## MAS250 Mathematics II (Materials)

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

Semester 1, 2019/20 | 10 Credits | ||||

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

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

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

No other modules have this module as a prerequisite.

## Outline syllabus

## Aims

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

## Learning outcomes

- Solve first-order ordinary differential equations (variables separable, homogeneous, linear).
- Solve second-order inhomogeneous ordinary differential equations with constant coefficients using trial functions for the particular integral.
- Partially differentiate functions of two variables and be able to apply the chain rule.
- 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 75% of assessment.

Five marked homeworks for 25% of assessment.

## Full syllabus

**Ordinary Differential Equations**

First-order equations:
variables separable, homogeneous and linear. Linear second-order
equations with constant coefficients: complementary function and
particular integral.

**Partial Differentiation**

Definition, second-order derivatives. Chain Rule for functions of two variables. Concept of a partial differential equation.

**Statistical Methods**

Moments, correlations. Linear regression.

**Basic Vector Calculus**

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

**Fourier Series**

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

**Partial Differential Equations**

Motivation with examples. 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.