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Physics 50: Math Methods (Spring 2014, UC Irvine). Instructor: Professor Michael Dennin. Mathematica and its applications to linear algebra, differential equations, and complex functions.
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Description
Fourier series and Fourier transforms. Other topics in integral transforms. Topics covered include: series representations for functions, complex numbers, matrices, vectors, tensors, abstract vector spaces, Fourier series and Fourier transformations, differential equations, derivatives and integrals, vector calculus, and partial differential equations.
Course content
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- Lecture 1.1 – Introduction, Part 1 Unlimited
- Lecture 1.2 – Introduction, Part 2 Unlimited
- Lecture 1.3 – Introduction, Part 3 Unlimited
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- Lecture 2.1 – Series Representations Functions Unlimited
- Lecture 2.2 – Solving Differential Equations Unlimited
- Lecture 2.3 – Complex Numbers Unlimited
- Lecture 2.4 – Phase Shift Linear System Unlimited
- Lecture 3.1 – Matrices Unlimited
- Lecture 3.2 – Mathematica Unlimited
- Lecture 3.3 – Applications Unlimited
- Lecture 5.1 – Central Question Unlimited
- Lecture 5.2 – Tensors Unlimited
- Lecture 5.3 – Examples of Tensors Unlimited
- Lecture 7.1 – Taylor Series, Overview of Vector Spaces Unlimited
- Lecture 7.2 – Linear Independence Not Equal to Orthogonal Unlimited
- Lecture 7.3 – Scalar Product Unlimited
- Lecture 9.1 – Fourier Series/ Fourier Transformations Unlimited
- Lecture 9.2 – Hermitian Operator Unlimited
- Lecture 9.3 – Hermitian Differentials Unlimited
- Lecture 11.1 – Differential Equations (DEQs) Unlimited
- Lecture 11.2 – Second-Order Differential Equations Unlimited
- Lecture 11.3 – Two Types of ODE’s Unlimited
- Lecture 13.1 – Derivatives and Integrals Unlimited
- Lecture 13.2 – Change of Variables Unlimited
- Lecture 15.1 – Review: eiφ & Plugging in a Solution Unlimited
- Lecture 15.2 – Series of Examples Unlimited
- Lecture 15.3 – Line Integrals Unlimited
- Lecture 15.4 – How to Compute Integral Given a Function Unlimited
- Lecture 17.1 – Vector Derivatives Unlimited
- Lecture 17.2 – Relation for the Curl Unlimited
- Lecture 17.3 – Electricity and Magnetism Unlimited
- Lecture 17.4 – Curls in Magnetic Field Unlimited
- Lecture 17.5 – Review in Mathematica Unlimited
- Lecture 19.1 – Separation of Variables Problems Unlimited
- Lecture 19.2 – Separation of Variables in Mathematica Unlimited
- Lecture 19.3 – Semi-Infinite Slab Problem Unlimited
- Lecture 19.4 – Final Review: Linear Physics Unlimited
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