Maple and Mathematica Resources for ME305 - Partial Differential Equations
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Introduction to Maple
Examples to Illustrate Commonly Used MAPLE Commands
Some Useful ODE Solutions Available In MAPLE
Finding Roots Using Maple
Orthogonality
Proof of the Orthogonality Property for Sines
Proof of the Orthogonality Property for Cosines
Proof of Orthogonality of Bessel Functions w.r.t. the Weighting Function r(x) = r.
Separation of Variables
Illustration of Separation of Variables Method - The Two Dimensional Laplace's Equation
Illustration of Separation of Variables Method - The One Dimensional Diffusion Equation
Illustration of Separation of Variables Method - The One Dimensional Wave Equation
Illustration of Separation of Variables Method - The One Dimensional Diffusion Equation in Cylindrical Co-ordinates
Illustration of Separation of Variables Method
Illustration of Separation of Variables Method and solution to One Dimensional Wave Equation in Cartesian Co-ordinates.
Solution of the wave equation for the vibration membrane problem.
Similarity Methods
Illustration of the Boltzmann Similarity Method
Boltzmann Similarity Method
Boltzmann Similarity Method
Laplace Transfer Methods
Illustration of Laplace Transform Methods
Illustration of Laplace Transform Methods
Assignment Solutions
Solution to Assignment #1
Solution to Assignment #2
Solution to Assignment #3
3D and Contour Plots of the solutions to Questions 1 and 2 of, Problem Set #4.
Assignment # 1 - Transient Conduction in a Half Space with Convection Cooling
Assignment # 2 - Separation of Variables Method
Assignment # 3 - Roots of Characteristic Equations and Fourier Coefficients
Assignment # 3
Problem Set #1, Question #2
Problem Set #1, Question #4
Problem Set #2, Question #1
Problem Set #3, Question #1
Problem Set #4, Question #3 - Plot of Dimensionless Solution
Problem Set #4, Question #4 - Plot of Dimensionless Solution