# Archived Course Outlines - Applied Math

**2020-21**

### Fall Term Courses - 2020

**AM9561A - Introduction to Numerical Analysis**

**Schedule:**TBA. Instructor: David Jeffrey (djeffrey@uwo.ca). First Class: TBA

**AM9576A - Introduction to Mathematical Biology**

**Schedule:** Online: Tuesdays 9:30am-10:30am local time(EST), Thursdays 9:30am-10:30am local time (EST). Instructor: Lindi Wahl (lwahl@uwo.ca). First Class: Thursday, September 10, 2020.

### Winter Term Courses - 2021

**AM9505B - Partial Differential Equations**

**Schedule:** Online via Zoom: tentatively Monday, Wednesday and Friday 4:30-5:30pm local time (EST) Instructor: Greg Reid (reid@uwo.ca). First Class: Monday, January 11, 2021.

**AM9624B - Introduction to Neural Networks**

**Schedule:** Mondays 11:30am-1:30pm and Thursdays 1:30pm-2:30pm (Synchronous with some content delivered asynchronously). Instructor: Lyle Muller (lmuller2@uwo.ca). First Class: Monday, January 11, 2020**Brief Overview:** This one-semester graduate course will provide you with an introduction to neural networks. You will learn the fundamentals of neural computation and explore how networks of neurons support brain information processing. You will be familiarised with mathematical models, programming and machine learning techniques. You will gain an in-depth knowledge of neural computations through weekly programming assignments.

**SC9502B - Scientific Computing**

**Schedule:** Online synchronously: Tuesdays 9:30am-11:10am and Wednesdays 11:30am-12:20pm local time (EST). Instructor: Mikko Karttunen (mkarttu@uwo.ca). First Class: Tuesday, January 12, 2021, at 12:00noon local time (EST).**Brief Overview:** The goal of this course is both to introduce students to high performance computing methods and numerical solutions to various problems, and in parallel programming paradigms. Students will work on projects using python, MPI and CUDA, and some basic Monte Carlo and stochastic methods.

**2019-20**

### Winter Term Courses - 2020

**AM9505B - Partial Differential Equations**

**Schedule:**Mondays 12:30-1:30pm & 3:00-5:00pm, MC 204, Wednesdays 12:30pm-1:30pm, MC 204. Instructor: Mikko Karttunen (mkarttu@uwo.ca)**Brief Overview:**Emphasis will be placed on understanding solutions and major phenomena for PDE. The course will be a balanced treatment about modeling and problem solving with PDE. Both numerical (e.g. finite differences) and analytical methods will be used to solve problems. There will be some guest lectures in the course from the department, to emphasize the breadth and unity of the subject.

**AM9524B - Nonlinear Dynamics**

**Tentative Schedule:** Thursdays 9am - 12noon, MC 204. Instructor: Pei Yu (pyu@uwo.ca). First class: Thursday, January 9, 2020, 10am.**Brief overview:**This course introduces bifurcation theory and methodologies, and applications to biological and physical systems. Recently developments in this area will also be discussed. Topics mainly focus on Maps and Ordinary Differential Equations, and Delay Differential Equations and Partial Differential Equations will also be discussed. Hopf bifurcation, Bogdanov-Takens bifurcation and homoclinic/heteroclinic bifurcations, which are mostly applied in applications, will be particularly considered. Manifold theory, normal form theory and perturbation theory will be introduced, with examples chosen from real problems and solved using both symbolic and numerical computations.

**AM9570B - Introduction to Mathematical Modelling and Simulation**

**Schedule:** Tuesdays 2:30pm-5:30pm MC 204.

**AM9624B - Introduction to Neural Networks**

**Schedule:** Tuesdays 12noon-1:30pm (lecture), Thursdays 1:00-2:30pm (programming lab), WIRB 1130. Instructors: Lyle Muller and Marieke Mur. First class: Tuesday, January 7, 2020.**Brief overview:**This one-semester graduate course will provide you with an introduction to neural networks. You will learn the fundamentals of neural computation and explore how networks of neurons support brain information processing. You will be familiarised with mathematical models, programming, and machine learning techniques. You will gain an in-depth knowledge of neural computations through weekly programming assignments.

**AM9625B - Introduction to General Relativity**

**Tentative Schedule:** Tuesdays 9:00am-10:30am, Fridays 1:30-3:00pm, MC 204. Instructor: Francesca Vidotto. First class: Tuesday, January 7, 2020.**Brief overview:** Einstein's General Relativity provides our best current knowledge of space and time: these emerge from the symmetries and the dynamics of the gravitational field. This course introduces the basis of the mathematical structure of this theory and discusses its conceptual novelty. Einstein's field equation will be derived and applied to a few physical cases, relevant for black holes and cosmology.

**AM9664B - Molecular Dynamics Simulations**

**Schedule:** Will not be offered this term.

**2018-19**

### Fall Term Courses - 2018

**AM9561A - A Graduate Introduction to Numerical Analysis**

**Schedule:** Mondays 12:30pm-1:30pm, Wednesdays and Fridays 8:30am-9:30am, MC 204.

**Schedule:** Tuesdays 1:30pm-3:30pm, and Thursdays 1:30pm-2:30pm, AHB 1B04.

**SC9601 - Scientific Computing PhD Seminar Course**

**Overview:** This seminar is a required course for the Scientific Computing collaborative program. It consists of seminars on interdisciplinary scientific computing methods given by students, researchers, and Compute-Canada/Sharcnet seminars.

### Winter Term Courses - 2019

**AM9505B - Partial Differential Equations**

**Schedule:** Tuesdays 2:00pm-3:30pm, and Thursdays 2:00-3:30pm, MC 204.**Brief overview:** Emphasis will be placed on understanding solutions and major phenomena for PDE. The course will be a balanced treatment about modeling and problem solving with PDE. Maple will be used to numerically and analytically solve problems. It will also be used to graph solutions to illustrate phenomena encountered during the course. This will be mostly through the use of programs that will be provided. No prior knowledge of Maple will be assumed. There will be some guest lectures in the course from the department, to emphasize the breadth and unity of the subject.

**AM9570B - Introduction to Mathematical Modelling and Simulation**

**Schedule:** Tuesdays 2:30pm-5:30pm, WSC 240.**Brief topics that may be covered:**

- Random Number Generators
- Monte Carlo Integration: Hit/Miss Integration
- Random Walks (RW)
- Solving Laplace's Equation (and other DE's) using RW
- Percolation and modelling of Forest Fires
- Cellular Automata: Lattice Gas, Kauffman Model
- Monte Carlo Simulation: Ising Model
- Damage spreading, Fractals, Chaos
- Molecular Dynamics: Hard Spheres and more
- Other interesting things I like

**AM9620B - Finite Elements**

**Schedule:** Mondays, Wednesdays, and Fridays 1:30pm-2:30pm, MC 204.**Brief topics overview:**

- Introduction and Disclaimers
- Finite elements introduced as bars forming a truss
- Some mathematical aspects
- Towards a systematic method
- The matrix approach
- Two-dimensional heat flow
- Variational form
- The Galerkin approach
- Element computation
- Other topics not in the main text book

**SC9502B - Scientific Computing**

**Schedule:** Mondays 3:00pm-4:30pm, and Thursdays 10:30am-12:00pm, MC 204.**Brief overview:** The goal of this course is both to introduce students to high performance computing methods, and in particular parallel programming paradigms. Students will work on projects using MPI and CUDA, OpenCL, and some basic Monte Carlo and stocastic methods.