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  2. Multivariate Calculus [MAT3486]

Faculty of Health, Engineering and Science

School: Engineering

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

    2015

  • Enrolment Period

    1

  • Version

    1

  • Credit Points

    15

  • Full Year Unit

     N

  • Mode of Delivery

    On Campus

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

Equivalent Rule

Unit was previously coded MAT3236

Learning Outcomes

On completion of this unit students should be able to:

  1. Communicate their understanding of concepts in multivariate calculus and explain their solutions to problems involving techniques of multivariate calculus in written form.
  2. Describe and analyse motion along a curve; and evaluate surface integrals.
  3. Effectively use a computer algebra system as an aid in solving multivariate calculus problems.
  4. Evaluate integrals of functions of two or three variables over bounded domains.
  5. Find the domain of definition of a function of several variables, calculate level curves and surfaces; calculate first and second order partial derivatives.
  6. Solve unconstrained and constrained nonlinear optimisation problems using differentiation.

Unit Content

  1. Double integrals over rectangular and non-rectangular regions; reversal of the order of integration; area as a double integral.
  2. First and second order partial derivatives; chain rule for functions of several variables.
  3. Functions of several variables: definition; domain and range graphs; level curves and level surfaces; traces.
  4. Introduction to polar, cylindrical and spherical co-ordinates; double and triple integrals in polar, cylindrical and spherical co-ordinates.
  5. Optimisation of functions of several variables; method of Lagrange multipliers.
  6. Parametric representation of curves; tangent lines and arc length in polar co-ordinates.
  7. Unit tangent and normal vectors of a curve; curvature; velocity and acceleration vectors for motion along a curve.
  8. Vector fields: gradient, divergence and curl; line integrals, surface integrals and flux integrals.

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 Board of Examiners.

ON CAMPUS
TypeDescriptionValue
AssignmentWorked problems30%
TestMid-semester test20%
Examination ^End of semester examination50%

^ Mandatory to Pass

Text References

  • ^ Stewart, J. (2011). Calculus (ISE) (7th ed.). Thompson/Brooks Cole.

^ Mandatory reference

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|1|1

Faculty of Health, Engineering and Science

School: Engineering

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

    2015

  • Enrolment Period

    2

  • Version

    1

  • Credit Points

    15

  • Full Year Unit

     N

  • Mode of Delivery

    On Campus

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

Equivalent Rule

Unit was previously coded MAT3236

Learning Outcomes

On completion of this unit students should be able to:

  1. Communicate their understanding of concepts in multivariate calculus and explain their solutions to problems involving techniques of multivariate calculus in written form.
  2. Describe and analyse motion along a curve; and evaluate surface integrals.
  3. Effectively use a computer algebra system as an aid in solving multivariate calculus problems.
  4. Evaluate integrals of functions of two or three variables over bounded domains.
  5. Find the domain of definition of a function of several variables, calculate level curves and surfaces; calculate first and second order partial derivatives.
  6. Solve unconstrained and constrained nonlinear optimisation problems using differentiation.

Unit Content

  1. Double integrals over rectangular and non-rectangular regions; reversal of the order of integration; area as a double integral.
  2. First and second order partial derivatives; chain rule for functions of several variables.
  3. Functions of several variables: definition; domain and range graphs; level curves and level surfaces; traces.
  4. Introduction to polar, cylindrical and spherical co-ordinates; double and triple integrals in polar, cylindrical and spherical co-ordinates.
  5. Optimisation of functions of several variables; method of Lagrange multipliers.
  6. Parametric representation of curves; tangent lines and arc length in polar co-ordinates.
  7. Unit tangent and normal vectors of a curve; curvature; velocity and acceleration vectors for motion along a curve.
  8. Vector fields: gradient, divergence and curl; line integrals, surface integrals and flux integrals.

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 Board of Examiners.

ON CAMPUS
TypeDescriptionValue
AssignmentWorked problems30%
TestMid-semester test20%
Examination ^End of semester examination50%

^ Mandatory to Pass

Text References

  • ^ Stewart, J. (2011). Calculus (ISE) (7th ed.). Thompson/Brooks Cole.

^ Mandatory reference

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|1|2