Advanced Mathematics for Civil Engineering

Aim: The purpose of this unit is to enable learners to develop knowledge and understanding of advanced mathematical techniques and be able to apply analytical skills to the solution of civil engineering problems. The knowledge and skills developed are used by other units in the qualification and they also provide a sound basis for extending the study of engineering to a higher level if desired.

On completion of this unit, learners will be able to:

use matrix algebra methods to describe and solve engineering problems

use vector methods of analysis to solve engineering problems

use calculus to model and solve engineering problems

use numerical analysis techniques to solve engineering problems

carry out statistical tests.

Learning outcome

1. be able to use matrix algebra to solve civil engineering problems

1.1 perform operations in matrix algebra

1.2 evaluate the determinants of a matrix

1.3 solve simultaneous equations using Cramer’s rule

1.4 obtain the inverse of a square matrix

1.5 apply Gaussian elimination to solve simultaneous equations

1.6 apply matrix algebra to solve engineering problems described by sets of simultaneous equations.

2. be able to use vectors methods to solve civil engineering problems

2.1 perform operations with vectors

2.2 solve civil engineering problems using vectors.

3. be able to use differential and integral calculus to solve civil engineering problems

3.1 determine first and higher order derivatives of functions

3.2 use differential calculus to solve problems

3.3 determine indefinite and definite integrals of algebraic and trigonometric functions and differential equations

3.4 use integral calculus to solve problems.

4. be able to apply numerical analysis to solve civil engineering problems.

4.1 use numerical iterative methods to find the roots of a function

4.2 apply numerical methods of integration to engineering variables

4.3 apply numerical methods for the solution of ordinary differential equation models

4.4 apply iterative numerical methods to the solution of partial differential equation models.

5. understand forms of statistical distribution

5.1 explain the uses of statistical distribution

5.2 explain the concept of degrees of freedom.

6. be able to use statistical tests

6.1 perform statistical tests of difference

6.2 perform statistical tests of correlation.

7. be able to use linear regression techniques

7.1 perform regression techniques

7.2 make predictions using linear regression techniques.