ECU Web Unit Outline
 
FACULTY OF HEALTH, ENGINEERING AND SCIENCE
SCHOOL OF ENGINEERING
Full Unit Outline - Enrolment Approved Thursday, 15 December 2011
Disclaimer
This unit outline 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
CREDIT POINTS 15
FULL YEAR UNIT No
PRE-REQUISITES MAT1108 - Foundations of Mathematics , or
WACE unit MAT3A/3B
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 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.
 
LEARNING OUTCOMES

On completion of this unit students should be able to:


  1. demonstrate an understanding of the concepts of limit, continuity, differentiation, and integration;
  2. demonstrate a proficiency in basic techniques of differentiation and integration;
  3. apply the techniques of calculus to solve optimisation problems, and to calculate areas and volumes;
  4. demonstrate competence in constructing and solving systems of linear equations;

  5. demonstrate competence in matrix and vector arithmetic; and

  6. communicate in written form their understanding of concepts and their solutions to problems involving the application of  techniques from calculus and analytic geometry.
 
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. Trigonometry - Introduction of radian measure; trigonometric identities; sine, cosine and tangent functions; unit circle; solution of trigonometric equations.
  3. 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.
  4. 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.
  5. Calculus Applications - Optimisation; curve sketching (rational functions); rectilinear motion; related rates problems; areas between and under curves; volumes of solids of revolution.
  6. 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
  7. 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).
 
TEACHING AND LEARNING PROCESSES
Lecture and workshops.
 
GRADUATE ATTRIBUTES

The following graduate attributes will be developed in this unit

  • Ability to communicate
  • Critical appraisal skills
  • Ability to generate ideas 
 
ASSESSMENT
Grading Schema 1
 
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.
 
Students must achieve at least 85% in a pre-requisite threshold skills test to be eligible to pass the unit.
 

Item

On-Campus Assessment

Value

  

Assignment

Problem Solving

20%

Test

In-semester tests*

30%

Examination

End of semester examination

50%

 
*This assessment item includes multiple assessments.
 
TEXTS
Stewart, J. (2008), Calculus (6th. I.S.E.). Melbourne: Thompson/Brooks Cole.
 
SIGNIFICANT REFERENCES
Anton, H., Bivens, I., & Davis, S. (2005). Calculus (8th ed.). New York: Wiley.
Callahan, J., & Hoffman, K. (1995). Calculus in context. New York: W. H. Freeman.
Edwards, C., & Penny, D. (1994). Calculus and analytic geometry (4th ed.). Upper Saddle River NJ: Prentice-Hall.
Ellis, R., & Gulick, D. (1994). Calculus with analytic geometry (5th ed.). Fort Worth: Saunders College Publishers.
Finney, R., & Thomas, G. (1990). Calculus. Reading MA: Addison-Wesley.
Grossman, S. (1992). Calculus (5th ed.). Fort Worth: Saunders College Publishers.
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.
Stein, S., & Barcellos, A. (1992). Calculus with analytic geometry (5th ed.). New York: McGraw-Hill.
Trim , D. (1993). Calculus. Englewood Cliffs, NJ: Prentice Hall.
Varberg, D. et al. (2000). Calculus (8th ed.). Englewood Cliffs, NJ: Prentice Hall.
 
 
 
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, Graduate Attributes 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 Student Equity, Diversity and Disability Service website:
http://intranet.ecu.edu.au/student/support/student-equity
 
 


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.
ECU Web Unit Outline