## MAS250 Mathematics II (Materials)

Semester 1, 2021/22 | 10 Credits | ||||

Lecturer: | Dr Nils Mole | Timetable | Reading List | ||

Aims | Outcomes | Teaching Methods | Assessment | Full Syllabus |

This module is part of a series of second-level modules designed for the particular group of engineers shown in brackets in the module title. Each module consolidates previous mathematical knowledge and develops new mathematical techniques relevant to the particular engineering discipline.

**Prerequisites:** MAS153 (Mathematics (Materials))

No other modules have this module as a prerequisite.

## Outline syllabus

## Office hours

1-2 pm on Tuesdays, but you are welcome to email questions to me at any time.

## Aims

- To consolidate previous mathematical knowledge.
- To continue introducing students to basic mathematical techniques used in the area of Engineering Materials.

## Learning outcomes

- Partially differentiate functions of two variables and be able to apply the chain rule.
- Be able to apply simple statistical methods (including linear regression using least squares, and t and χ2 tests) to datasets.
- Understand and manipulate gradient, divergence, curl and Laplacian.
- Expand a function defined over a finite domain in a Fourier series.
- Solve simple partial differential equations e.g. Laplace's equation, wave equation and heat conduction equation.

## Teaching methods

Lectures, tutorials, independent study

36 lectures, 12 tutorials

## Assessment

One two-hour written examination for 80% of assessment.

Four marked homeworks for 20% of assessment.

## Full syllabus

**Partial Differentiation**

Chain Rule for functions of two variables. Small increments. Concept of a partial differential equation.

**Statistical Methods**

Moments, correlations. Linear regression. Tests (Student t, chi-squared).

**Basic Vector Calculus**

Scalar and vector fields. Gradient, divergence, curl, Laplacian.

**Fourier Series**

Periodic functions. Trigonometric series. Fourier coefficients. Examples. Even and odd functions. Cosine and sine series.

**Partial Differential Equations**

Laplace’s equation. Wave equation. Heat conduction equation. Separation of variables. Boundary conditions. Examples.

## Reading list

Type | Author(s) | Title | Library | Blackwells | Amazon |
---|---|---|---|---|---|

B |
Kreyszig | Advanced Engineering Mathematics | |||

B |
O'Neill | Advanced Engineering Mathematics | |||

B |
Stroud | Engineering Mathematics | 510.2462 (S) | Blackwells | Amazon |

(

**A**= essential,

**B**= recommended,

**C**= background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.