Math 525a Sylabus - Fall '17
We will cover chapters 1 to 4 in the textbook (Trench) and some additional
topics.
Chapter 1 The Real Numbers
1.1 The Real Number System
1.2 Mathematical Induction
1.3 The Real Line
Additional topics
Complex numbers
Logic
Construction of reals
Chapter 2 Differential Calculus of Functions of One Variable
2.1 Functions and Limits
2.2 Continuity
2.3 Differentiable Functions of One Variable
2.4 L'Hospital's Rule
2.5 Taylor's Theorem
Chapter 3 Integral Calculus of Functions of One Variable
3.1 Definition of the Integral
3.2 Existence of the Integral
3.3 Properties of the Integral
3.4 Improper Integrals
3.5 A More Advanced Look at Existence of the Proper Riemann Integral
Additional topics
Riemann-Stieljes integral
Chapter 4 Infinite Sequences and Series
4.1 Sequences of Real Numbers
4.2 Earlier Topics Revisited With Sequences
4.3 Infinite Series of Constants
4.4 Sequences and Series of Functions
4.5 Power Series
Additional topics
Metric spaces