School: Science

This unit information may be updated and amended immediately prior to semester. To ensure you have the correct outline, please check it again at the beginning of semester.

Your unit may be subject to government or third party COVID-19 vaccination requirements. Please consider this before enrolling in this unit, and speak with the unit coordinator if this raises any concerns.

  • Unit Title

    Multivariate Calculus
  • Unit Code

    MAT3486
  • Year

    2022
  • Enrolment Period

    1
  • Version

    2
  • Credit Points

    15
  • Full Year Unit

    N
  • Mode of Delivery

    On Campus
  • Unit Coordinator

    Dr Steven James RICHARDSON

Description

This unit deals with the calculus of functions of two and three variables and a selection of topics from vector analysis

Prerequisite Rule

(Students must pass 1 unit from MAT1236 OR Students must pass 2 units from MAT1250 AND MAT1251)

Equivalent Rule

Unit was previously coded MAT3236

Learning Outcomes

On completion of this unit students should be able to:

  1. Solve multivariate calculus problems by applying appropriate analytical and numerical techniques.
  2. Analyse applied calculus problems in multivariate contexts using appropriate analytical and numerical techniques.
  3. Effectively utilise numerical computer packages to investigate mathematical concepts in abstract and applied contexts.
  4. Independently communicate solutions to problems involving the application of analytical and numerical techniques in a coherent written form.

Unit Content

  1. Vector Valued Functions: definition; domain and limits; parametric representation of curves; differentiation and integration; unit tangent vector; tangent lines; arc length; curvature and torsion; normal and binormal vectors; curvilinear motion; normal and tangential components of acceleration.
  2. Functions of several variables: definition; domain and range graphs; level curves and level surfaces; first and second order partial derivatives; chain rule for functions of several variables; gradient vector; directional derivatives; tangent planes.
  3. Optimisation of functions of several variables: locating and characterising local extrema; optimisation on bounded domains; method of Lagrange multipliers.
  4. Double integrals over rectangular and non-rectangular regions; reversal of the order of integration; area as a double integral.
  5. Introduction to polar, cylindrical and spherical co-ordinates; double and triple integrals in polar, cylindrical and spherical co-ordinates.
  6. Vector fields: gradient, divergence and curl; line integrals, surface integrals and flux integrals; the fundamental theorem for line integrals; conservative vector fields; Green's theorem; the divergence theorem; Stokes' theorem;

Additional Learning Experience Information

One three hour lecture/tutorial per week. Use will be made of computer packages where appropriate.

Assessment

GS1 GRADING SCHEMA 1 Used for standard coursework units

Students please note: The marks and grades received by students on assessments may be subject to further moderation. All marks and grades are to be considered provisional until endorsed by the relevant School Progression Panel.

ON CAMPUS
TypeDescriptionValue
AssignmentWorked problems25%
TestMid-semester test25%
ExaminationEnd of semester examination50%

Disability Standards for Education (Commonwealth 2005)

For the purposes of considering a request for Reasonable Adjustments under the Disability Standards for Education (Commonwealth 2005), inherent requirements for this subject are articulated in the Unit Description, Learning Outcomes and Assessment Requirements of this entry. The University is dedicated to provide support to those with special requirements. Further details on the support for students with disabilities or medical conditions can be found at the Access and Inclusion website.

Academic Integrity

Integrity is a core value at Edith Cowan University, and it is expected that ECU students complete their assessment tasks honestly and with acknowledgement of other people's work. This means that assessment tasks must be completed individually (unless it is an authorised group assessment task) and any sources used must be referenced.

Breaches of academic integrity can include:

Plagiarism

Copying the words, ideas or creative works of other people, without referencing in accordance with stated University requirements. Students need to seek approval from the Unit Coordinator within the first week of study if they intend to use some of their previous work in an assessment task (self-plagiarism).

Unauthorised collaboration (collusion)

Working with other students and submitting the same or substantially similar work or portions of work when an individual submission was required. This includes students knowingly providing others with copies of their own work to use in the same or similar assessment task(s).

Contract cheating

Organising a friend, a family member, another student or an external person or organisation (e.g. through an online website) to complete or substantially edit or refine part or all of an assessment task(s) on their behalf.

Cheating in an exam

Using or having access to unauthorised materials in an exam or test.

Serious outcomes may be imposed if a student is found to have committed one of these breaches, up to and including expulsion from the University for repeated or serious acts.

ECU's policies and more information about academic integrity can be found on the student academic integrity website.

All commencing ECU students are required to complete the Academic Integrity Module.

Assessment Extension

In some circumstances, Students may apply to their Unit Coordinator to extend the due date of their Assessment Task(s) in accordance with ECU's Assessment, Examination and Moderation Procedures - for more information visit https://askus2.ecu.edu.au/s/article/000001386.

Special Consideration

Students may apply for Special Consideration in respect of a final unit grade, where their achievement was affected by Exceptional Circumstances as set out in the Assessment, Examination and Moderation Procedures - for more information visit https://askus2.ecu.edu.au/s/article/000003318.

