## MATH1970 Differential Equations

### 10 creditsClass Size: 200

Module manager: Professor A.V. Mikhailov
Email: sashamik@maths.leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2008/09

### Pre-requisites

 MATH1960 Calculus

### This module is mutually exclusive with

 MATH1400 Modelling with Differential Equations MATH1460 Mathematics for Geophysical Sciences 1 MATH1932 Calculus, ODEs and Several-Variable Calculus

This module is approved as an Elective

### Module summary

Differential equations provide a powerful mathematical method for modelling physical, chemical and biological phenomena. This introduction to the theory of differential equations cover basic methods for solving ordinary differential equations, that is, equations in which the functions depend on a single variable.

### Objectives

On completion of this module, students should be able to:

a) Solve a variety of first-and second-order differential equations;
b) Derive and solve ODEs arising from applications..

### Syllabus

1. Introduction. Basic definitions, examples. Geometrical interpretation. Graphical and numerical solutions.
2. First order ordinary differential equations: Linear equations, separable equations. Homogeneous equations, Bernoulli equation. Change of variables. Exact equations.
3. Second order linear ordinary differential equations. Equations with constant coefficients. equations with non-constant coefficients. Homogeneous equations: principle of superposition, solution space, basis, Wronskians, AbelÂ¿s identity. Method of reduction of order. Inhomogeneous equations, methods of undetermined coefficients, variation of parameters.
4. Systems of linear ordinary differential equations: Homogeneous solutions. Fundamental solution matrix. Wronskians. Inhomogeneous systems. Variation of parameters.
5. Phase plane methods: Introduction. Critical points. Stability. Matrix exponential.

### Teaching methods

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

 Delivery type Number Length hours Student hours Lecture 21 1.00 21.00 Tutorial 11 1.00 11.00 Private study hours 68.00 Total Contact hours 32.00 Total hours (100hr per 10 credits) 100.00

### Opportunities for Formative Feedback

Regular example sheets.

### Methods of assessment

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

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 15.00 Total percentage (Assessment Coursework) 15.00

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 00 mins 80.00 Standard exam (closed essays, MCQs etc) 0 hr 00 mins 5.00 Total percentage (Assessment Exams) 85.00

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