Amath 250 notes

Please note the term associated with each file, and use at your own discretion! Multiparticle quantum mechanics. I have included them on this page for the benefit of the public. Applications include an introduction to Hamilton's Principle and optimal control. Finite element methods for elliptic and parabolic equations: weak forms; existence of solutions; optimal convergence; higher-order methods. In addition, emphasis will be placed on computational analysis of differential equations and on applications in science and engineering. Curved space-time and the Einstein field equations. The solution of problems using variational methods — the Euler-Lagrange equations. Elements of compressible flow. Basic equations of elasticity. Topics covered include: acoustics, including pitch and harmonics, basic Fourier analysis, the mathematics behind the differing pitch and timbre of string, wind and percussion instruments, scales and temperaments, digital music, musical synthesis.

Note that not every course that I have taken have associated summary notes. Wavelets and multiresolution analysis.

Stable and unstable manifolds. I created all documents in MS Word format. The Friedmann-Robertson-Walker cosmological models. Discrete and continuous spectra. You may look at it and decide if you would like to use it for your own studying purposes. Curved space-time and the Einstein field equations. Finite volume methods for hyperbolic conservation laws: linear and nonlinear hyperbolic systems; stability; numerical conservation. Applications are used as motivation. You may look at it and decide if you would like to use it for your own studying purposes. Basic discretization methods on structured and unstructured grids. Scalar first order differential equations, second-order differential equations, systems of differential equations. The Fourier Transform and the diffusion equation. They also outline all concepts that students must be familiar with. Partial differential equations: finite difference methods for elliptic, hyperbolic and parabolic equations; stability and convergence. Additional topics as time permits.

Laplace transforms applied to linear vector differential equations, transfer functions, the convolution theorem. Basic equations of elasticity.

amath 250 introduction to differential equations by j wainwright and j west

In addition, emphasis will be placed on computational analysis of differential equations and on applications in science and engineering. Ordinary differential equations: multistep and Runge-Kutta methods; stability and convergence; systems and stiffness; boundary value problems.

Curved space-time and the Einstein field equations.

amath 350

You may look at it and decide if you would like to use it for your own studying purposes. First order non-linear partial differential equations and the method of characteristics. Introduction to wave motion and geophysical fluid mechanics. I created all documents in MS Word format.

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The Fourier Transform and the diffusion equation.

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