Course information
Instructor: Prof. John Hunter
Lectures: MWF 9:00–9:50 a.m., Hart Hall 1150
Discussion sections:
MAT125A-A01. Thur 9:00–9:50 a.m., Hutchison Hall 102
MAT125A-A02. Thur 1:10–2:00 p.m., Hoagland Hall 113
Office hours: MWF 2:30–3:30 p.m.
CRN: 29189 (A01); 29190 (A02)
Text: Elementary Real Analysis, Thompson, Bruckner, and Bruckner, Second Edition, 2008
TA:
Matthew Reed
Office: MSB 2139
Office hours:
T 12:00–2:00 p.m.
W 12:00–1:00 p.m.
Department of Mathematics
University of California
Davis, CA 95616, USA
University of California
Davis, CA 95616, USA
e-mail: jkhunter@ucdavis.edu
Office Phone: (530) 554-1397
Office: Mathematical Sciences Building 3230
Syllabus
The Department Syllabus is here.
Topics
Depending on how much time is available,
I plan to cover roughly the following sections
from the text by Thompson, Bruckner, and Bruckner:
-
Chapter 5. Continuous Functions
- 5.1 Introduction toLimits
- 5.2 Properties of limits
- 5.4 Continuity
- 5.5 Properties of continuous functions
- 5.6 Uniform continuity
- 5.7 Extremal properties
- 5.8 Darboux property
- 5.9 Points of discontinuity
-
Chapter 7. Differentiation
- 7.1 Introduction
- 7.2 Definition of the derivative
- 7.3 Properties of the derivative
- 7.4 Continuous differentiability
- 7.5 Local extrema
- 7.6 Mean value theorem
- 7.12 Taylor polynomials
-
Chapter 9. Sequences and Series
- 9.1 Introduction
- 9.2 Pointwise limits
- 9.3 Uniform limits
- 9.4 Uniform convergence and continuity
- 9.6 Uniform convergence and derivatives
- 10.1 Introduction
- 10.2 Power series: Convergence
- 10.3 Uniform convergence
- 10.4 Functions represented by power series
- 10.5 Taylor series
- 13.1 Introduction
- 13.2 Examples
- 13.4 Convergence
- 13.5 Sets in a metric space
- 13.6 Functions