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 MathematicsUnit Code
MAT1137Year
2016Enrolment Period
1Version
1Credit Points
15Full Year Unit
N
Mode of Delivery
On Campus
Description
This unit is intended for those students who have previously studied mathematics to a minimum level of either MAT1108 Foundations of Mathematics, or WACE MAT3A/3B (or equivalent). 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 WACE MAT3C/3D (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
(Scaled Score in MAT3A/3B > 49.99 OR Students must pass 1 units from MAT1108)
Equivalent Rule
Unit was previously coded MAT1136, UPU0111
Learning Outcomes
On completion of this unit students should be able to:
- Apply the techniques of calculus to solve optimisation problems, and to calculate areas and volumes.
- Communicate in written form their understanding of concepts and their solutions to problems involving the application of techniques from calculus and analytic geometry.
- Demonstrate a proficiency in basic techniques of differentiation and integration.
- Demonstrate an understanding of the concepts of limit, continuity, differentiation, and integration.
- Demonstrate competence in constructing and solving systems of linear equations.
- Demonstrate competence in matrix and vector arithmetic.
Unit Content
- Algebra - Revision of algebraic manipulation including factorisation; adding, multiplying and dividing fraction expressions; and index laws. Solution of equations and inequalities involving rational expressions.
- 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.
- Calculus Applications - Optimisation; curve sketching (rational functions); rectilinear motion; related rates problems; areas between and under curves; volumes of solids of revolution.
- 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.
- 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).
- Trigonometry - Introduction of radian measure; trigonometric identities; sine, cosine and tangent functions; unit circle; solution of trigonometric equations.
- 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| Type | Description | Value |
|---|
| Assignment | Problem solving assignment | 20% |
| Test | In-semester tests | 30% |
| Examination ^ | End of semester examination | 50% |
^ Mandatory to Pass
Text References
- ^ Stewart, J. (2012). Calculus (7th. I.S.E.). Melbourne: Thompson/Brooks Cole.
- Hughes-Hallett, D., et.al. (2005). Calculus: Single and multivariable (4th ed.). New York: Wiley.
- Larson, R., Hostetler, R., & Edwards, B. (2006). Calculus (8th ed.). New York: Houghton Mifflin.
- Anton, H., Bivens, I., & Davis, S. (2005). Calculus (8th ed.). New York: Wiley.
^ 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.
MAT1137|1|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 MathematicsUnit Code
MAT1137Year
2016Enrolment Period
2Version
1Credit Points
15Full Year Unit
N
Mode of Delivery
On Campus
Description
This unit is intended for those students who have previously studied mathematics to a minimum level of either MAT1108 Foundations of Mathematics, or WACE MAT3A/3B (or equivalent). 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 WACE MAT3C/3D (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
(Scaled Score in MAT3A/3B > 49.99 OR Students must pass 1 units from MAT1108)
Equivalent Rule
Unit was previously coded MAT1136, UPU0111
Learning Outcomes
On completion of this unit students should be able to:
- Apply the techniques of calculus to solve optimisation problems, and to calculate areas and volumes.
- Communicate in written form their understanding of concepts and their solutions to problems involving the application of techniques from calculus and analytic geometry.
- Demonstrate a proficiency in basic techniques of differentiation and integration.
- Demonstrate an understanding of the concepts of limit, continuity, differentiation, and integration.
- Demonstrate competence in constructing and solving systems of linear equations.
- Demonstrate competence in matrix and vector arithmetic.
Unit Content
- Algebra - Revision of algebraic manipulation including factorisation; adding, multiplying and dividing fraction expressions; and index laws. Solution of equations and inequalities involving rational expressions.
- 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.
- Calculus Applications - Optimisation; curve sketching (rational functions); rectilinear motion; related rates problems; areas between and under curves; volumes of solids of revolution.
- 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.
- 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).
- Trigonometry - Introduction of radian measure; trigonometric identities; sine, cosine and tangent functions; unit circle; solution of trigonometric equations.
- 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| Type | Description | Value |
|---|
| Assignment | Problem solving assignment | 20% |
| Test | In-semester tests | 30% |
| Examination ^ | End of semester examination | 50% |
^ Mandatory to Pass
Text References
- ^ Stewart, J. (2012). Calculus (7th. I.S.E.). Melbourne: Thompson/Brooks Cole.
- Anton, H., Bivens, I., & Davis, S. (2011). Calculus (10th ed.). New York, NY: Wiley.
- Briggs, W. (2011). Calculus: early transcendentals. Boston: Pearson.
- Morris, C., & Stark, M. (2015). Fundamentals of Calculus [electronic resourse]. Hoboken, New Jersey: John Wiley & Sons, Inc.
- Hughes-Hallet, D., Gleason, A.M, McCallum, W.G., et al (2013). Calculus: Single and multivariable (6th ed.). New York, NY: Wiley.
- Rogawski, J. (2015). Calculus (3rd ed.). New York, NY: Macmillan Education.
^ 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.
MAT1137|1|2
