## PHYS1290 Maths 1- Scalars and Vectors

### 10 creditsClass Size: 255

Module manager: Dr Almut Beige
Email: A.Beige@leeds.ac.uk

Taught: Semester 1 (Sep to Jan) View Timetable

Year running 2022/23

### Pre-requisite qualifications

A Level Physics and Maths or equivalent

Module replaces

PHYS1150

This module is not approved as a discovery module

### 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).

Learning outcomes
Manipulate numerical and other quantitative information, and apply manipulative skills to the solution of problems.

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

### Syllabus

Vector calculus
Complex numbers
Differentiation and Integration
First order differential equations

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Private study hours 78.00 Total Contact hours 22.00 Total hours (100hr per 10 credits) 100.00

### Opportunities for Formative Feedback

Regular assignments, and 1 diagnostic test

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Regular Coursework 20.00 Total percentage (Assessment Coursework) 20.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 30 mins 80.00 Total percentage (Assessment Exams) 80.00

Students will have to complete an in-person exam at the end of the module. This will take place during the examinations period at the end of the semester and will be time bound. Students must submit a serious attempt at all assessments for this module, in order to pass the module overall.