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26. PDEs and waves
- Class notes • 5 pages • 2019
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Water Waves in 2D. Using Dirichlet Boundary conditions in an example to solve the wave equation for a rectangular region. Procedure how to solve Wave equation in this way using Fourier series.
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22. PDEs and waves
- Class notes • 5 pages • 2019
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Matlab Script graphing Wave Equation solution of separation of variables with Fourier series. Heat Flow equation example solving and graphing with Matlab. PDEs and waves, shows part way through deriving the PDE for the wave equation.
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19. Representing periodic functions by Fourier series
- Class notes • 5 pages • 2019
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Separation of variables to solve the Heat equation and represent as a summation solution. Example of copper bar and solving for its solution to transfer of heat over time. Includes matlab code of graphing of solution. Different Boundary conditions: Dirichlet and Neumann boundary conditions, motivation for Fourier series.
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10. Second and higher order ODEs
- Class notes • 5 pages • 2019
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Proof for multiple roots for solutions. Theory for the general solution for nonhomogeneous linear ODEs and an example. Method of undetermined guessing and an example which is plotted with matlab code. An example of an IVP for nonhomogeneous solutions.
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probability notes
- Class notes • 58 pages • 2018
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the above notes cover all the topic of probability with every solved question in details.the course will be helpful in studying mathematics 4 in engineering.
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Exam (elaborations) TEST BANK FOR Advanced Engineering Mathematics [Volume 1] By Herbert Kreyszig and Erwin Kreyszig (Student Solutions Manual and Study Guide)
- Exam (elaborations) • 257 pages • 2021
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Exam (elaborations) TEST BANK FOR Advanced Engineering Mathematics [Volume 1] By Herbert Kreyszig and Erwin Kreyszig (Student Solutions Manual and Study Guide) 
P A R T A 
Ordinary 
Differential 
Equations (ODEs) 
Chap. 1 First-Order ODEs 
Sec. 1.1 Basic Concepts. Modeling 
To get a good start into this chapter and this section, quickly review your basic calculus. Take a look at 
the front matter of the textbook and see a review of the main differentiation and integration formulas. Also, 
Appen...
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2. First order ordinary differential equations
- Class notes • 3 pages • 2019
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Example of solving the time it takes for water to flow out of a tank and its Matlab code. Solving Exact ODEs with example.
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4. Second and higher order ODEs
- Class notes • 4 pages • 2019
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Solving Linear ODEs: definition of linear/nonlinear and homogeneous/nonhomogeneous. General solution to first order ODE with integrating factor. Example of a first order linear IVP. Explanation to why the General solution formula works. Example of Hormone levels and their rates of changes. Using Matlab to solve ODEs.
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34. More partial differential equations
- Class notes • 6 pages • 2019
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Further Fourier Series looking at a Maclaurin Series, inner product, weight function, orthogonal and norm. These have definitions equations and examples. Define an orthogonal set and examples of these. Legrendre Polynomials, Bessel functions and generalised fourier series. Definition for completeness of functions. Complex Fourier series and example.
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31. More partial differential equations
- Class notes • 4 pages • 2019
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Gamma Function and solving the integral. Gamma Function for half integers and Matlab Script. Bessel Function series and plot with different values for nu. Bessel functions, special cases and the Bessel equation General Solution. Indicial Equation and its derivation. Frobenius Theorem and the different cases for different solutions.
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