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)

Corequisite(s)

Nil

Teaching method

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)
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Fee-paying program for domestic and international students
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* 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.