Partial Differential Equations: YouTube Workbook with Dr Chris Tisdell
Open, multimodal PDE learning with active workbook spaces.
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- • Learn standard PDE solution methods through guided, step-by-step examples
- • Use the companion YouTube lessons to follow each chapter’s subsection
- • Practice actively with workbook “active learning spaces” and annotations
- • Compare approaches across transport, wave, heat, Laplace, and Fourier methods
- • Build intuition for Green’s functions, harmonic functions, and maximum principles
الوصف
This workbook teaches core ideas and solution techniques for first- and second-order partial differential equations through worked examples, active learning prompts, and companion YouTube video lessons by Dr Chris Tisdell. It begins with the transport equation and builds step-by-step methods such as directional derivatives, changes of variables, and the method of characteristics. The book then develops approaches for the wave and heat equations, including factoring and Duhamel’s principle, and it extends to classifying second-order PDEs. Later chapters introduce integral transform methods—Laplace transforms and Fourier transforms—before concluding with Green’s functions, harmonic functions, and maximum principles. Designed for open access, the text repeatedly includes “active learning spaces” where you fill in solutions and annotate alongside the videos.
فهرس المحتويات
How to use this book What makes this book dierent? Acknowledgement Chapter 1 The Transport Equation 1.1 Introduction - Where are we going? 1.2 Solution Method to Transport Equation via Directional Derivatives 1.3 Derivation of the Most Basic Transport Equation 1.4 Transport Equation Derivation Chapter 2 Solve PDE via a Change of Variables 2.1 Change of Co-ordinates and PDE 2.2 Non-constant Co-efficients Chapter 3 PDE and the method of characteristics 3.1 Introduction 3.2 The semi-linear Cauchy problem 3.3 Quasi-linear Case Chapter 4 Solving the Wave Equation 4.1 Introduction 4.2 A Factoring Approach 4.3 Initial Value Problem: Wave Equation 4.4 Inhomogenous Case 4.5 Duhamel’s Principle 4.6 Derivation of Wave Equation 4.7 Second-Order PDEs: Classication and Solution Method 4.8 Independent Learning - Reflection Method: Initial/Boundary Value Problem 4.9 Independent Learning - Reflection method: Nonhomogenous PDE 4.10 PDE with Purely Second-Order Derivatives and Classication 4.11 Classifying Second-Order PDE with First-Order Derivatives Chapter 5 The Heat Equation 5.1 Introduction 5.2 Diffusion on the Whole Line 5.3 The Modified Problem 5.4 Independent Learning - Heat Equation: Inhomogenous Case 5.5 Independent Learning - Duhamel’s Principle 5.6 Solving Heat Equation on Half Line 5.7 Derivation of Heat Equation in 1-Dimension 5.8 Similarity Solutions to PDE Chapter 6 Laplace Transforms 6.1 Introduction 6.2 Inverse Laplace Transforms 6.3 Using Tables to Calculate Transforms 6.4 First Shifting Theorem 6.5 Introduction to Heaviside Functions 6.6 Second Shifting Theorem: Laplace Transforms 6.7 Transform of Derivatives 6.8 Solving IVPs with Laplace Transforms 6.9 Applications of Laplace Transforms to PDE Chapter 7 Applications of Fourier Transforms to PDE 7.1 Introduction to Fourier Transforms 7.2 First Shifting Theorem of Fourier Transforms 7.3 Second Shifting Theorem of Fourier Transforms 7.4 Convolution Theorem of Fourier Transforms Chapter 8 Introduction to Green’s Functions 8.1 Introduction 8.2 Green’s First Identity 8.3 Uniqueness for the Dirichlet Problem 8.4 Existence for the Dirichlet Problem Chapter 9 Harmonic Functions and Maximum Principles 9.1 Introduction 9.2 First Mean Value Theorem for Harmonic Functions 9.3 Maximum Principle for Subharmonic Functions 9.4 Independent Learning - More Properties of Harmonic Functions Bibliography
معاينة
Hi and thanks so much for choosing to download this book. You’re now part of a learning
community of over 10 million readers around the world who engage with my learning resources
– welcome!
This workbook is designed to be used in conjunction with the my free online video tutorials.
The subsections in each chapter have their own dedicated video tutorial.
View each online video via the hyperlinks located at the start of each learning module, with
workbook and paper or tablet at the ready. Or click on the Partial differential equations playlist
where all the videos for the workbook are located in chronological order:
Partial Differential Equations
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