Advanced Calculus and Differential Equation Techniques

Code

MTHS2003

School

Mathematical Sciences

Level

2

Credits

10

Semesters

Autumn UK

Summary

The first part of the course introduces the differential and integral calculus of functions of several variables. The remaining part of the course is associated with the development of techniques for the solution of boundary and initial value problems for ordinary and partial differential equations.

Topics include:

• differential calculus of functions of two variables;
• multi-variable integration;
• ordinary differential equations;
• basic Laplace transform techniques;
• introduction to Fourier series;
• partial differential equations and separation of variables.

Target Students

Available to BSc and MSci students in Chemistry, Built Environment, Psychology and Business.

Classes

• One 2-hour workshop each week for 11 weeks
• One 1-hour lecture each week for 11 weeks

Each week there will normally be two lecture hours and an hour of worked examples or a tutorial/problem class.

Assessment

• 10% Coursework 1: Exercise 1
• 10% Inclass Exam 1 (Written): Inclass Exam written
• 80% Exam 1 (2-hour): Written examination

Assessed by end of autumn semester

Educational Aims

Learning Outcomes

Knowledge and understanding of mathematics necessary to support the application of calculus to a variety of problems. 

To apply mathematical methods, tools and notations proficiently in the analysis and solution of engineering and scientific problems.
 

On successful completion of this module students will be able to:

Solve simple first-order and second-order ODEs;

Calculate integrals of functions of more than one variable;

Apply Laplace transform techniques in order to solve ODEs;

Calculate Fourier series representations of periodic functions;

Solve simple PDEs be separation of variable

Conveners

• James Walton