# Module Overview

### Mathematics 2

The aim of Mathematics 2 is to enable the student to master a broad range of standard mathematical techniques in linear algebra, analysis and calculus to a high level of proficiency. This proficiency is required to support engineering subjects and forms the basis for further mathematical study in year 2.

MATH H1019

##### ECTS Credits

5

*Curricular information is subject to change

Geometry and Matrices:

Matrix definition. Matrix algebra. Matrix determinant, special matrices and the matrix of a geometric transformation. Matrix multiplication as geometric composition. Inverse matrix formula for 2X2.

Linear Algebra:

Systems of linear equations in matrix form. Solution of system of linear equations using row reduction (Gaussian elimination). Interpretation of the solution of systems of linear equations.

Vectors and Matrices:

Vector and Scalar products with geometric and engineering context application. Using vectors to calculate planes in 3D .

Functions:

Application of engineering functions to 1-D models such as growth and decay models.Types of function (even, odd, convex, concave, monotone, continuous, differentiable). Piecewise defined functions. Rational functions. Curves in 2D described in parametrized (vector) form.

Further Differentiation:

Second derivatives. Parametric differentiation. Applying differentiation to engineering problems.

Function investigation using differentiation:

Increasing and decreasing functions. Stationary points. Classifying stationary points. Points of inflexion.

Indefinite Integration:

The anti-derivative. Linearity of the integral. Application to position, velocity and acceleration calculations.

Definite Integration:

Calculations and properties. Fundamental Theorem of Calculus. Area under a graph. Area between two curves. Solids of revolution. Simpson’s rule and Trapezoid rule.

Programming Skills:

Programming Basics: documentation (use of comments and indentation), Use of built-in I/O and mathematical functions, debugging and testing. Datatypes: Numbers, characters, arrays. Control Structures: selection structures ( if etc. using conditional expressions), repetition structures (for).

Module Content & Assessment
Assessment Breakdown %
Other Assessment(s)30
Formal Examination70