## 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

Examples: 40 hours.

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%.