MATH13217 - Advanced Calculus
Term 1 - 2017


All details in this unit profile for MATH13217 have been officially approved by CQUniversity and represent a learning partnership between the University and you (our student). The information will not be changed unless absolutely necessary and any change will be clearly indicated by an approved correction included in the profile.

Overview

The unit covers 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, we investigate derivatives and integrals of vector functions with applications to arc length, curvature of space curves and motion in space. Then 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. Multiple integrals are studied 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 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 we investigate the calculus of vector fields. We define and study 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. Note: If you have completed unit MATH12172 then you cannot take this unit.

Details

Career Level Undergraduate
Unit Level Level 3
Credit Points 6
Student Contribution Band [not found]
Fraction of Full-Time Student Load 0.125

Pre-requisites or Co-requisites

Prerequisite MATH12224 Calculus and Linear Algebra B

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).

Offerings

Term 1 - 2017
  • Distance

Website

This unit has a website, within the Moodle system, which is available two weeks before the start of term. It is important that you visit your Moodle site throughout the term. Go to Moodle

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.

Class Timetable

Assessment Overview

Assessment Task Weighting
1. Written Assessment 25%
2. Written Assessment 25%
3. Written Assessment 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 Procedures for more details of interim results and final grades.

All University policies are available on the IMPortal.

You may wish to view these policies:

  • Grades and Results Procedure
  • Assessment Policy and Procedure (Higher Education Coursework)
  • Review of Grade Procedure
  • Academic Misconduct Procedure
  • Monitoring Academic Progress (MAP) Policy and Procedure – Domestic Students
  • Monitoring Academic Progress (MAP) Policy and Procedure – International Students
  • Refund and Excess Payments (Credit Balances) Policy and Procedure
  • Student Feedback – Compliments and Complaints Policy and Procedure
  • Acceptable Use of Information and Communications Technology Facilities and Devices Policy and Procedure

This list is not an exhaustive list of all University policies. The full list of University policies are available on the IMPortal.

Feedback, Recommendations and Responses

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.

Feedback Source Recommendation
Students are not happy with the resources; They complaint they cannot see who is lecturing. Evaluation Record our videos for the next course; Keep more resources available for students to follow.
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. Calculate derivatives and integrals 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 as well as calculate tangent planes, linear approximations and differentials.
  4. Apply the chain rule, directional derivatives and the gradient vector to solve problems, particularly multivariable optimisation problems either with or without constraints.
  5. Calculate double & triple integrals over general regions, and also in polar, cylindrical and spherical coordinates.
  6. Apply the change of variables technique to simplify the evaluation of a double or triple integral.
  7. Evaluate line integrals both in space and of vector fields, plus solve problems involving the curl and divergence of a vector field.
  8. Calculate the surface integral of a scalar function or of a vector field, plus use Green’s theorem, Stokes’ Theorem and the Divergence Theorem to solve problems.
  9. Use mathematical software to visualise, analyse and solve problems in multivariable calculus.

Alignment of Assessment Tasks to Learning Outcomes

Assessment Tasks Learning Outcomes
1 2 3 4 5 6 7 8 9
1 - Written Assessment        
2 - Written Assessment            
3 - Written Assessment

Alignment of Graduate Attributes to Learning Outcomes

  • Introductory Level
  • Intermediate Level
  • Graduate Level
Graduate Attributes Learning Outcomes
1 2 3 4 5 6 7 8 9
1. Communication
2. Problem Solving
3. Critical Thinking
4. Information Literacy
5. Team Work                  
6. Information Technology Competence
7. Cross Cultural 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
1 - Written Assessment    
2 - Written Assessment    
3 - Written Assessment    

Prescribed Textbooks

Multivariable Calculus : Concepts and Contexts
Author/s: Stewart, J. Year: 2010
Edition: 4E Publisher: Brooks-Cole, Cengage Learning
City: Belmont State: CA
Country: U.S.A.
View textbooks at the CQUniversity Bookshop

IT Resources

You will need access to the following IT resources:
  • CQUniversity Student Email
  • Internet
  • Unit Website (Moodle)
All submissions for this unit must use the Harvard (author-date) referencing style (details can be obtained here). For further information, see the Assessment Tasks below.
Unit CoordinatorYucang Wang (y.wang2@cqu.edu.au)
Note: Check the Term-Specific section for any additional contact information provided by the teaching team
Week Begin Date Module/Topic Chapter Events and Submissions
Week 1 06-03-2017

Three Dimensional Coordinate Systems, Vectors, The Dot and Cross Product, Equations of Lines and Planes, Functions and Surfaces, Cylindrical and Spherical Coordinates

All of Chapter 9

Week 2 13-03-2017

Vector Functions and Space Curves, Derivatives and Integrals of Vector Functions, Arc Length and Curvature, Motion in Space

Sections 10.1 to 10.4

Week 3 20-03-2017

Parametric Surfaces, Functions of Several Variables, Limits and Continuity, Partial Derivatives, Tangent Planes and Linear Approximations

Section 10.5 plus

Sections 11.1 to 11.4 (part)

Week 4 27-03-2017

Differentials, The Chain Rule and Implicit Differentiation, Directional Derivatives and the Gradient Vector

Sections 11.4 to 11.6

Week 5 03-04-2017

Maximum and Minimum Values, Lagrange Multipliers

Sections 11.7 & 11.8

Vacation Week 10-04-2017
Week 6 17-04-2017

Double Integrals over Rectangles and General Regions, Double Iterated Integrals, Double Integrals in Polar Coordinates

