# Astronomy BSc/MSci

# 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.