ECU Web Unit Outline
 
FACULTY OF HEALTH, ENGINEERING AND SCIENCE
SCHOOL OF ENGINEERING
Full Unit Outline - Enrolment Approved Tuesday, January 24, 2012
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
DESCRIPTION

This unit covers differential and integral calculus of functions of a single variable and introduces students to sequences and series, first order differential equations, and complex arithmetic.

 

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 done MAS3C/3D. To cover this content gap these students will either need to attend the intense bridging course offered in the week prior to the start of each semester or self-study this content through materials that will be available on the Blackboard site for this unit. Students who are not mathematically strong (e.g. <70% in MAT3C/3D), or who struggle in the bridging course 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. identify hyperbolic and inverse circular functions, graph them and calculate their derivatives;
  3. integrate functions by parts; integrate rational functions of polynomials; evaluate improper integrals;
  4. evaluate indeterminate forms; determine whether infinite sequences and series converge or diverge; represent functions by their Taylor series and Fourier Series;
  5. solve a variety of first-order ordinary differential equations; and
  6. 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 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. Sequences and Series - Infinite sequences; infinite series; convergence tests (integral test, comparison test, alternating series test); absolute convergence; power series, radius and interval of convergence; representing functions as power series; Taylor series; Taylor polynomials; Fourier Series, convergence, differentiation and integration of Fourier series.
  5. 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.
 
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 assignment

30%

Test

In-semester tests

20%

Examination

End of semester exam

50%

 
TEXTS
Stewart, J. (2008). Calculus (6th ed., ISE). Melbourne: Thompson / Brooks Cole.
 
SIGNIFICANT REFERENCES
Anton, H., Bivens, I., & Davis, S. (2005). Calculus (8th ed.). New York: Wiley.
Edwards, C., & Penny, D. (2002). Calculus and analytic geometry (6th ed.). New York: Prentice-Hall.
Ellis, R., & Gulick, D. (2004). Calculus with analytic geometry (6th ed.). Fort Worth: Saunders College Publishers.
Hughes-Hallet, D., Gleason, A.M, McCallum, W. G., 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.
 
 
 
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