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MATH13217 - Advanced Calculus

General Information

Unit Synopsis

In this unit, you will study topics in multivariable calculus - differential and integral calculus as applied to scalar and vector functions of more than one variable. After reviewing vectors and the geometry of space, you will investigate derivatives and integrals of vector functions with applications to arc length, curvature of space curves and motion in space. Partial differentiation is studied by defining limits and continuity in two dimensions, and is used to define tangent planes, linear approximations and differentials. The chain rule is developed for functions of more than one variable as well as directional derivatives and the gradient vector, which leads into multivariate optimisation with and without constraints. You will study multiple integrals by expanding the concept of single variable integrals to double and triple integrals which are evaluated as iterated integrals. These ideas are further developed to show you how to calculate volumes, surface areas, masses and centroids of very general regions in two and three dimensional space as well as probability for bivariate distributions. Finally you will investigate the calculus of vector fields, line integrals and surface integrals. The connection between these new types of integrals and multiple integrals is given in three theorems - Green’s Theorem, Stokes’ Theorem and the Divergence Theorem - which turn out to be higher-dimensional versions of the Fundamental Theorem of Calculus. Mathematical software is used to investigate and solve most problems in the unit.

Details

Level Undergraduate
Unit Level 3
Credit Points 6
Student Contribution Band SCA Band 1
Fraction of Full-Time Student Load 0.125
Pre-requisites or Co-requisites

Prerequisite: MATH12224 

Anti-requisite: MATH12172

Important note: Students enrolled in a subsequent unit who failed their pre-requisite unit, should drop the subsequent unit before the census date or within 10 working days of Fail grade notification. Students who do not drop the unit in this timeframe cannot later drop the unit without academic and financial liability. See details in the Assessment Policy and Procedure (Higher Education Coursework).

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Unit Availabilities from Term 1 - 2020

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Term 1 - 2021 Profile
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Term 1 - 2022 Profile
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Term 1 - 2023 Profile
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Term 1 - 2024 Profile
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Term 1 - 2025 Profile
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Attendance Requirements

All on-campus students are expected to attend scheduled classes - in some units, these classes are identified as a mandatory (pass/fail) component and attendance is compulsory. International students, on a student visa, must maintain a full time study load and meet both attendance and academic progress requirements in each study period (satisfactory attendance for International students is defined as maintaining at least an 80% attendance record).

Assessment Overview

Recommended Student Time Commitment

Each 6-credit Undergraduate unit at CQUniversity requires an overall time commitment of an average of 12.5 hours of study per week, making a total of 150 hours for the unit.

Assessment Tasks

Assessment Task Weighting
1. Written Assessment 25%
2. Written Assessment 25%
3. Examination 50%

This is a graded unit: your overall grade will be calculated from the marks or grades for each assessment task, based on the relative weightings shown in the table above. You must obtain an overall mark for the unit of at least 50%, or an overall grade of ‘pass’ in order to pass the unit. If any ‘pass/fail’ tasks are shown in the table above they must also be completed successfully (‘pass’ grade). You must also meet any minimum mark requirements specified for a particular assessment task, as detailed in the ‘assessment task’ section (note that in some instances, the minimum mark for a task may be greater than 50%).

Consult the University's Grades and Results Policy for more details of interim results and final grades

Past Exams

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Every unit is reviewed for enhancement each year. At the most recent review, the following staff and student feedback items were identified and recommendations were made.

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Students appreciated the support offered to the small number of enrolled students as a whole or individually during the course
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Continue to offer a positive supported learning experience
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The learning and teaching practices have been maintained.
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Students were pleased with all aspects of the unit.
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Unit content is aligned to the Australian curriculum with relevance for students' future teaching career.
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Continue to ensure unit content matches the latest Australian mathematics curriculum standards.
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Update the unit Moodle site.
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Add detailed weekly study instructions and supporting resources to the unit Moodle site.
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Unit learning Outcomes

On successful completion of this unit, you will be able to:

  1. Solve geometric problems in three dimensional space using vectors and their operators
  2. Differentiate and integrate of vector functions to solve problems involving arc length and curvature of space curves
  3. Apply the concept of the limit, continuity and partial derivative of a function of many variables to calculate tangent planes, linear approximations and differentials
  4. Optimise multivariable problems, either with or without constraints, using the chain rule, directional derivatives and the gradient vector
  5. Calculate double and triple integrals over general regions, and also in polar, cylindrical and spherical coordinates
  6. Simplify the evaluation of a double or triple integral by applying the change of variables technique
  7. Solve problems involving the curl and divergence of a vector field
  8. Investigate the calculus of vector fields, line integrals and surface integrals through Green’s theorem, Stokes’ Theorem and the Divergence Theorem
  9. Use mathematical software to visualise, analyse and solve problems in multivariable calculus.

Alignment of Assessment Tasks to Learning Outcomes
Assessment Tasks Learning Outcomes
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1 - Written Assessment • • • • •
2 - Written Assessment • • •
3 - Examination • • • • • • • •
Alignment of Graduate Attributes to Learning Outcomes
• Introductory Level
• Intermediate Level
• Graduate Level
Graduate Attributes Learning Outcomes
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1 - Communication • • • • • • • • •
2 - Problem Solving • • • • • • • • •
3 - Critical Thinking • • • • • • • • •
4 - Information Literacy • • • • • • • • •
6 - Information Technology Competence • • • • • • • • •
8 - Ethical practice • • • • • • • • •
Alignment of Assessment Tasks to Graduate Attributes
• Introductory Level
• Intermediate Level
• Graduate Level
Assessment Tasks Graduate Attributes
1 2 3 4 5 6 7 8 9 10
1 - Written Assessment • • • • • •
2 - Written Assessment • • • • • •
3 - Examination • • • • • •