## 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, 2022/23 10 Credits Lecturer: Dr Gary Verth 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.

## 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.