Mathematics 2D: Topics In Linear Algebra And Calculus MATHS2006

  • Academic Session: 2019-20
  • School: School of Mathematics and Statistics
  • Credits: 10
  • Level: Level 2 (SCQF level 8)
  • Typically Offered: Semester 2
  • Available to Visiting Students: Yes
  • Available to Erasmus Students: Yes

Short Description

This course aims to develop related topics in linear algebra and multivariable calculus. The emphasis is on methods and applications.

Timetable

Lectures on Wednesdays and Fridays at 9.00 am or Wednesdays and Fridays at 10.00 am or Wednesdays and Fridays at 11.00 am. Fortnightly tutorials on Mondays.

Requirements of Entry

Mathematics 1R or 1X at grade D and 1S or 1T or 1Y at grade D and a pass in the level 1 Skills test.

Excluded Courses

Mathematics 2S, Mathematics 2Y and Mathematics 2Z

Co-requisites

Mathematics 2A: Multivariable Calculus, Mathematics 2B: Linear Algebra or Mathematics 2AA: Multivariable Calculus (Enhanced) and Mathematics 2AB: Linear Algebra (Enhanced).

Assessment

  One degree examination (80%) (1 hour 30 mins); coursework (20%).

Main Assessment In: April/May

Course Aims

This course aims to develop related topics in linear algebra and multivariable calculus. The emphasis is on methods and applications.

Intended Learning Outcomes of Course

By the end of this course, students should be able to:

 

■ Use diagonalisation of a matrix to solve systems of Ordinary Differential Equations and difference equations;

■ Recognise quadratic forms, understand the connection with symmetric matrices and determine their rank and signature; diagonalise quadratic forms.

■ Know the definitions and basic properties of Real and Hermitian inner products, the idea of orthogonality and be able to use Gram-Schmidt orthogonalisation.

■ Understand the properties of eigenvalues and eigenvectors of symmetric, orthogonal, unitary and similar matrices.

■ Find stationary points for functions of several variables; classify them using first principles and the Hessian criterion.

■ Use the method of Lagrange multipliers to solve practical extreme value problems

■ Use the properties of Beta and Gamma functions to evaluate certain integrals.

■ Find Fourier series for given functions defined on finite intervals

■ Be able to learn and apply formulae used in this course.

Minimum Requirement for Award of Credits

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.