160203

# Multivariable Calculus

The techniques of 100-level calculus are applied and extended in the study of infinite series, vector-valued functions and functions of two or more variables. Topics include convergence of power series, partial derivatives, double and triple integrals with applications to surface area and volumes, line and surface integrals.

## Course code

Qualifications are made up of courses. Some universities call these papers. Each course is numbered using six digits.

160203

## Level

The fourth number of the course code shows the level of the course. For example, in course 219206, the fourth number is a 2, so it is a 200-level course (usually studied in the second year of full-time study).

200-level

## Credits

Each course is worth a number of credits. You combine courses (credits) to meet the total number of credits needed for your qualification.

15

Mathematics

## Course planning information

### Prerequisite courses

Complete first
One of 160101, 160112, 160133 or 228172

You need to complete the above course or courses before moving onto this one.

### General progression requirements

You must complete at least 45 credits from 100-level before enrolling in 200-level courses.

## Learning outcomes

What you will learn. Knowledge, skills and attitudes you’ll be able to show as a result of successfully finishing this course.

• 1 Discuss the concept of convergence and be able to select and apply appropriate tests of convergence for sequences and series.
• 2 Utilise techniques for evaluating indeterminate forms.
• 3 Utilise parametric equations and polar coordinates.
• 4 Describe, discuss and utilise the calculus of vectors in two and three dimensions including their application to motion.
• 5 Describe, discuss and utilise differential calculus of multivariable functions, including directional and partial derivatives, the gradient, the multivariable chain rule and Lagrange multipliers.
• 6 Explain double and triple integrals and how they arise as limits of sums; have the ability to work with double and triple integrals in various coordinate systems and use them to calculate volumes, surface areas and masses.
• 7 Display detailed knowledge of line integrals and how they arise as limits of sums; have a good understanding of Green’s Theorem in the plane.

Learning outcomes can change before the start of the semester you are studying the course in.

## Assessments

Assessment Learning outcomes assessed Weighting
Written Assignment 1 2 3 4 5 6 7 25%
Test 1 2 3 4 5 6 7 25%
Test 1 2 3 4 5 6 7 25%
Exam (centrally scheduled) 1 2 3 4 5 6 7 25%

Assessment weightings can change up to the start of the semester the course is delivered in.

You may need to take more assessments depending on where, how, and when you choose to take this course.

### Explanation of assessment types

Computer programmes
Computer animation and screening, design, programming, models and other computer work.
Creative compositions
Animations, films, models, textiles, websites, and other compositions.
Exam College or GRS-based (not centrally scheduled)
An exam scheduled by a college or the Graduate Research School (GRS). The exam could be online, oral, field, practical skills, written exams or another format.
Exam (centrally scheduled)
An exam scheduled by Assessment Services (centrally) – you’ll usually be told when and where the exam is through the student portal.
Oral or performance or presentation
Debates, demonstrations, exhibitions, interviews, oral proposals, role play, speech and other performances or presentations.
Participation
You may be assessed on your participation in activities such as online fora, laboratories, debates, tutorials, exercises, seminars, and so on.
Portfolio
Creative, learning, online, narrative, photographic, written, and other portfolios.
Practical or placement
Field trips, field work, placements, seminars, workshops, voluntary work, and other activities.
Simulation
Technology-based or experience-based simulations.
Test
Laboratory, online, multi-choice, short answer, spoken, and other tests – arranged by the school.
Written assignment
Essays, group or individual projects, proposals, reports, reviews, writing exercises, and other written assignments.

## Textbooks needed

Textbooks can change. We recommend you wait until at least seven weeks before the semester starts to buy your textbooks.

### Compulsory

#### CALCULUS, EARLY TRANSCENDENTALS, INTERNATIONAL METRIC EDITION

Author
JAMES STEWART
ISBN
9780357113516
Edition
9TH EDITION
Publisher
CENGAGE LEARNING

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