MAT3486|2|1

School: Science

This unit information may be updated and amended immediately prior to semester. To ensure you have the correct outline, please check it again at the beginning of semester.

Your unit may be subject to government or third party COVID-19 vaccination requirements. Please consider this before enrolling in this unit, and speak with the unit coordinator if this raises any concerns.

  • Unit Title

    Multivariate Calculus
  • Unit Code

    MAT3486
  • Year

    2022
  • Enrolment Period

    2
  • Version

    2
  • Credit Points

    15
  • Full Year Unit

    N
  • Mode of Delivery

    On Campus
  • Unit Coordinator

    Dr Steven James RICHARDSON

Description

This unit deals with the calculus of functions of two and three variables and a selection of topics from vector analysis

Prerequisite Rule

(Students must pass 1 unit from MAT1236 OR Students must pass 2 units from MAT1250 AND MAT1251)

Equivalent Rule

Unit was previously coded MAT3236

Learning Outcomes

On completion of this unit students should be able to:

  1. Solve multivariate calculus problems by applying appropriate analytical and numerical techniques.
  2. Analyse applied calculus problems in multivariate contexts using appropriate analytical and numerical techniques.
  3. Effectively utilise numerical computer packages to investigate mathematical concepts in abstract and applied contexts.
  4. Independently communicate solutions to problems involving the application of analytical and numerical techniques in a coherent written form.

Unit Content

  1. Vector Valued Functions: definition; domain and limits; parametric representation of curves; differentiation and integration; unit tangent vector; tangent lines; arc length; curvature and torsion; normal and binormal vectors; curvilinear motion; normal and tangential components of acceleration.
  2. Functions of several variables: definition; domain and range graphs; level curves and level surfaces; first and second order partial derivatives; chain rule for functions of several variables; gradient vector; directional derivatives; tangent planes.
  3. Optimisation of functions of several variables: locating and characterising local extrema; optimisation on bounded domains; method of Lagrange multipliers.
  4. Double integrals over rectangular and non-rectangular regions; reversal of the order of integration; area as a double integral.
  5. Introduction to polar, cylindrical and spherical co-ordinates; double and triple integrals in polar, cylindrical and spherical co-ordinates.
  6. Vector fields: gradient, divergence and curl; line integrals, surface integrals and flux integrals; the fundamental theorem for line integrals; conservative vector fields; Green's theorem; the divergence theorem; Stokes' theorem;

Additional Learning Experience Information

One three hour lecture/tutorial per week. Use will be made of computer packages where appropriate.

Assessment

GS1 GRADING SCHEMA 1 Used for standard coursework units

Students please note: The marks and grades received by students on assessments may be subject to further moderation. All marks and grades are to be considered provisional until endorsed by the relevant School Progression Panel.

ON CAMPUS
TypeDescriptionValue
AssignmentWorked problems25%
TestMid-semester test25%
ExaminationEnd of semester examination50%

Disability Standards for Education (Commonwealth 2005)

For the purposes of considering a request for Reasonable Adjustments under the Disability Standards for Education (Commonwealth 2005), inherent requirements for this subject are articulated in the Unit Description, Learning Outcomes and Assessment Requirements of this entry. The University is dedicated to provide support to those with special requirements. Further details on the support for students with disabilities or medical conditions can be found at the Access and Inclusion website.

Academic Integrity

Integrity is a core value at Edith Cowan University, and it is expected that ECU students complete their assessment tasks honestly and with acknowledgement of other people's work. This means that assessment tasks must be completed individually (unless it is an authorised group assessment task) and any sources used must be referenced.

Breaches of academic integrity can include:

Plagiarism

Copying the words, ideas or creative works of other people, without referencing in accordance with stated University requirements. Students need to seek approval from the Unit Coordinator within the first week of study if they intend to use some of their previous work in an assessment task (self-plagiarism).

Unauthorised collaboration (collusion)

Working with other students and submitting the same or substantially similar work or portions of work when an individual submission was required. This includes students knowingly providing others with copies of their own work to use in the same or similar assessment task(s).

Contract cheating

Organising a friend, a family member, another student or an external person or organisation (e.g. through an online website) to complete or substantially edit or refine part or all of an assessment task(s) on their behalf.

Cheating in an exam

Using or having access to unauthorised materials in an exam or test.

Serious outcomes may be imposed if a student is found to have committed one of these breaches, up to and including expulsion from the University for repeated or serious acts.

ECU's policies and more information about academic integrity can be found on the student academic integrity website.

All commencing ECU students are required to complete the Academic Integrity Module.

Assessment Extension

In some circumstances, Students may apply to their Unit Coordinator to extend the due date of their Assessment Task(s) in accordance with ECU's Assessment, Examination and Moderation Procedures - for more information visit https://askus2.ecu.edu.au/s/article/000001386.

Special Consideration

Students may apply for Special Consideration in respect of a final unit grade, where their achievement was affected by Exceptional Circumstances as set out in the Assessment, Examination and Moderation Procedures - for more information visit https://askus2.ecu.edu.au/s/article/000003318.

MAT3486|2|2