# MATU9M2 - Mathematics II

SCQF Level: 8
Availability: Semester module, Spring
Course Prerequisite: MATU9M1
Credit Value: 20 (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