# PSI Lectures/All Math Topics

## Complex Analysis

• 2010 Maths and Mathematica (Introduction to Complex Analysis/Computer Skills) Pedro Vieira
• 2011 FRONT Complex Analysis - Tibra Ali
• 2013 FRONT Complex Analysis - Tibra Ali
• 2014 FRONT Complex Analysis - Tibra Ali
• 2015 FRONT Complex Analysis - Tibra Ali
• 2016 FRONT Complex Analysis - Tibra Ali

## Differential Equations

• 2011 FRONT Differential Equations - Sarah Croke
• ? 2012 FRONT Special Functions and Differential Equations - Dan Wohns

## Differential Geometry

• 2014 FRONT Differential Geometry – Denis Dalidovich

## Green's Functions

• 2011 FRONT Integral Transforms and Green's Functions - David Kubiznak
• 2012 FRONT Integral transforms Green's Functions - David Kubiznak
• 2013 FRONT Integral Transforms Green's Function - David Kubiznak
• 2014 FRONT Green’s Functions – Denis Dalidovich
• 2015 FRONT Greens Function - Denis Dalidovich

## Lie Groups and Lie Algebras + Algebra

### 2014 - Gang Xu - Lie Groups and Lie Algebras

• Lecture 1 - Introduction: motivation, definition, examples, properties.
• Lecture 2 - Structure of a group: Representation of a group, structure constant, Poincare group
• Lecture 3 - Adjoint Representation, Highest weight method to construct representations of su(2)
• Lecture 4 - finding a su(2) subalgebra in a general simple Lie algebra, the root diagram of rank-2 Lie algebra, Dynkin diagram

## Special Functions and Distributions

### 2011 FRONT Special Functions and Distributions - Dan Wohns

• Lecture 1 - Dirac delta; Test functions; Distributions and their derivatives.
• Lecture 2 - Orthogonal polynomials; Recurrence relations; Weights.
• Lecture 3 - Generalized Rodrigues' formulae; Classification of orthogonal polynomials; Sturm-Liouville theory.
• Lecture 4 - Gamma; Zeta; Hypergeometric functions

### 2012 FRONT Special Functions and Differential Equations - Dan Wohns

• Lecture 1 - Distributions: test functions, Dirac delta function, Derivatives of distributions, Multiplication of distributions by functions
• Lecture 2 - Solution Methods: Reduction of order, Variation of parameters, Power series method, WKB approximation
• Lecture 3 - Orthogonal Functions - Sturm-Liouville theory, Parseval's theorem, Orthogonal polynomials
• Lecture 4 - Special Functions and Complex Variables: Gamma function, Stirling's approxximation, Saddle point method, Zeta function

### 2013 FRONT Distributions Special Functions - Dan Wohns

• Lecture 1 - Distribuitions, Test functions, Derivatives of distributions, Multiplication of distributions with functions
• Lecture 2 - Composition of distributions with functions, Orthogonal functions, Sturm-Liouville theory, Parseval's Theorem, Orthogonal polynomials
• Lecture 3 - Orthogonal polynomials, gamma function, Zeta function, Hypergeometric functions
• Lecture 4 - Asymptotic Series, Stirling's approximation, Saddle point method

### 2014 FRONT Distributions and Special Functions – Dan Wohns

• Lecture 1: Distributions, Test functions, Derivatives of distributions
• Lecture 2: Multiplication of distributions with functions, Composition of distributions with functions, Functional derivatives, Gamma, Zeta
• Lecture 3: Orthogonal functions, Sturm-Liouville theory, Parseval's theorem, Orthogonal polynomials
• Lecture 4: Asymptotic series, Stirling's approximation, Saddle-point method

### 2018 FRONT Math for QFT - Daniel Wohns

(distributions + some QFT stuff)

### 2019 FRONT Math for QFT - Dan Wohns

(distribution + some QFT stuff)

## Variational Calculus and Gaussian Integrals

• 2011 FRONT Evaluation of Integrals and Calculous of Variations -Denis Dalidovich
• 2012 FRONT Calculus of Variation and Gaussian Integrals - Lilia Anguelova
• 2013 FRONT Variational Calculus Gaussian Integrals - Denis Dalidovich

## Mathematica (Wolfram)

• 2010 FRONT Maths and Mathematica - Pedro Vieira
• 2011 FRONT Mathematica - Pedro Vieira
• 2012 FRONT Mathematica - Pedro Vieira
• 2013 FRONT Mathematica and Computational Methods in Physics - Erik Schnetter
• 2015 FRONT Mathematica Introduction - Pedro Vieira
• 2016 FRONT Mathematica - Erik Schnetter
• 2017 FRONT Mathematica - Erik Schnetter
• 2018 FRONT Introduction to Mathematica - Gang Xu (originally called "Numerical Methods")