Teaching Responsibility
LJMU Schools involved in Delivery:
Computer Science and Mathematics
Learning Methods
Lecture
Practical
Module Offerings
6113MATHS-JAN-CTY
Aims
Extend students' mastery of calculus in application areas such as vectors, complex numbers transforms and series.
To use functions of a complex variable to evaluate real integrals.
To extend theory introduced in 5105MATHS: Differential Equations at Level 5 and provide an introductory course on solving Partial Differential Equations (PDEs).
Learning Outcomes
1.
Apply the theorems of Gauss, Green and Stokes to solve a range of real-world problems drawn from subjects such as engineering and physics.
2.
Synthesise techniques from complex analysis to solve problems in calculus.
3.
Construct Fourier Series approximations to piecewise continuous functions and be able to graph out periodic extensions of these series.
4.
Classify PDEs as hyperbolic, parabolic or elliptic and construct the solution of a selection of simple PDEs on finite, semi-infinite and infinite domains.
Module Content
Outline Syllabus:1) Complex Analysis
• Continuity and analytic functions.
• Complex integration.
• Cauchy’s Theorem.
2) Vector Calculus
• The del operator.
• Calculating the gradient of a scalar function and the divergence and curl of vector-valued functions.
• The theorems of Green, Gauss and Stokes.
3) Partial Differential Equations
• Representing piecewise continuous functions using full and half-range Fourier Series.
• Classification of PDEs.
• Solution of simple two-dimensional PDEs on finite domains using separation of variables.
• Using Full Fourier Transforms to solve PDEs on infinite domains, and Fourier Sine and Cosine Transforms to solve PDEs on semi-infinite domains.
Additional Information:This module gives students the opportunity to apply mathematics to scientific problems.