Fredholm Alternative Theorem
- 4.05: Problems
- 05: Non-sinusoidal Harmonics and Special Functions
- 5.01: Function Spaces
- 5.02: Classical Orthogonal Polynomials
- 5.03: Fourier-Legendre Series
- 5.04: Gamma Function
- 5.05: Fourier-Bessel Series
- 5.06: Appendix- The Least Squares Approximation
- 5.07: Problems
- 06: Problems in Higher Dimensions
- 6.01: Vibrations of Rectangular Membranes
- 6.02: Vibrations of a Kettle Drum
- 6.03: Laplaces Equation in 2D
- 6.04: Three Dimensional Cake Baking
- 6.05: Laplaces Equation and Spherical Symmetry
- 6.06: Spherically Symmetric Vibrations
- 6.07: Baking a Spherical Turkey
- 6.08: Schrodinger Equation in Spherical Coordinates
- 6.09: Curvilinear Coordinates
- 6.10: Problems
- 07: Green's Functions
- 7.00: Prelude to Green's Functions and Nonhomogeneous Problems
- 7.01: Initial Value Greens Functions
- 7.02: Boundary Value Greens Functions
- 7.03: The Nonhomogeneous Heat Equation
- 7.04: Greens Functions for 1D Partial Differential Equations
- 7.05: Greens Functions for the 2D Poisson Equation
- 7.06: Method of Eigenfunction Expansions
- 7.07: Greens Function Solution of Nonhomogeneous Heat Equation
- 7.08: Summary
- 7.09: Problems
- 08: Complex Representations of Functions
- 8.01: Complex Representations of Waves
- 8.02: Complex Numbers
- 8.03: Complex Valued Functions
- 8.04: Complex Differentiation
- 8.05: Complex Integration
- 8.06: Laplaces Equation in 2D Revisited
- 8.07: Problems
- 09: Transform Techniques in Physics
- 9.01: Introduction
- 9.02: Complex Exponential Fourier Series
- 9.03: Exponential Fourier Transform
- 9.04: The Dirac Delta Function
- 9.05: Properties of the Fourier Transform
- 9.06: The Convolution Operation
- 9.07: The Laplace Transform
- 9.08: Applications of Laplace Transforms
- 9.09: The Convolution Theorem
- 9.10: The Inverse Laplace Transform
- 9.11: Transforms and Partial Differential Equations
- 9.12: Problems
- 10: Numerical Solutions of PDEs
- 10.01: Ordinary Differential Equations
- 10.02: The Heat Equation
- 10.03: Truncation Error
- 10.04: Stability
- 11: A - Calculus Review - What Do I Need to Know From Calculus?
- 11.01: What Do I Need To Know From Calculus
- 11.02: Hyperbolic Functions
- 11.03: Derivatives
- 11.04: Integrals
- 11.05: Geometric Series
- 11.06: Power Series
- 11.07: The Binomial Expansion
- 11.08: Problems
- 11.9: Problems
- 12: B - Ordinary Differential Equations Review
- 12.01: First Order Differential Equations
- 12.02: Second Order Linear Differential Equations
- 12.03: Forced Systems
- 12.04: Cauchy-Euler Equations
- 12.05: Problems