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  2. Multivariate Calculus [MAT3486]

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.

  • Unit Title

    Multivariate Calculus

  • Unit Code

    MAT3486

  • Year

    2021

  • 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;

Learning Experience

Students will attend on campus classes as well as engage in learning activities through ECUs LMS

JoondalupMount LawleySouth West (Bunbury)
Semester 213 x 2 hour lectureNot OfferedNot Offered
Semester 213 x 1 hour workshopNot OfferedNot Offered

For more information see the Semester Timetable

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 Misconduct

Edith Cowan University has firm rules governing academic misconduct and there are substantial penalties that can be applied to students who are found in breach of these rules. Academic misconduct includes, but is not limited to:

  • plagiarism;
  • unauthorised collaboration;
  • cheating in examinations;
  • theft of other students' work;

Additionally, any material submitted for assessment purposes must be work that has not been submitted previously, by any person, for any other unit at ECU or elsewhere.

The ECU rules and policies governing all academic activities, including misconduct, can be accessed through the ECU website.

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.

  • Unit Title

    Multivariate Calculus

  • Unit Code

    MAT3486

  • Year

    2021

  • 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;

Learning Experience

Students will attend on campus classes as well as engage in learning activities through ECUs LMS

JoondalupMount LawleySouth West (Bunbury)
Semester 213 x 2 hour lectureNot OfferedNot Offered
Semester 213 x 1 hour workshopNot OfferedNot Offered

For more information see the Semester Timetable

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 Misconduct

Edith Cowan University has firm rules governing academic misconduct and there are substantial penalties that can be applied to students who are found in breach of these rules. Academic misconduct includes, but is not limited to:

  • plagiarism;
  • unauthorised collaboration;
  • cheating in examinations;
  • theft of other students' work;

Additionally, any material submitted for assessment purposes must be work that has not been submitted previously, by any person, for any other unit at ECU or elsewhere.

The ECU rules and policies governing all academic activities, including misconduct, can be accessed through the ECU website.

MAT3486|2|2