## Course Content » 2nd Year Modules

Choose a module from the table below:

 MAT211 MAT212 MAT221

###### MAT211 Mathematics 211

20 credits

Pre-requisites: [MAM111 and MAM121 (pre-2009)] OR [MAM151 and MAM152] OR [MAT105]
Sequences.
Infinite series (convergence tests, alternating series, conditional convergence, power series, Taylor & Maclaurin Series).
Vectors & vector-valued functions.
Partial derivative (chain rule, maxima and minima of functions of two variables, Lagrange Multipliers).
Multiple Integrals.
Elementary Linear Algebra
Matrices and Gaussian elimination, determinants.
Vector Spaces (subspaces, linear independence, basis, dimension, Solution of Ax=0 and Ax=b, graphs and networks, linear transformation).
Linear Programming and Game Theory.
Orthogonality (projection and least spaces, Gram-Schmidt, Fast Fourier transform).
Eigenvalues and eigenvectors.
Positive definite matrices (Finite element method).

Main Outcomes

On completing this module students will be able to

Use different convergence tests for series.
Use their knowledge of multi-variable calculus to solve problems in various contexts.
Use their knowledge of vector calculus to solve problems in a variety of contexts.
Use computer software such as MAPLE to solve problems.
Use their knowledge of linear algebra to solve problems in business, sciences and engineering (eg. linear modes in business, science, and engineering).
Select appropriate methods to solve problems.
Carry out proofs of mathematical statements.
Use computer software in linear algebra to solve real world problems.
Relevant People ###### MAT212 Mathematics 212

20 credits

Pre-requisites: [MAM111 and MAM121 (pre-2009)] OR [MAM151 and MAM152] OR [MAT105]

Co-requisite: MAT211

First-Order equations.
Homogeneous linear differential equations with constant coefficients.
Nonhomogeneous linear differential equations.
Numercial solutions of nonlinear algebraic equations.
Newton's methods for systems of nonlinear equations.
Polynomial Interpolation.
Numerical differentiations and numerical integration.
Iterative methods for linear system.

Main Outcomes

On completing this module students will be able to

Formulate differential equations from given physical situations.
Solve linear ordinary differential equations.
Interpret the solutions in the given physical context.
Solve linear systems of differential equations.
Use Newton's method to solve systems of nonlinear equations.
Use different formulas for polynomial interpolation.
Use different formulas to numerical differentiation and numerical integration with error estimates.
Relevant People ###### MAt221 Mathematics 221

15 credits

Pre-requisites: [MAM111 and MAM121 (pre-2009)] OR [MAM151 and MAM152] OR [MAT105]

Co-requisite: MAT211

Vector Calculus and Vector fields
Line integrals and independence of path.
Green's Theorem.
Surface Integrals and the Divergence theorem.
Stokes' Theorem.
Applications to fluid flow and heat.
Elementary Modern Algebra
Sets, relations, functions, partitions and binary operations on sets.
Integers, rational numbers and real numbers.
Introduction to groups and rings and partially ordered sets.
Cardinal numbers and ordinal numbers.

Main Outcomes

On completing this module students will be able to

Perform basic operations in vector fields.
Evaluate and interpret line integrals.
Use Green's Theorem to evaluate line integrals.
Use the Divergence Theorem to evaluate surface integrals.
Apply Stokes' Theorem to vector fields.
Identify properties of sets, relations and functions.
Identify and prove properties of groups, rings and partially ordered sets.
Relevant People 