Calculus 2

Course aim

To develop concepts in calculus and apply them to problems using analytic and software techniques. To develop elementary skills for proving mathematical statements.

Course content

Module 1: Introduction to Analysis

Numerical sequences, examples, definition of limit, properties of limits, also lim inf and lim sup; Numerical series, examples (including geometric, harmonic, telescopic, and p-series). Convergence tests: general term test, comparison test, ratio test, root test, integral test, alternating series test. Absolute and conditional convergence; Power series: Motivation, formula for coefficients, radius of convergence, examples. Term-by-term integration and differentiation. Power series of the exponential, sine, cosine, logarithm. Uniform convergence. Abel’s theorem. Applications.

Module 2: ODE's and Techniques of Integration

Linear and separable differential equations of first order. Inverse trigonometric functions and their derivatives, hyperbolic functions. Techniques of integration: Integration by parts, integration using partial fractions, trigonometric integrals, trigonometric substitutions. Improper integrals. Applications of integration in mechanics: area, volume of regular bodies, centre of mass, moment of inertia, work. Linear differential equations of second order: reduction of order, homogenous and inhomogeneous equations, constant coefficient o.d.e's, applications in mechanics and electrical circuits. MATLAB exercises.

Textbook(s)

Edwards, C.H. and Penney, D.E. 2008, Calculus, 7th, Prentice Hall

1950, MATLAB, Version 7 or later

Prerequisite(s)

Common to all relevant programs
Subject Area & Catalogue Number	Course Name
MATH 1054	Calculus 1

Corequisite(s)

Nil

Teaching method

Component	Duration
INTERNAL, MAWSON LAKES
Lecture	4 hrs (2x2 hrs) x 13 weeks
Tutorial	1 hour x 12 weeks
Computer Practical	1 hour x Wks 6, 8, 10, 12

Note: These components may or may not be scheduled in every study period. Please refer to the timetable for further details.

Assessment

Continuous assessment, Examination, MATLAB Group Project

Fees

EFTSL*: 0.125
Commonwealth Supported program (Band 2)
To determine the fee for this course as part of a Commonwealth Supported program, go to:
How to determine your Commonwealth Supported course fee. (Opens new window)

Fee-paying program for domestic and international students
International students and students undertaking this course as part of a postgraduate fee paying program must refer to the relevant program home page to determine the cost for undertaking this course.

Non-award enrolment
Non-award tuition fees are set by the university. To determine the cost of this course, go to:
How to determine the relevant non award tuition fee. (Opens new window)

Not all courses are available on all of the above bases, and students must check to ensure that they are permitted to enrol in a particular course.

* Equivalent Full Time Study Load. Please note: all EFTSL values are published and calculated at ten decimal places. Values are displayed to three decimal places for ease of interpretation.