Information about this course can be found
here on the Pure Mathematics web page.
Email me by clicking
here.
My consulting time for this course is 1.30-2.30 on Thursdays. If you cannot
come at that time email or ring me to make an appointment.
Tutorials at 2.00 Monday in Room 1.08 and 3.00 Monday in Room G05 in Weeks 3, 5, 7, 9,
11 and 13.
There will be only one lecture in Week 13 on Monday the 7th June at 3.00 in G05
when I will revise and talk about the examination.
Handouts
Class Exercises and Tutorial Exercises
Course guide
All references are to the textbook. Real Analysis. A First Course
Russell A.Gordon
- Week 1:
- 1.1 What is a real number ?
- 1.2 Absolute Value, Interval and Inequalities. Omitted Lemma 1.11, Theorem 1.12,
Theorem 1.13.
- 1.3 The Completeness Axiom
- Week 2:
- Finish 1.3.
- 1.4 Countable and Uncountable Sets.
- 1.5 Real functions. This adds nothing
to what you know already from Maths 1 so I will omit it but assume you know it.
- 2.1 Convergent Sequences up to Theorem 2.5
- Week 3:
- Tutorials on Monday. Room 108 at 2.00 and Room G08 at 3.00.
- 2.1 Finish convergent sequences starting with Theorem 2.5. Omit Def 2.6
- 2.2 Monotone Sequences and Cauchy Sequences
- Week 4:
- Finish Monotone Sequences and Cauchy Sequences
- 2.3 Subsequences. Omit Def 2.20, Thm 2.21 and Thm 2.22.
- 3.1 The Limit of a Function
- Week 5:
- Finish 3.1 The Limit of a Function
- 3.2 Continuous Functions
- 3.3 Intermediate and Extreme Values
- Week 6:
Finish 3.3. Omit Def 3.23, Thm 3.24, Def 3.25, Thm 3.26.
- 3.4 Uniform Continuity. Omit Thm 3.29, Thm 3.30.
- Omit 3.5 Monotone Functions
- 4.1 The Derivative of a Function.
- Week 7:
- 4.2 The Mean Value Theorem. Omit Thm 4.15, 4.16 4.17 and 4.18
- Omit 4.3 Further Topics on Differentiation.
- Week 8:
- 5.1 The Riemann Integral
- 5.2 Conditions for Riemann Integrability
- Week 9:
- More about 5.2 Conditions for Riemann Integrability
- 5.3 The Fundamental Theorem of Calculus
- Week 10:
- More about 5.2 Conditions for Riemann Integrability
- 5.3 The Fundamental Theorem of Calculus
- Week 11:
- More about 5.3 The Fundamental Theorem of Calculus
- Omit 5.4 and 5.5.
- 6.1 Convergence of infinite series
- 6.2 The Comparison Test. Omit Thm 6.7.
- Week 12:
Last changed Wednesday, 28 November, 2007.
© 2007 The University of Adelaide.
|