# Course Description

# Course Name

**Mathematics 2**

**Session: VDNS3121**

# Hours & Credits

18 Credit Points

# Prerequisites & Language Level

**Taught In English**

- There is no language prerequisite for courses at this language level.

# Overview

This paper is divided between algebra and calculus components (which can be taken as separate 9 point papers). The algebra component covers vectors, matrices, linear transformations, eigenvalues and introduces aspects of discrete mathematics. The calculus component covers sequences and series, inverse trigonometric and hyperbolic functions, advanced integration techniques, differential equations and their applications.

Algebra and Calculus form the basic tools used to produce most mathematical frameworks for modelling quantifiable phenomena. For example, to model the movement of an object through space we need first to create an algebraic structure in which to specify where our object is, and then we can study how that position changes with time (i.e. its movement) using calculus.Many other problems arising in areas such as Economics or Chemistry, can be examined in a mathematical way using the same basic ideas. For example, we may need to minimise a manufacturing cost or the time for a chemical reaction to take place or the effects of river pollution; in each case the techniques used for the minimisation are based on a mixture of algebra and calculus theories.

This paper aims to develop skills with these tools both for use in other subjects and in preparation for further study of Mathematics.

MATH 170 is the natural continuation of MATH 160 and provides the basis for progression to 200-level Mathematics, as well as a good mathematical background to support other subjects.

**Course Structure**

Main topics:

Algebra:

-Algebra and geometry of 3-dimensional vectors

-Manipulation of matrices and matrix equations

-Introduction to linear transformations

-Eigenvalues and eigenvectors

-Discrete mathematics, including mathematical induction, Diophantine equations and basic counting techniques

Calculus:

-Sequences, series and Taylor series

-Natural log, exponential, hyperbolic, inverse trigonometric and hyperbolic functions

-Methods of integration

-Arc length; volumes and surfaces of revolution

-Solving differential equations

**Learning Outcomes**

Demonstrate in-depth understanding of the central concepts and theories

*Course content subject to change