# Certificate in Mathematical Methods (CM2)

The Certificate in Mathematical Methods (CM2) is an intensive program covering a variety of mathematical methods, with special focus on those which are applicable to real-world problems. Through the recorded lectures delegates will learn topics that are normally covered in the first two years of a university mathematics degree.

## The CM2 course syllabus includes the following topics:

• Complex Numbers
• Vector algebra
• Matrix algebra
• Ordinary differential equations
• Infinite Series
• Functions
• Calculus for several variables
• Vector calculus

### Complex Variables

• Basic Properties
• Elementary Functions
• Complex Differentiation
• Complex Integration
• Infinite Series
• The Theory of Residues
• Zeros of polynomials
• Conformal Mapping

### Transform Methods

• Laplace and Fourier transforms
• Applications

### Linear Algebra

• Linear equations
• Vector spaces
• Linear mappings
• Eigenvalues and eigenvectors
• Gram-Schmidt process

### Differential Equations

• Fourier Series
• Variation of parameters
• Linear ordinary differential equations
• Non-linear ordinary differential equations

### Numerical Analysis II – Finite Difference Methods

• Parabolic equations
• Hyperbolic equations
• Elliptic equations

### Introduction to Probability

• Introduction
• Random Variables
• Continuous Random Variables
• Multivariate Random Variables

### Mathematical Methods

• Elliptic Equations and related
• methods
• Mathematics of Hyperbolic
• Equations

### Analysis

• Number systems
• Continuity
• Sequences
• Differentiation and Integration
• Uniform Convergence
• Power series

### Numerical Analysis I

• Errors
• Roots of equations
• Interpolation
• Numerical Linear Algebra
• Integration
• Differential Equations

• Asymptotic expansions of integrals
• Non-linear ordinary differential
• equations
• Integral Equations & Boundary
• Value Problems

### Group Theory

• Subgroups
• Finite groups and Group tables
• The groups
• Lagrange’s theorem
• Permutation groups
• Isomorphism
• Isometry and Matrix Groups
• The Dihedral group
• Cyclic groups
• Direct Products and Finitely Generated Abelian Groups
• Coset groups