UC Davis Math 125B
Real Analysis

Basic information

CRN code: 72372
Room/Time of the Lectures: 10:00-11:40a.m. MTWR in Wellman 115
Instructor: Professor Alexander Soshnikov
Office: 3140 Mathematical Sciences Building
Office Hours: F 10:00a.m.- 11:50a.m., plus by appointment.
E-mail: soshniko@math.ucdavis.edu
 
Midterm: August 28 (Monday), in class.
Final: September 14 (Thursday), in class.
Grading: HW Problem sets 10%, Midterm 40%, Final 50%
Webpage: http://www.math.ucdavis.edu/~soshniko/125b
 

Textbooks:

An Introduction to Analysis by William R. Wade (4th Edition) Prentice Hall, 2004, ISBN#0-13-145333-5.

Other Useful Textbooks:

Elementary Real Analysis (Second Edition, 2008) by Brian S. Thomson, Judith B. Bruckner, and Andrew M. Bruckner

pdf file of the textbook available at http://classicalrealanalysis.com/download.aspx

On Google Docs: [docs.google.com]

On MS SkyDrive: [skydrive.live.com]

and Understanding Analysis by Stephen Abbott

Syllabus

is available at http://www.math.ucdavis.edu/courses/syllabi

Homework

Homework will be assigned each Thursday and will be due in class following Monday.

No late submission allowed except for cases of true emergency.

While the students are allowed (and encouraged!) to discuss homework problems in groups, each student has to write down his/her own homework!

Extra problems (i.e. problems not from the textbook) are part of the hws and WILL contribute to the grade.

Homework 1 (due Monday, August 14, in class):

Reading:

Sections 5.1-5.3

Problems from the textbook: 5.1.1 (b), 5.1.3, 5.1.5, 5.1.9, 5.1.10, 5.2.2, 5.2.3 b), 5.2.5, 5.2.8, 5.2.11

Solutions of HW1

Homework 2 (due Monday, August 21, in class):

Reading:

Sections 5.3-5.4, 8.1-8.2

Problems from the textbook: 5.3.2, 5.3.5, 5.3.6, 5.3.9, 5.4.0, 5.4.3, 5.4.5, 5.4.8, 8.2.1, 8.2.4

Solutions of HW2 (part 1)

Solutions of HW2 (part 2)

Homework 3 (due Monday, August 28, in class):

Reading:

Sections 11.1-11.3

Problems from the textbook: 11.1.3, 11.1.4, 11.1.5 (c), 11.1.6 (b), 11.2.1, 11.2.3, 11.2.5, 11.2.8, 11.2.9, 11.3.3

Trial Midterm

Trial Midterm

Homework 4 (due Tuesday, September 5, in class):

Reading:

Sections 11.3-11.6

Problems from the textbook: 11.3.5, 11.4.1, 11.4.3, 11.4.6, 11.4.9, 11.5.1, 11.5.4, `11.5.5, 11.5.6, 11.6.1 (b)

Homework 5 (due Tuesday, September 12, in class):

Reading:

Sections 11.6, 12.1-12.2

Problems from the textbook: 11.6.2 c), 11.6.3, 11.6.4, 11.6.5, 11.6.7, 12.1.2, 12.1.4, 12.1.8, 12.2.2, 12.2.5

Lectures:

Lecture 1 (August 7):

Introduction. The Riemann Integral (Section 5.1)

Lecture 2 (August 8):

The Riemann Intergal (Section 5.1). Riemann Sums (Section 5.2)

Lecture 3 (August 9):

Riemann Sums (Section 5.2)

Lecture 4 (August 10):

Riemann Sums (Section 5.2)

Lecture 5 (August 14):

Fundamental Theorem of Calculus (Section 5.3)

Lecture 6 (August 15):

Improper Integrals (Section 5.4)

Lecture 7 (August 16):

Improper Integrals (Section 5.4).

Lecture 8 (August 17):

Euclidean Spaces. Linear Transformations (Sections 8.1-8.2)

Lecture 9 (August 21):

Partial Derivatives and Partial Integrals (Section 11.1).

Lecture 10 (August 22):

Partial Derivatives and Partial Integrals (Section 11.1).

Lecture 11 (August 23):

Differentiability (Section 11.2).

Lecture 12 (August 24):

Differentiability (Section 11.2). Derivatives, Differentials, and Tangent Planes (Section 11.3)

Midterm Exam (August 28)

Grading Curve for the midterm: A

Lecture 13 (August 29):

Derivatives, Differentials, and Tangent Planes (Section 11.3). Chain Rule (Section 11.4).

Lecture 14 (August 30):

Mean Value Theorem and Taylor's Formula (Section 11.5)

Lecture 15 (August 31):

Inverse Function Theorem (Section 11.6)

Lecture 16 (September 5):

Implicit Function Theorem (Section 11.6)

Lecture 17 (September 6):

Integrating Indicator Functions (Section 12.1)

Lecture 18 (September 7):

Multivariate Riemann integral (Section 12.2).

Lecture 19 (September 11):

Iterated integrals. Fubini Theorem (Section 12.3)

Lecture 20 (September 12):

Change of variables (Section 12.4)

Lecture 21 (September 13):

Change of variables (Section 12.4)

Final Exam (September 14)

Trial Final Exam