## MAS250 Mathematics II (Materials)

 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.

## Office hours

1-2pm on Wednesdays, but you are welcome any time I am free.

## 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.