Mathematics 2A: Multivariable Calculus

University of Glasgow

Course Description

• Course Name

Mathematics 2A: Multivariable Calculus

• Host University

University of Glasgow

• Location

Glasgow, Scotland

• Area of Study

Calculus, Mathematics

• Language Level

Taught In English

• Prerequisites

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.

• Course Level Recommendations

Lower

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

Hours & Credits

• SCQF Credits

10
• Recommended U.S. Semester Credits
2.5 - 3
• Recommended U.S. Quarter Units
1
• Overview

Short Description
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.

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.

Course Disclaimer

Courses and course hours of instruction are subject to change.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.

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