# 2005/06 Undergraduate Module Catalogue

## PHYS1150 Basic Mathematical Methods

### 10 creditsClass Size: 100

**Module manager:** Professor M D Savage**Email:** m.d.savage@leeds.ac.uk

**Taught:** Semester 1 (Sep to Jan) View Timetable

**Year running** 2005/06

### Pre-requisite qualifications

A Level Mathematics or equivalent.**This module is not approved as an Elective**

### Objectives

On completion of this module you should be able to:- differentiate and integrate a wide range of functions of one variable;

- add, subtract,multiply and divide complex numbers in Cartesian and polar form;

- derive and use Euler's equation;

- use De Moivre's theorem to calculate the nth roots of a complex number;

- use the parallelogram and triangle laws to add and subtract vectors;

- use vectors in component form to calculate the modulus and a unit vector;

- calculate scalar and vector products;

- write down the equation of a line and a plane in vector form;

- differentiate vectors;

- write down expressions for velocity and acceleration in Cartesian and polar coordinates;

- distinguish between linear and nonlinear ordinary differential equations;

- solve first order ordinary differential equations using three methods(separation of variables, integrating factor and homogeneous equation methods).

**Skills outcomes**

Basic mathematical skills in calculus, vectors and differential equations.

The ability to model a physical problem using mathematics.Basic mathematical skills in calculus, vectors and differential equations.

The ability to model a physical problem using mathematics.

### Syllabus

Review of elementary functions and their inverses;hyperbolic functions and their inverses. Partial fractions.

Review of A-level trigonometry. Review of A-Level calculus.

Vectors: vector addition and subtraction, modulus and unit vector. Resolution of a vector. Scalar and vector products. Application to the geometry of lines and planes. Differentiation of vectors, velocity and acceleration in polar coordinates.

Differential Equations: Linear and nonlinear equations. First order ordinary differential equations, 3 methods of solution (separation of variables, integrating factor and homogeneous equation method) . Application of first order equations to mechanics.

Complex Numbers: Argand diagram, Cartesian and polar forms, complex conjugate, modulus. Euler's equation, De Moivre's theorem and nth roots of a complex number. Loci and roots of polynomials.

### Teaching methods

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

Lectures 22 x 1 hour;Example classes/workshops: 10 x 1 hour.

### Private study

Reading: 28 hours;Examples: 40 hours.

### Opportunities for Formative Feedback

5 assignments.### Methods of assessment

Due to COVID-19, teaching and assessment activities are being kept under review - see module enrolment pages for information

1 x 2 hour written examination at the end of the semester: 85%;5 assignments submitted during the semester: 15%.

### Reading list

The reading list is available from the Library websiteLast updated: 16/08/2007

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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