## MAS250 Mathematics II (Materials)

Note: This is an old module occurrence.

You may wish to visit the module list for information on current teaching.

Semester 1, 2018/19 | 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

## Office hours

1-2pm on Wednesdays, but you are welcome 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

- 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.

## Timetable

Mon | 09:00 - 09:50 | lecture | Hicks Lecture Theatre 3 | ||||

Mon | 10:00 - 10:50 | tutorial | (group MT) | Hicks Lecture Theatre 3 | |||

Wed | 09:00 - 09:50 | lecture | Hicks Lecture Theatre 3 | ||||

Thu | 16:00 - 16:50 | lecture | Hicks Lecture Theatre C |