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

    Introductory Applied Mathematics
  • Unit Code

    MAT1137
  • Year

    2017
  • 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 is intended for those students who have previously studied mathematics to a minimum level of MAT1108 Foundations of Mathematics (or equivalent - for example, ATAR Mathematics Methods passed at year 11 level). It is also appropriate for those students requiring bridging into MAT1236 Calculus 1, or for students from non-mathematics disciplines wishing to enhance their mathematics skills. It is also the recommended entry point for students who have not performed strongly in ATAR Mathematics Methods (or equivalent) and who therefore require further consolidation and extension.

The unit covers mathematical modelling using functions and graphs, and also concepts, techniques and applications of differential and integral calculus and analytic geometry. The applications of differentiation include the solution of optimisation problems. For integration the applications to area and volume are considered. The section on analytic geometry focuses on the properties of vectors in 2 and 3-dimensional space and the solution of linear systems of equations.

Prerequisite Rule

Students must pass 1 unit from MAT1108

Equivalent Rule

Unit was previously coded MAT1136, UPU0111

Learning Outcomes

On completion of this unit students should be able to:

  1. Apply the techniques of calculus to solve optimisation problems, and to calculate areas and volumes.
  2. Communicate in written form their understanding of concepts and their solutions to problems involving the application of techniques from calculus and analytic geometry.
  3. Demonstrate a proficiency in basic techniques of differentiation and integration.
  4. Demonstrate an understanding of the concepts of limit, continuity, differentiation, and integration.
  5. Demonstrate competence in constructing and solving systems of linear equations.
  6. Demonstrate competence in matrix and vector arithmetic.

Unit Content

  1. Algebra - Revision of algebraic manipulation including factorisation; adding, multiplying and dividing fraction expressions; and index laws. Solution of equations and inequalities involving rational expressions.
  2. Calculus - Differentiation (power, product, quotient and chain rules) and differentiability; derivatives of exponential, logarithm and trigonometric functions; higher order derivatives; anti-differentiation of polynomial, trigonometric, and exponential functions; integration by substitution; definite integrals, the area problem and the fundamental theorem of calculus.
  3. Calculus Applications - Optimisation; curve sketching (rational functions); rectilinear motion; related rates problems; areas between and under curves; volumes of solids of revolution.
  4. Functions and Graphs - Functions and relations; function notation; domain and range; translations and scaling; composite functions; inverse functions; exponential functions and natural base; logarithm functions, logarithm laws and change of base; limits and continuity.
  5. Matrices - Matrix addition, subtraction and multiplication; special matrices (identity, singular, diagonal, column and row); determinants of 2 by 2 matrices; solution of systems of linear equations (no more than 3 by 3).
  6. Trigonometry - Introduction of radian measure; trigonometric identities; sine, cosine and tangent functions; unit circle; solution of trigonometric equations.
  7. Vectors - Vectors in 2D and 3D; vector addition and scalar multiplication; vector magnitude; dot product and cross product (in 3D); parallel and perpendicular vectors; position vectors, relative displacement and relative velocity

Additional Learning Experience Information

Lecture and workshops.

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
Assignment ^Essential skills exercises10%
AssignmentProblem solving assignments15%
TestIn-semester test25%
Examination ^End of semester examination50%

^ Mandatory to Pass


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.

MAT1137|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

    Introductory Applied Mathematics
  • Unit Code

    MAT1137
  • Year

    2017
  • 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 is intended for those students who have previously studied mathematics to a minimum level of MAT1108 Foundations of Mathematics (or equivalent - for example, ATAR Mathematics Methods passed at year 11 level). It is also appropriate for those students requiring bridging into MAT1236 Calculus 1, or for students from non-mathematics disciplines wishing to enhance their mathematics skills. It is also the recommended entry point for students who have not performed strongly in ATAR Mathematics Methods (or equivalent) and who therefore require further consolidation and extension.

The unit covers mathematical modelling using functions and graphs, and also concepts, techniques and applications of differential and integral calculus and analytic geometry. The applications of differentiation include the solution of optimisation problems. For integration the applications to area and volume are considered. The section on analytic geometry focuses on the properties of vectors in 2 and 3-dimensional space and the solution of linear systems of equations.

Prerequisite Rule

Students must pass 1 unit from MAT1108

Equivalent Rule

Unit was previously coded MAT1136, UPU0111

Learning Outcomes

On completion of this unit students should be able to:

  1. Apply the techniques of calculus to solve optimisation problems, and to calculate areas and volumes.
  2. Communicate in written form their understanding of concepts and their solutions to problems involving the application of techniques from calculus and analytic geometry.
  3. Demonstrate a proficiency in basic techniques of differentiation and integration.
  4. Demonstrate an understanding of the concepts of limit, continuity, differentiation, and integration.
  5. Demonstrate competence in constructing and solving systems of linear equations.
  6. Demonstrate competence in matrix and vector arithmetic.

Unit Content

  1. Algebra - Revision of algebraic manipulation including factorisation; adding, multiplying and dividing fraction expressions; and index laws. Solution of equations and inequalities involving rational expressions.
  2. Calculus - Differentiation (power, product, quotient and chain rules) and differentiability; derivatives of exponential, logarithm and trigonometric functions; higher order derivatives; anti-differentiation of polynomial, trigonometric, and exponential functions; integration by substitution; definite integrals, the area problem and the fundamental theorem of calculus.
  3. Calculus Applications - Optimisation; curve sketching (rational functions); rectilinear motion; related rates problems; areas between and under curves; volumes of solids of revolution.
  4. Functions and Graphs - Functions and relations; function notation; domain and range; translations and scaling; composite functions; inverse functions; exponential functions and natural base; logarithm functions, logarithm laws and change of base; limits and continuity.
  5. Matrices - Matrix addition, subtraction and multiplication; special matrices (identity, singular, diagonal, column and row); determinants of 2 by 2 matrices; solution of systems of linear equations (no more than 3 by 3).
  6. Trigonometry - Introduction of radian measure; trigonometric identities; sine, cosine and tangent functions; unit circle; solution of trigonometric equations.
  7. Vectors - Vectors in 2D and 3D; vector addition and scalar multiplication; vector magnitude; dot product and cross product (in 3D); parallel and perpendicular vectors; position vectors, relative displacement and relative velocity

Additional Learning Experience Information

Lecture and workshops.

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
Exercise ^Essential skills exercises5%
ExercisePractice exercises10%
AssignmentProblem solving assignments10%
TestMid-semester test25%
Examination ^End of semester examination50%

^ Mandatory to Pass

Core Reading(s)

  • Stewart, J. (2012). Calculus (7 (ISE). Melbourne, Australia: Thompson/Brooks Cole.

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.

MAT1137|2|2