# Partial Differential Equations by Christopher C. Tisdell PDF

Partial differential equations form tools for modelling, predicting and understanding our world. Scientists and engineers use them in the analysis of advanced problems. In this eBook, award-winning educator Dr Chris Tisdell demystifies these advanced equations. Highlights of this eBook include an integration of the lessons with YouTube videos; and the design of active learning spaces. By engaging with this eBook, its examples and Chris’s YouTube videos, you’ll be well-placed to better understand partial differential equations and their solutions techniques. Download now!

## Content

• How to use this book
• What makes this book different?
• Acknowledgement
1. The Transport Equation
1. Introduction – Where are we going?
2. Solution Method to Transport Equation via Directional Derivatives
3. Derivation of the Most Basic Transport Equation
4. Transport Equation Derivation
2. Solve PDE via a Change of Variables
1. Change of Co-ordinates and PDE
2. Non-constant Co-efficients
3. PDE and the method of characteristics
1. Introduction
2. The semi-linear Cauchy problem
3. Quasi-linear Case
4. Solving the Wave Equation
1. Introduction
2. A Factoring Approach
3. Initial Value Problem: Wave Equation
4. Inhomogenous Case
5. Duhamel’s Principle
6. Derivation of Wave Equation
7. Second-Order PDEs: Classication and Solution Method
8. Independent Learning – Reflection Method: Initial/Boundary Value Problem
9. Independent Learning – Reflection method: Nonhomogenous PDE
10. PDE with Purely Second-Order Derivatives and Classication
11. Classifying Second-Order PDE with First-Order Derivatives
5. The Heat Equation
1. Introduction
2. Diffusion on the Whole Line
3. The Modified Problem
4. Independent Learning – Heat Equation: Inhomogenous Case
5. Independent Learning – Duhamel’s Principle
6. Solving Heat Equation on Half Line
7. Derivation of Heat Equation in 1-Dimension
8. Similarity Solutions to PDE
6. Laplace Transforms
1. Introduction
2. Inverse Laplace Transforms
3. Using Tables to Calculate Transforms
4. First Shifting Theorem
5. Introduction to Heaviside Functions
6. Second Shifting Theorem: Laplace Transforms
7. Transform of Derivatives
8. Solving IVPs with Laplace Transforms
9. Applications of Laplace Transforms to PDE
7. Applications of Fourier Transforms to PDE
1. Introduction to Fourier Transforms
2. First Shifting Theorem of Fourier Transforms
3. Second Shifting Theorem of Fourier Transforms
4. Convolution Theorem of Fourier Transforms
8. Introduction to Green’s Functions
1. Introduction
2. Green’s First Identity
3. Uniqueness for the Dirichlet Problem
4. Existence for the Dirichlet Problem
9. Harmonic Functions and Maximum Principles
1. Introduction
2. First Mean Value Theorem for Harmonic Functions
3. Maximum Principle for Subharmonic Functions
4. Independent Learning – More Properties of Harmonic Functions
• Bibliography