Partial Differential Equations YouTube Workbook with Dr Chris Tisdell
Christopher C. Tisdell
Description
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!
About the author
“With more than a million YouTube hits, Dr Chris Tisdell is
the equivalent of a best-selling author or chart-topping musician. And the
unlikely subject of this mass popularity? University mathematics.” [Sydney
Morning Herald, 14/6/2012
http://ow.ly/o7gti].
Chris Tisdell has been inspiring, motivating and engaging
large mathematics classes at UNSW, Sydney for over a decade. His lectures are
performance-like, with emphasis on contextualisation, clarity in presentation
and a strong connection between student and teacher.
He blends the live experience with out-of-class learning,
underpinned by flexibility, sharing and openness. Enabling this has been his
creation, freely sharing and management of future-oriented online learning
resources, known as Open Educational Resources (OER). They are designed to
empower learners by granting them unlimited access to knowledge at a time,
location and pace that suits their needs. This includes: hundreds of YouTube
educational videos of his lectures and tutorials; an etextbook with each
section strategically linked with his online videos; and live interactive
classes streamed over the internet.
His approach has changed the way students learn mathematics,
moving from a traditional closed classroom environment to an open, flexible and
forward-looking learning model.
Indicators of esteem include: a prestigious educational
partnership with Google; an etextbook with over 500,000 unique downloads;
mathematics videos enjoying millions of hits from over 200 countries; a UNSW
Vice-Chancellor’s Award for Teaching Excellence; and 100% student satisfaction
rating in teaching surveys across 15 different courses at UNSW over eight
years.
Chris has been an educational consultant to The Australian Broadcasting
Corporation and has advised the Chief Scientist of Australia on educational
policy.
Subscribe to his YouTube channel for more
http://www.youtube.com/DrChrisTisdell.
Content
- How
to use this book
- What
makes this book different?
- Acknowledgement
- The
Transport Equation
- Introduction
- Where are we going?
- Solution
Method to Transport Equation via Directional Derivatives
- Derivation
of the Most Basic Transport Equation
- Transport
Equation Derivation
- Solve
PDE via a Change of Variables
- Change
of Co-ordinates and PDE
- Non-constant
Co-efficients
- PDE
and the method of characteristics
- Introduction
- The
semi-linear Cauchy problem
- Quasi-linear
Case
- Solving
the Wave Equation
- Introduction
- A
Factoring Approach
- Initial
Value Problem: Wave Equation
- Inhomogenous
Case
- Duhamel’s
Principle
- Derivation
of Wave Equation
- Second-Order
PDEs: Classication and Solution Method
- Independent
Learning - Reflection Method: Initial/Boundary Value Problem
- Independent
Learning - Reflection method: Nonhomogenous PDE
- PDE
with Purely Second-Order Derivatives and Classication
- Classifying
Second-Order PDE with First-Order Derivatives
- The
Heat Equation
- Introduction
- Diffusion
on the Whole Line
- The
Modified Problem
- Independent
Learning - Heat Equation: Inhomogenous Case
- Independent
Learning - Duhamel’s Principle
- Solving
Heat Equation on Half Line
- Derivation
of Heat Equation in 1-Dimension
- Similarity
Solutions to PDE
- Laplace
Transforms
- Introduction
- Inverse
Laplace Transforms
- Using
Tables to Calculate Transforms
- First
Shifting Theorem
- Introduction
to Heaviside Functions
- Second
Shifting Theorem: Laplace Transforms
- Transform
of Derivatives
- Solving
IVPs with Laplace Transforms
- Applications
of Laplace Transforms to PDE
- Applications
of Fourier Transforms to PDE
- Introduction
to Fourier Transforms
- First
Shifting Theorem of Fourier Transforms
- Second
Shifting Theorem of Fourier Transforms
- Convolution
Theorem of Fourier Transforms
- Introduction
to Green’s Functions
- Introduction
- Green’s
First Identity
- Uniqueness
for the Dirichlet Problem
- Existence
for the Dirichlet Problem
- Harmonic
Functions and Maximum Principles
- Introduction
- First
Mean Value Theorem for Harmonic Functions
- Maximum
Principle for Subharmonic Functions
- Independent
Learning - More Properties of Harmonic Functions
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