# Astronomy BSc/MSci

# Mathematics 2A: Multivariable Calculus MATHS2001

**Academic Session:**2019-20**School:**School of Mathematics and Statistics**Credits:**10**Level:**Level 2 (SCQF level 8)**Typically Offered:**Semester 1**Available to Visiting Students:**Yes**Available to Erasmus Students:**Yes

#### Short Description

This course on multivariate calculus gives a practical introduction to differentiating and integrating in multiple dimensions, and to fundamental concepts found in diverse fields such as geometry and physics. It is an essential course for intending honours students. The emphasis in on methods and applications.

#### Timetable

Lectures on Tuesdays and Thursdays at 10am, or on Tuesdays and Thursdays at 11 am. There may be extra lectures on Monday of teaching week 1. Weekly tutorials on Mondays which cover Maths 2A and Maths 2B course material.

#### 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 2X: Calculus 1

#### Assessment

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

**Main Assessment In:** December

#### Course Aims

This course aims to develop topics in multivariable calculus. It is an essential course for intending honours students. The emphasis in on methods and applications.

#### Intended Learning Outcomes of Course

By the end of the course, students should have attained the following learning objectives:

■ Partial differentiation: Drawing three dimensional surfaces using cross-sections and contours; definition of a partial derivative; the chain rule for partial derivatives;

■ solving simple PDEs by using a given change of variable.

■ Differential vector calculus: Parametrisation of curves in two and three dimensions; scalar and vector fields; definitions of div, grad and curl; identities involving these derivatives; potentials and conservative vector fields.

■ Double and triple integration: Volume under a surface and double integration; obtaining limits for a given domain; change of order of integration; change to polar coordinates and the area element; interpretation of triple integral; spherical polar coordinates; general change of variables and the Jacobian.

■ Line and surface integrals: Definitions of arc length and line integral; conservative vector fields and path-independence of line integrals; parametric description of a surface; definition of a surface integral; use of polar coordinates.

■ Green's theorem and the divergence theorem: Comparison between the fundamental theorem of calculus, Green's theorem and the divergence theorem; applications of Green's theorem to evaluating closed line integrals; applications of the divergence theorem to evaluating closed surface integrals.

■ 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.