Ma 001d:  Series (Winter 2016-17)

ANNOUNCEMENTS

Registration for Winter term opens Thursday, November 17, 2016.

This page was last updated:  .


COURSE DESCRIPTION

This is a course intended for those students in the special calculus-intensive section (Section 1) of Ma 1a who did not have infinite series, Taylor polynomials and complex numbers during Ma 1a.


PREREQUISITES

Ma001a Section 1


SCHEDULE

TR 09:00 - 09:55, 151 Sloan.


INSTRUCTORS

Elena Mantovan
PROFESSOR OF MATHEMATICS
EXECUTIVE OFFICER FOR MATHEMATICS
262 Sloan
626-395-4342


TA's

Daniel Siebel

dsiebel@caltech.edu

Sloan 356


OFFICE HOURS

Sundays 8-9pm in Sloan 351


POLICIES

Grades

Based on weekly homework.

Homework Policy

Homework problems will be assigned weekly and posted online. There will be a total of six homework sets. The problems assigned in a given week are due the following Monday at 4:00 PM, turned in as one set. Please turn in the problems to the math department's box for Ma1d on the 2nd floor in Sloan.

For privacy reasons, please staple a cover sheet to your assignments, meaning a sheet blank except for your name. Your score will be displayed behind the cover sheet when the homework is returned to you.

In your solutions, you may use results from class, from Apostol, or the results stated as problems already assigned. Be explicit about citations when using such results; e.g., state the theorem number or the exercise number.

Late Homework

You can get one extension for one homework set of 2 days, no questions asked, if requested before the deadline. In all other circumstances you have to provide a letter from the Dean or from the Health Center.

Collaboration

Each assignment will consist of four problems. The first problem is supposed to test your basic understanding. You should do it by yourself. The other three problems will be more advanced and you are encouraged to collaborate on those. However, your write-up must be entirely your own.


TOPICS COVERED

Convergence of sequences, Convergence of series, Power series and Taylor expansions, Uniform convergence of sequences of functions, Complex Numbers and Laurent Series, Fourier series


TEXTBOOKS

Apostol, Tom M., Calculus, Volume 1, 1991, Wiley, ISBN: 0-471-00005-1.


LECTURE NOTES

Date Description
Tuesday, 10th Jan Convergence of Sequences: Definition and Examples
Thursday, 12th Jan Lim sup, lim inf and Cauchy sequences
Tuesday, 17th Jan Convergence of Series: ratio test, integral test
Thursday, 19th Jan Alternive sign test, n-th root test
Tuesday, 24th Jan Cauchy's Product Formula; Power Series, definition of exp, sin, cos
Thursday, 26th Jan Defintion of cosh, sinh; examples of Taylor expansions
Tuesday, 31st Jan Taylor approximation of log, L'Hospital; definition of Uniform Convergence
Thursday, 5th Feb Examples for uniform convergence, integrals of uniform limits
Tuesday, 7th Feb Differentiating & integrating power series term by term; review of complex numbers
Thursday, 9th Feb Open and closed sets; vanishing orders
Tuesday, 14th Feb Laurent Series, Computing the inverse of Taylor series
Thursday, 16th Feb Example for Laurent Series converging in annulus, Definition of trigonometric polynomials
Tuesday, 21th Feb Computing examples for Fourier Series

HOMEWORK

Due Date Problem Sets Solutions
Monday, 23rd Jan, 4pm Problem Set 1  
Monday, 30th Jan, 4pm Problem Set 2  
Monday, 6th Feb, 4pm Problem Set 3  
Monday, 13th Feb Problem Set 4  
Tuesday, 21th Feb, 4pm Problem Set 5  
Monday, 27th Feb, 4pm Problem Set 6  
     
     

EXAMS

None


READING