Nguồn ngoài
Partial Differential Equations
A partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model. PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, or quantum mechanics.
- Tác giả
- Niels Walet
- Nhà xuất bản
- University of Manchester
- Nguồn
- LibreTexts
- Giấy phép
- CC BY-NC-SA
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 58 mục
- 01: Introduction to Partial Differential Equations
- 1.01: Ordinary Differential Equations
- 1.02: PDE’s
- 02: Classication of Partial Dierential Equations
- 2.0E: 2.E: Classification of Partial Differential Equations (Exercises)
- 2.01: Examples of PDE
- 2.02: Second Order PDE
- 2.03: More than 2D
- 03: Boundary and Initial Conditions
- 3.01: Introduction to Boundary and Initial Conditions
- 3.02: Explicit Boundary Conditions
- 3.03: Implicit Boundary Conditions
- 3.04: More Realistic Examples of Boundary and Initial Conditions
- 04: Fourier Series
- 4.01: Taylor Series
- 4.02: Introduction to Fourier Series
- 4.03: Periodic Functions
- 4.04: Orthogonality and Normalization
- 4.05: When is it a Fourier Series
- 4.06: Fourier series for even and odd functions
- 4.07: Convergence of Fourier series
- 05: Separation of Variables on Rectangular Domains
- 5.01: Cookbook
- 5.02: Parabolic Equation
- 5.03: Hyperbolic Equation
- 5.04: Laplace’s Equation
- Boundary Conditions
- 5.06: Inhomogeneous Equations
- 06: DAlemberts Solution to the Wave Equation
- 6.01: Background to D’Alembert’s Solution
- 6.02: New Variables
- 6.03: Examples
- 07: Polar and Spherical Coordinate Systems
- 7.01: Polar Coordinates
- 7.02: Spherical Coordinates
- 08: Separation of Variables in Polar Coordinates
- 8.01: Example
- 8.02: Three cases for λ
- 8.03: Putting it all together
- 09: Series Solutions of ODEs (Frobenius Method)
- 9.01: Frobenius’ Method
- 9.02: Singular Points
- 9.03: Special Cases
- 10: Bessel Functions and Two-Dimensional Problems
- 10.01: Temperature on a Disk
- 10.02: Bessel’s Equation
- 10.03: Gamma Function
- 10.04: Bessel Functions of General Order
- 10.05: Properties of Bessel functions
- 10.06: Sturm-Liouville theory
- 10.07: Our Initial Problem and Bessel Functions
- 10.08: Fourier-Bessel Series
- 10.09: Back to our Initial Problem
- 11: Separation of Variables in Three Dimensions
- 11.01: Modelling the Eye
- 11.02: Properties of Legendre Polynomials
- 11.03: Fourier-Legendre Series
- 11.04: Modelling the eye–revisited