ECU Web Unit Outline
 
FACULTY OF HEALTH, ENGINEERING AND SCIENCE
SCHOOL OF ENGINEERING
Full Unit Outline - Enrolment Approved Wednesday, 4 June 2014
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 Calculus 1
UNIT CODE MAT1236
CREDIT POINTS 15
FULL YEAR UNIT No
PRE-REQUISITES MAT1137 - Introductory Applied Mathematics , or
WACE MAT3C/3D, or
TEE Calculus
MODE OF DELIVERY On-campus
  This version of the unit will be offered from 1/07/2014
DESCRIPTION

This unit is intended for students who already have a basic level of understanding of differential and integral calculus and its applications. Students will be introduced to more advanced techniques of calculus and its application required for foundational study in engineering and applied science.

 

Although students with WACE MAT3C/3D will be given the option to enroll directly into MAT1236 Calculus 1 they need to be aware that they will not have all of the assumed knowledge if they have not completed MAS3C/3D. To cover this content gap, students will be provided with bridging material on the unit Blackboard site. Students who are not mathematically strong (e.g. who do not have a mark of at least 70% in WACE MAT3C/3D), or who struggle with the bridging material provided, are encouraged to enroll in MAT1137 Introductory Applied Mathematics before progressing to MAT1236 in a later semester.
 
LEARNING OUTCOMES

On completion of this unit, students should be able to:

  1. demonstrate competence in complex arithmetic;
  2. demonstrate competence in vector calculus and its application to curvilinear motion;
  3. demonstrate competence in differentiation of implicit, inverse and hyperbolic functions;
  4. identify and apply appropriate integration techniques;
  5. apply appropriate differentiation and integration techniques to solve applied problems;
  6. solve first order separable and linear differential equations in both abstract and applied contexts;
  7. identify key features of functions of two variables, evaluate partial derivatives, and apply optimisation techniques in applied problems;
  8. utilise Fourier and Taylor series in approximating functions;
  9. communicate their understanding of concepts, and explain their solutions to problems involving the application of calculus techniques, in a coherent written form.
 
UNIT CONTENT
  1. Functions - Review of Algebra, review of functions (domain, range, composition, exponentials and logarithms); inverse functions; limits and continuity; piece-wise defined functions; L'Hopitals rule.
  2. Calculus - Review of derivatives and differentiability; implicit differentiation; derivatives of parametric equations; inverse trigonometric functions and their derivatives; hyperbolic functions and their derivatives; review of integration and the fundamental theorem of calculus; trigonometric integrals; integration by substitution, by parts, by completing the square and by partial fractions; improper integrals; integration using tables.
  3. Differential Equations - First order separable differential equations; first order linear differential equations; applications.
  4. Vector Calculus - Vector functions (domain and range); differentiation and integration; curvilinear motion.
  5. Functions of Several Variables - Domain and range; partial derivatives; critical points and classification; maxima and minima (second derivative test); optimisation.
  6. Applied Calculus - Utilise techniques for differentiation and integration and solving differential equations in applied contexts.
  7. Series - Taylor series approximations of functions; Fourier series approximations to functions; differentiation and integration of series.
  8. Complex numbers - Definition of 'i'; complex solutions of quadratics; complex plane; Cartesian form (addition, subtraction, multiplication and division); polar form (multiplication and division); conjugates (properties and location in complex plane); reciprocal of non-zero complex number; defining regions of the complex plane with equations and inequalities; De Moivres's theorem; solutions of z^n=C in the complex plane; Euler's formula.
 
TEACHING AND LEARNING PROCESSES
Lectures and tutorials.
 
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.
 

Item

On-Campus Assessment

Value

Mandatory to Pass

Assignment

Problem solving assignment

20%

Test

In-semester tests

30%

Examination

End of semester exam

50%

Yes
 
TEXTS
Stewart, J. (2012). Calculus (7th ed., ISE). Melbourne, Australia: Thomson/Brooks Cole.
 
SIGNIFICANT REFERENCES
Anton, H., Bivens, I., & Davis, S. (2011). Calculus (10th ed.). New York, NY: Wiley.
Edwards, C., & Penny, D. (2002). Calculus and analytic geometry (6th ed.). New York, NY: Prentice Hall.
Ellis, R., & Gulick, D. (2004). Calculus with analytic geometry (6th ed.). Fort Worth, TX: Saunders College Publishers.
Hughes-Hallet, D., Gleason, A.M, McCallum, W. G., et al (2013). Calculus: Single and multivariable (6th ed.). New York, NY: Wiley.
Larson, R., Hostetler, R., & Edwards, B. (2006). Calculus (8th ed.). New York, NY: Houghton Mifflin.
 
 
 
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