Module manager: Dr M. Ivanchenko
Email: m.ivanchenko@leeds.ac.uk
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2009/10
A good A-level Mathematics grade or equivalent.
| MATH1400 | Modelling with Differential Equations |
| MATH1410 | Modelling Force and Motion |
| MATH1970 | Differential Equations |
| MATH2365 | Vector Calculus |
This module is approved as an Elective
This module introduces students to basic techniques of Mathematics required for the geophysical sciences such as functions of several variables, ordinary differential equations, Fourier series, introduction to linear systems.
On completion of this module, students should be able to:
a) calculate partial derivatives of explicitly and implicitly defined functions and use the chain rule;
b) calculate the Taylor series of a given function of two variables about a given point;
c) find and classify critical points of a function of two variables;
d) solve simple first order ordinary differential equations and linear second order ordinary differential equations;
e) determine whether a function is periodic and calculate its Fourier series;
f) solve simple linear problems using Laplace transforms.
1. Functions of Several Variables, examples, visualisation by graphs or contours, limits and continuity. Partial derivatives, meaning and calculation, higher derivatives. Chain rule and applications. Taylor series in two variables. Maxima and minima of functions of two or more variables.
2. Ordinary Differential Equations, examples and definitions. Solution of first order ODEs, including separation of variables, integrating factors for linear ODEs, homogeneous equations and exact differentials. Solution of second order linear equations with constant coefficients.
3. Fourier Series, examples and formulae. Even and odd functions, half range series, complex form of a Fourier series. Formulae for arbitrary periods. Applications to vibrating strings.
4. Linear systems. Response of linear system to harmonic input. Example of the seismometer. Solution of linear problems by Laplace transform. Transfer function.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 22 | 1 | 22 |
| Tutorial | 11 | 1 | 11 |
| Private study hours | 67 | ||
| Total Contact hours | 33 | ||
| Total hours (100hr per 10 credits) | 100 | ||
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| Tutorial Performance | . | 15 |
| Total percentage (Assessment Coursework) | 15 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 2.0 Hrs 0 Mins | 85 |
| Total percentage (Assessment Exams) | 85 | |
Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated
The reading list is available from the Library website
Last updated: 3/22/2010
Errors, omissions, failed links etc should be notified to the Catalogue Team