MATH 3003 Analysis
Credit Points 10
Legacy Code 200023
Coordinator Rehez Ahlip Opens in new window
Description Analysis provides the theoretical basis of real and complex numbers, including differentiation and integration. Topics include: field axioms and completeness, sequences, series, convergence, compactness, continuity, differentiability, integrability, and related theorems in both the real and complex number systems.
School Computer, Data & Math Sciences
Discipline Mathematics
Student Contribution Band HECS Band 1 10cp
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Level Undergraduate Level 3 subject
Pre-requisite(s) MATH 2001
Equivalent Subjects LGYA 3794 - Advanced Mathematical Topics
Learning Outcomes
- Explain the difference between pointwise and uniform convergence
- Test for convergence sequences and uniform convergence of series of functions on a given interval
- Apply interchange theorems for uniformly convergent sequences and series
- Explain the definition of the Riemann integral
- Calculate upper and lower sums and integrals of simple functions
- Prove and apply theorems concerning classes of integrable functions and integrability of sums and products
- Find limits of sequences via the use of Riemann sums
- Test for differentiability of a function of a complex variable using the Cauchy-Riemann equations
- Explain what is meant by an analytic function
- Apply the Cauchy-Riemann equations to harmonic functions
- Parametrize a path and then to evaluate some complex integrals directly
- Evaluate complex integrals by using results such as the Cauchy integral formulae and residue theorem
- Work out Taylor and Laurent series for some of the simpler functions
Subject Content
- completeness
- limits
- compactness
- cauchy sequences
- uniform Continuity
- uniform convergence
- Continuity
- differentiability
- Rolle's theorem and mvt
- Riemann integral
- differentiation of complex functions
- cauchy-Riemann equations
- analytic functions
- contour integrals
- Cauchy's theorem
- Taylor and Laurent series
- residues
- evaluation of certain real integrals
Assessment
The following table summarises the standard assessment tasks for this subject. Please note this is a guide only. Assessment tasks are regularly updated, where there is a difference your Learning Guide takes precedence.
| Item | Length | Percent | Threshold | Individual/Group Task |
|---|---|---|---|---|
| Intra-session Exam | 50 minutes | 20 | N | Individual |
| Intra-session Exam | 50 minutes | 20 | N | Individual |
| Final Exam | 2 hours | 60 | N | Individual |
Prescribed Texts
- Bartle D F & Sherbert D R Inroduction to Real Analysis. Wiley John, 2010
- Osbourne A D , Complex Variables and their Applications,1st Edition , 1999. Pearson Education
Teaching Periods
Autumn
Campbelltown
Day
Subject Contact Rehez Ahlip Opens in new window
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Parramatta - Victoria Rd
Day
Subject Contact Rehez Ahlip Opens in new window