# Mathematics and Statistics Group

## MAT913: Mathematics and its Applications III

**SCQF Level: **8

**Availability: **Semester module, Autumn

**Course Prerequisite: **MAT912

**Credit Value: **22 (I module)

### Aims

To provide techniques for the solution of some differential equations,
to extend the theory of differential calculus to functions of more than
one variable, to consider the approximation of arbitrary functions by
polynomials, and to develop an understanding of infinite series. To
acquaint students with the theory of probability, to illustrate some of
its applications to solve real world problems, and to demonstrate its
relevance to statistical analysis.

### Learning Outcomes

Students should be able to differentiate functions of several variables,
solve certain types of differential equations, obtain Taylor
approximations of arbitrary functions, and determine whether infinite
series converge or diverge; use counting techniques, calculate basic and
conditional probability; derive the mean and variance for a range of
discrete and continuous distributions, use these distributions in
real-life situations; and understand and implement simple hypothesis
tests and confidence intervals.

### Content

A1: Optimisation, solution of differential equations

A2: Partial differentiation

A3: Taylor's theorem - the approximation of functions by polynomials;
sequences and series; Taylor series

B1: Basic probability, conditional probability, random variables

B2: Probability models using the binomial, Poisson, exponential and
normal distributions

B3: The role of probability in elementary statistical analysis

### Transferable Skills

Logical and analytical thinking, problem solving, and numeracy.

### Bibliography

H. ANTON et al. "Calculus Early Transcendentals Combined" (eighth
edition), 2005 or

R. A. ADAMS, "Calculus: A Complete Course", Addison-Wesley, (fifth
edition), 2002

S. LIPSCHUTZ & M. LIPSON, "Schaum's Outline of Probability ", McGraw
Hill (second edition) 2000.

### Teaching Format

There will be four lectures and one 1.5 hour tutorial per week.

### Assessment

Coursework (including 2 class tests) 40%, examination 60%.

Please note: this page updates the information on page 9 of the Student
Handbook 2004/5