# PY/MA 370 Mathematical Methods for the Physical Sciences I

### Videos

Introduction to Math Methods. Syllabus

**Curves and line integrals review**

Review of curves (Mon Jan 25, 2021)

Review of line integrals, part 1 (Th Jan 28, 2021)

Review of line integrals, part 2 (Mon Jan 25, 2021)

**Surface integrals**

Surface integrals, part 1 (Th Jan 28, 2021)

Surface integrals, part 2 (Fri Jan 29, 2021)

**Flux integrals**

Flux integrals, part 1 (Fri Jan 29, 2021)

Flux integrals, part 2 (Fri Jan 29, 2021)

Flux integrals, part 3 (Mon Feb 1, 2021)

**Stokes' Theorem**

Stokes' Theorem, part 1 (Th Feb 4, 2021)

Stokes' Theorem, part 2 (Th Feb 4, 2021)

**Divergence Theorem**

Divergence Theorem, part 1 (Mon Feb 1, 2021)

Divergence Theorem, part 2 (Mon Feb 1, 2021)

Instructions for Assignment 1 (Spring 2019)

**Vector fields in Cylindrical and Spherical coordinates**

Vector fields in cylindrical coordinates, intro (Fri Feb 5, 2021)

Cylindrical vector fields, examples, Spherical vector fields (Mon Feb 8, 2021)

Divergence Theorem for cylindrical and spherical vector fields (Th Feb 11, 2021)

Stokes Theorem for cylindrical and spherical vector fields (Fri Feb 12, 2021)

Review for Exam 1 (Mon Feb 15, 2021)

**Complex functions, their derivatives and integrals**

Complex numbers, complex functions, analytic functions (Fri Feb 19, 2021)

Integrals of complex functions (Mon Feb 22, 2021)

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

Laurent series, intro (Th Feb 25, 2021)

Laurent series, types of singularities, residues (Fri Feb 26, 2021)

The Residue Theorem, examples (Mon Mar 1, 2021)

Assignment 2 questions, more examples (Th Mar 4, 2021)

More examples and evaluating real integrals using the Residue Theorem (Fri Mar 5, 2021)

Review for Exam 2 (Mon Mar 8, 2021)

**Fourier Series**

Introduction to Fourier series (Fri Mar 12, 2021)

Even and odd functions (Fri Mar 12, 2021)

Boxcar function (Fri Mar 12, 2021)

Using Fourier series to find series sums (Mon Mar 15, 2021)

Trigonometric formulas

Example 3 (Mon Mar 15, 2021)

Example 2 (Mon Mar 15 and Th Mar 18, 2021)

Complex Fourier series and Parseval's Theorem (Th Mar 18, 2021)

Example with Parseval's Theorem (Th Mar 18, 2021)

Sawtooth example (Th Mar 18, 2021)

**Fourier Transform**

Introduction to Fourier transform (Fri Mar 19, 2021)

Inverse Fourier transform, some applications (Fri Mar 19, 2021)

Box and sinc functions (Fri Mar 19, 2021)

Delta function, constant function, Gaussian (Mon Mar 22, 2021)

Symmetries and example 1 (Mon Mar 22, 2021)

Examples 2 and 3 (Mon Mar 22 and Th Mar 25, 2021)

Relating Fourier series with Fourier transform (Th Mar 25, 2021)

Applications of Fourier transform in MRI (Th Mar 25, 2021)

Review for Exam 3 (Mon Mar 29, 2021)

**Series solutions**

Introduction to Series Solutions (Fri Mar 26, 2021)

Convergence of the solution, steps of the process (Fri Mar 26, 2021)

Example 1 (Fri April 2, 2021)

Example 2 (Mon April 5, 2021)

**Group Theory**

Introduction to groups via symmetry groups of molecules (Th April 8, 2021)

Group axioms, examples of groups, water molecule (Th April 8, 2021)

Group axioms, example 1 (Th April 8 and Fri April 9, 2021)

Group axioms, example 2 (Fri April 9, 2021)

Multiplication (Cayley) tables (Mon April 12, 2021)

Isomorphisms of groups (Mon April 12, 2021)

Groups with one to four elements (Mon April 12, 2021)

Cyclic groups, product of cyclic groups (Th April 15, 2021)

Product of cyclic groups, part 2 (Th April 15, 2021)

Determining isomorphism classes of cyclic groups - practice problems (Fri April 16, 2021)

Dihedral groups (Fri April 16, 2021)

Group presentations and Cayley tables - practice problems (Mon April 19, 2021)

Isomorphic groups - practice problems. Permutation groups (Mon April 19, 2021)

**Symmetry groups of molecules**

Symmetry groups of molecules (Th April 22, 2021)

First examples of symmetry groups (Th April 22, 2021)

Further examples of symmetry groups (Fri April 23, 2021)

Linear molecules (Fri April 23, 2021)

Review for Exam 4, series (Mon April 26, 2021)

Review for Exam 4, groups (Th April 29, 2021)

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