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September 23, 2023

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Description

Physics 50: Math Methods (Spring 2014, UC Irvine). Instructor: Professor Michael Dennin. Mathematica and its applications to linear algebra, differential equations, and complex functions.

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 Curriculum

    • Lecture 1.1 – Introduction, Part 1 Unlimited
    • Lecture 1.2 – Introduction, Part 2 Unlimited
    • Lecture 1.3 – Introduction, Part 3 Unlimited
    • 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 4.1 – Geometry Unlimited
    • Lecture 4.2 – Components Versus Vector Unlimited
    • Lecture 4.3 – Vector Examples Unlimited
    • Lecture 4.4 – Textbook Examples: Plane Problems Unlimited
    • Lecture 4.5 – Linear Vector Spaces & Linear Transformations Unlimited
    • Lecture 5.1 – Central Question Unlimited
    • Lecture 5.2 – Tensors Unlimited
    • Lecture 5.3 – Examples of Tensors Unlimited
    • Lecture 6.1 – Examples of Tensors (cont.) Unlimited
    • Lecture 6.2 – Change of Basis Unlimited
    • Lecture 6.3 – Diagonalization Unlimited
    • Lecture 6.4 – Finding a New Basis Unlimited
    • Lecture 6.5 – Hermitian Matrix 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 8.1 – Subspace Unlimited
    • Lecture 8.2 – Apples and Oranges Problem, Part 1 Unlimited
    • Lecture 8.3 – Apples and Oranges Problem, Part 2 Unlimited
    • Lecture 8.4 – Apples and Oranges Problem, Part 3 Unlimited
    • Lecture 9.1 – Fourier Series/ Fourier Transformations Unlimited
    • Lecture 9.2 – Hermitian Operator Unlimited
    • Lecture 9.3 – Hermitian Differentials Unlimited
    • Lecture 10.1 – Normalization Unlimited
    • Lecture 10.2 – Assuming and Assumptions & Fourier Series Unlimited
    • Lecture 10.3 – Graphical Plots Unlimited
    • Lecture 10.4 – Assuming and Assumptions Unlimited
    • Lecture 10.5 – Fourier Series 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 12.1 – Superposition Unlimited
    • Lecture 12.2 – Higher Order Differential Equation Unlimited
    • Lecture 12.3 – Real Space and Frequency Space Unlimited
    • Lecture 12.4 – Fourier Transforms Unlimited
    • Lecture 12.5 – Harmonic Oscillator Equation Unlimited
    • Lecture 12.6 – Mathematica Unlimited
    • Lecture 13.1 – Derivatives and Integrals Unlimited
    • Lecture 13.2 – Change of Variables Unlimited
    • Lecture 14.1 – Derivatives in 2D and 3D Unlimited
    • Lecture 14.2 – Integration Unlimited
    • Lecture 14.3 – Line Integral, Path Integral, Contour Integral Unlimited
    • Lecture 14.4 – Surface Integral and Volume Integral Unlimited
    • Lecture 14.5 – Loading Packages in Mathematica 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 16.1 – Two-Dimensional Situations: Green’s Theorem Unlimited
    • Lecture 16.2 – Basic Physics Unlimited
    • Lecture 16.3 – Curl (or Circulation) Unlimited
    • Lecture 16.4 – Index Notation Unlimited
    • Lecture 16.5 – Flux 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 18.1 – Partial Differential Equations Unlimited
    • Lecture 18.2 – Dispersion Relations Unlimited
    • Lecture 18.3 – Fundamental Steps for Separation of Variables 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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