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  2. Differential Equations [MAT2437]

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

    Differential Equations

  • Unit Code

    MAT2437

  • Year

    2016

  • Enrolment Period

    1

  • Version

    2

  • Credit Points

    15

  • Full Year Unit

     N

  • Mode of Delivery

    On Campus

Description

This unit introduces students to the theory of ordinary differential equations and explores a selection of solution methods including series solutions and Laplace transforms.

Prerequisite Rule

Students must pass 1 units from MAT1236

Equivalent Rule

Unit was previously coded MAT2236

Learning Outcomes

On completion of this unit students should be able to:

  1. Communicate their understanding of concepts and techniques, and explain their solutions to problems involving differential equations, in a coherent written form.
  2. Make effective use of a computer algebra system as an aid to solving differential equations.
  3. Solve a wide variety of first and second-order ODEs.
  4. Use the method of Laplace transforms to solve initial value problems.
  5. Use the method of separation of variables and Fourier series solutions to solve PDEs.

Unit Content

  1. First-order ODEs: linear; separable, direction fields; existence and uniqueness theorems; homogeneous and exact; integrating factor method; applications to mechanics and electric circuit theory.
  2. Introduction to PDEs: Boundary value problems; Fourier series solutions; separation of variables; application to the heat equation.
  3. Laplace Transforms: Definition of Laplace transform; Shifting Theorems; Heaviside step function; inverse Laplace transforms and Convolution Theorem; Dirac delta functions; solving systems of equations by Laplace transforms.
  4. Second-order ODEs: reduction of order; method of undetermined coefficients; variation of parameters; application to forced oscillations.
  5. Systems of First-Order ODEs: homogeneous and non-homogeneous linear systems; non-linear systems; phase portraits and stability

Additional Learning Experience Information

Lectures, tutorials and computer laboratories.

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.

Due to the professional competency skill development associated with this Unit, student attendance/participation within listed in-class activities and/or online activities including discussion boards is compulsory. Students failing to meet participation standards as outlined in the unit plan may be awarded an I Grade (Fail - incomplete). Students who are unable to meet this requirement for medical or other reasons must seek the approval of the unit coordinator.

ON CAMPUS
TypeDescriptionValue
AssignmentPractical problems20%
TestIn-semester tests15%
Laboratory Work ^MATLAB based lab activities15%
Examination ^End of semester examination50%

^ Mandatory to Pass

Text References

  • ^ Abell, M. L. & Braselton, J. P. (2014). Introductory Differential Equations (4th ed.). New York, NY: Academic Press.
  • Blanchard, P. Devanwy, R & Hall, G. (2010). Differential equations. Pacific Grove, CA: Brooks/Cole.
  • Brannan, J.R., & Boyce, W.E. (2011). Differential equations - An introduction to modern methods and applications (2nd ed.). New York, NY: John Wiley.
  • Brown, C. (2007). Differential equations [electrionic resource]: a modelling approach. Los Angeles, CA: Sage Publications.
  • Zill, D.G. & Cullen, M. (2009). Differential equations with boundary-value problems. Pacific Grove, CA: 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.

MAT2437|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

    Differential Equations

  • Unit Code

    MAT2437

  • Year

    2016

  • Enrolment Period

    2

  • Version

    2

  • Credit Points

    15

  • Full Year Unit

     N

  • Mode of Delivery

    On Campus

Description

This unit introduces students to the theory of ordinary differential equations and explores a selection of solution methods including series solutions and Laplace transforms.

Prerequisite Rule

Students must pass 1 units from MAT1236

Equivalent Rule

Unit was previously coded MAT2236

Learning Outcomes

On completion of this unit students should be able to:

  1. Communicate their understanding of concepts and techniques, and explain their solutions to problems involving differential equations, in a coherent written form.
  2. Make effective use of a computer algebra system as an aid to solving differential equations.
  3. Solve a wide variety of first and second-order ODEs.
  4. Use the method of Laplace transforms to solve initial value problems.
  5. Use the method of separation of variables and Fourier series solutions to solve PDEs.

Unit Content

  1. First-order ODEs: linear; separable, direction fields; existence and uniqueness theorems; homogeneous and exact; integrating factor method; applications to mechanics and electric circuit theory.
  2. Introduction to PDEs: Boundary value problems; Fourier series solutions; separation of variables; application to the heat equation.
  3. Laplace Transforms: Definition of Laplace transform; Shifting Theorems; Heaviside step function; inverse Laplace transforms and Convolution Theorem; Dirac delta functions; solving systems of equations by Laplace transforms.
  4. Second-order ODEs: reduction of order; method of undetermined coefficients; variation of parameters; application to forced oscillations.
  5. Systems of First-Order ODEs: homogeneous and non-homogeneous linear systems; non-linear systems; phase portraits and stability

Additional Learning Experience Information

Lectures, tutorials and computer laboratories.

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.

Due to the professional competency skill development associated with this Unit, student attendance/participation within listed in-class activities and/or online activities including discussion boards is compulsory. Students failing to meet participation standards as outlined in the unit plan may be awarded an I Grade (Fail - incomplete). Students who are unable to meet this requirement for medical or other reasons must seek the approval of the unit coordinator.

ON CAMPUS
TypeDescriptionValue
AssignmentPractical problems20%
TestIn-semester tests15%
Laboratory Work ^MATLAB based lab activities15%
Examination ^End of semester examination50%

^ Mandatory to Pass

Text References

  • ^ Abell, M. L. & Braselton, J. P. (2014). Introductory Differential Equations (4th ed.). New York, NY: Academic Press.
  • Blanchard, P. Devanwy, R & Hall, G. (2010). Differential equations. Pacific Grove, CA: Brooks/Cole.
  • Brannan, J.R., & Boyce, W.E. (2011). Differential equations - An introduction to modern methods and applications (2nd ed.). New York, NY: John Wiley.
  • Brown, C. (2007). Differential equations [electrionic resource]: a modelling approach. Los Angeles, CA: Sage Publications.
  • Zill, D.G. & Cullen, M. (2009). Differential equations with boundary-value problems. Pacific Grove, CA: 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.

MAT2437|2|2