Sections 12.1 to 12.4

Assignment 1 Due Friday (21 Apr 17) 05:00 PM AEST
Week 7 24-04-2017

Applications of Double Integrals, Surface Area

Sections 12.5 & 12.6

Week 8 01-05-2017

Triple Integrals and Triple Integrals in Cylindrical and Spherical Coordinates

Sections 12.7 & 12.8

Week 9 08-05-2017

Change of Variables in Multiple Integrals, Vector Fields, Line Integrals

Section 12.9 plus

Sections 13.1 & 13.2

Week 10 15-05-2017

The Fundamental Theorem for Line Integrals, Green's Theorem

Sections 13.3 & 13.4

Assignment 2 Due Friday (19 May 17) 05:00 PM AEST
Week 11 22-05-2017

Curl and Divergence, Surface Integrals

Sections 13.5 & 13.6

Week 12 29-05-2017

Stoke's Theorem, The Divergence Theorem, Summary

Sections 13.7 to 13.9

Review/Exam Week 05-06-2017
Exam Week 12-06-2017
Written Assessment Due Friday (16 Jun 17) 11:00 PM AEST

1 Written Assessment

Assessment Title Assignment 1
Task Description

Submit full worked solutions to exercises selected from the Stewart Textbook. The exercises cover topics from Weeks 1 to 5 of the course. The selected exercises and other details are given on the Moodle website.

Assessment Due Date Week 6 Friday (21-Apr-2017) 05:00 PM AEST
Submit by 5pm on Friday of Week 6
Return Date to Students Week 8 Friday (05-May-2017)
Results will be available to students approximately two weeks after the submission date.
Weighting 25%
Assessment Criteria

Full details about assignment 1 are available on the Moodle website.

Referencing Style Harvard (author-date)
Submission Online

Assignment 1 must be submitted online through the MATH13217 Moodle website.

Learning Outcomes Assessed
This section can be expanded to view the assessed learning outcomes

1. Solve geometric problems in three dimensional space using vectors and their operators.

2. Calculate derivatives and integrals 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 as well as calculate tangent planes, linear approximations and differentials.

4. Apply the chain rule, directional derivatives and the gradient vector to solve problems, particularly multivariable optimisation problems either with or without constraints.

9. Use mathematical software to visualise, analyse and solve problems in multivariable calculus.

Graduate Attributes
This section can be expanded to view the assessed graduate attributes

1. Communication

2. Problem Solving

3. Critical Thinking

4. Information Literacy

6. Information Technology Competence

8. Ethical practice



2 Written Assessment

Assessment Title Assignment 2
Task Description

Submit full worked solutions to exercises selected from the Stewart Textbook. The exercises cover topics from Weeks 6 to 9 of the course. The selected exercises and other details are given on the Moodle website.

Assessment Due Date Week 10 Friday (19-May-2017) 05:00 PM AEST
Submit by 5pm on Friday of Week 10
Return Date to Students Week 12 Friday (02-Jun-2017)
Results will be available to students approximately two weeks after the submission date.
Weighting 25%
Assessment Criteria

Full details about assignment 2 are available on the Moodle website.

Referencing Style Harvard (author-date)
Submission Online

Assignment 2 must be submitted online through the MATH13217 Moodle website.

Learning Outcomes Assessed
This section can be expanded to view the assessed learning outcomes

5. Calculate double & triple integrals over general regions, and also in polar, cylindrical and spherical coordinates.

6. Apply the change of variables technique to simplify the evaluation of a double or triple integral.

9. Use mathematical software to visualise, analyse and solve problems in multivariable calculus.

Graduate Attributes
This section can be expanded to view the assessed graduate attributes

1. Communication

2. Problem Solving

3. Critical Thinking

4. Information Literacy

6. Information Technology Competence

8. Ethical practice



3 Written Assessment

Assessment Title Written Assessment
Task Description

The take home exam will be available in the Moodle course website on Friday, 5 May 2017 at 9:00 am. You have to answer all questions showing full working. Submit your answers hand-written or typed or combination online in pdf, doc, docx or rtf format.

Assessment Due Date Exam Week Friday (16-Jun-2017) 11:00 PM AEST
Submit by 11pm on Friday of Exam Week
Return Date to Students The take home exam papers will be returned to the students after the certification date.
Weighting 50%
Assessment Criteria

Marks will be allocated on working, presentation, and conclusions.

Referencing Style Harvard (author-date)
Submission Online

Submit online in pdf, doc, docx or rtf format with a total size less than 50 MB

Learning Outcomes Assessed
This section can be expanded to view the assessed learning outcomes

1. Solve geometric problems in three dimensional space using vectors and their operators.

2. Calculate derivatives and integrals 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 as well as calculate tangent planes, linear approximations and differentials.

4. Apply the chain rule, directional derivatives and the gradient vector to solve problems, particularly multivariable optimisation problems either with or without constraints.

5. Calculate double & triple integrals over general regions, and also in polar, cylindrical and spherical coordinates.

6. Apply the change of variables technique to simplify the evaluation of a double or triple integral.

7. Evaluate line integrals both in space and of vector fields, plus solve problems involving the curl and divergence of a vector field.

8. Calculate the surface integral of a scalar function or of a vector field, plus use Green’s theorem, Stokes’ Theorem and the Divergence Theorem to solve problems.

9. Use mathematical software to visualise, analyse and solve problems in multivariable calculus.

Graduate Attributes
This section can be expanded to view the assessed graduate attributes

1. Communication

2. Problem Solving

3. Critical Thinking

4. Information Literacy

6. Information Technology Competence

8. Ethical practice




© 2017 CQUniversity
Page generated by apps-prod-01.cqu.edu.au at Sun Mar 26 05:39:09 AEST 2017