# Mathematical Methods for the Physical Sciences

### Videos

Introduction to Math Methods. Syllabus

**Curves and line integrals review**

Review of curves (Th Jan 20, 2022)

Review of line integrals, part 1

Review of line integrals, part 2 (Th Jan 20, 2022)

**Surface integrals**

Surface integrals, part 1 (Fri Jan 21, 2022)

Surface integrals, part 2 (Fri Jan 21, 2022)

**Flux integrals**

Flux integrals, part 1 (Mon Jan 24, 2022)

Flux integrals, part 2 (Mon Jan 24, 2022)

Flux integrals, part 3 (Th Jan 27, 2022)

**Divergence Theorem**

Divergence Theorem, part 1 (Th Jan 27, 2022)

Divergence Theorem, part 2

**Stokes' Theorem**

Stokes' Theorem, part 1 (Fri Jan 28, 2022)

Stokes' Theorem, part 2 (Fri Jan 28, 2022)

Instructions for Assignment 1 (Spring 2019)

**Vector fields in Cylindrical and Spherical coordinates**

Vector fields in cylindrical coordinates, intro (Mon Jan 31, 2022)

Cylindrical vector fields, examples, Spherical vector fields (Mon Jan 31 and Th Feb 3, 2022)

Divergence Theorem for cylindrical and spherical vector fields (Th Feb 3 and Fri Feb 4, 2022)

Stokes Theorem for cylindrical and spherical vector fields (Fri Feb 4, 2022)

Review for Exam 1 (Mon Feb 7, 2022)

**Complex functions, their derivatives and integrals**

Complex numbers, complex functions, analytic functions (Fri Feb 11, 2022)

Integrals of complex functions (Mon Feb 14, 2022)

**Laurent series, residues and the Residue Theorem**

Laurent series, intro (Th Feb 17, 2022)

Laurent series, types of singularities, residues (Fri Feb 18, 2022)

The Residue Theorem, examples (Mon Feb 21, 2022)

Assignment 2 questions, more examples (Th Feb 24, 2022)

More examples and evaluating real integrals using the Residue Theorem (Fri Feb 25, 2022)

Review for Exam 2 (Mon Feb 28, 2022)

**Fourier Series**

Introduction to Fourier series (Fri Mar 4, 2022)

Even and odd functions (Fri Mar 4, 2022)

Boxcar function (Fri Mar 4, 2022)

Using Fourier series to find series sums (Mon Mar 14, 2022)

Trigonometric formulas (Mon Mar 14, 2022)

Example 3 (Mon Mar 14, 2022)

Example 2 (Mon Mar 14, 2022)

Complex Fourier series and Parseval's Theorem (Th Mar 18, 2022)

Example with Parseval's Theorem (Th Mar 18, 2022)

Sawtooth example (Th Mar 18, 2022)

**Fourier Transform**

Introduction to Fourier transform (Fri Mar 18, 2022)

Inverse Fourier transform, some applications (Fri Mar 18, 2022)

Box and sinc functions (Fri Mar 18, 2022)

Delta function, constant function, Gaussian (Mon Mar 21, 2022)

Symmetries and example 1 (Mon Mar 21, 2022)

Examples 2 and 3 (Mon Mar 21, 2022)

Relating Fourier series with Fourier transform (Th Mar 24, 2022)

Applications of Fourier transform in MRI (Th Mar 24, 2022)

Review for Exam 3 (Mon Mar 28, 2022)

**Series solutions**

Introduction to Series Solutions (Fri Mar 25, 2022)

Convergence of the solution, steps of the process (Fri Mar 25, 2022)

Example 1 (Fri April 1, 2022)

Example 2 (Mon April 4, 2022)

**Group Theory**

Introduction to groups via symmetry groups of molecules (Th April 7, 2022)

Group axioms, examples of groups, water molecule (Th April 7, 2022)

Group axioms, example 1 (Th April 7 and Fri April 8, 2022)

Group axioms, example 2 (Fri April 8, 2022)

Multiplication (Cayley) tables (Mon April 11, 2021)

Isomorphisms of groups (Mon April 11, 2022)

Groups with one to four elements (Mon April 11, 2022)

Cyclic groups, product of cyclic groups (Th April 14, 2022)

Product of cyclic groups, part 2 (Th April 14, 2022)

Determining isomorphism classes of cyclic groups - practice problems (Th April 14, 2022)

Dihedral groups (Fri April 15, 2022)

Group presentations and Cayley tables - practice problems (Fri April 15, 2022)

Isomorphic groups - practice problems. Permutation groups (Mon April 18, 2022)

**Symmetry groups of molecules**

Symmetry groups of molecules (Mon April 18, 2022)

First examples of symmetry groups (Mon April 18, 2022)

Further examples of symmetry groups (Th April 21, 2022)

Linear molecules (Fri April 22, 2022)

Review for Exam 4, series (Mon April 25, 2025)

Review for Exam 4, groups (Th April 28, 2022)

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