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To get started with this blank TiddlyWiki, you'll need to modify the following tiddlers:
* SiteTitle & SiteSubtitle: The title and subtitle of the site, as shown above (after saving, they will also appear in the browser title bar)
* MainMenu: The menu (usually on the left)
* DefaultTiddlers: Contains the names of the tiddlers that you want to appear when the TiddlyWiki is opened
You'll also need to enter your username for signing your edits: <<option txtUserName>>

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Your username for signing your edits. Write it as a WikiWord (eg JoeBloggs)

<<option txtUserName>>
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<<option chkAutoSave>> AutoSave
<<option chkRegExpSearch>> RegExpSearch
<<option chkCaseSensitiveSearch>> CaseSensitiveSearch
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----
Also see AdvancedOptions

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We will have a ''@@color(red):Midterm exam on Tuesday, November 10th, 2009@@''. The ''@@color(red):Final exam will be on Tuesday, December 8th, 2009, from 12-3pm@@''.

Welcome to the Math 118A Wiki!

To navigate this page, simply follow the links on your left. 

# [[Instructor]]: Who I am, and how to contact me.
# [[Teaching Assistant]]: There will be one TA for this course. 
# [[Location]]: Where the class will meet.
# [[Syllabus]]: Information about the course.
# [[Weekly Readings]]: Here I will post the readings for each week, and the lesson objectives. Please take a look at it before the class.
# [[Homework]]: I will post the homework here. 
# [[Lecture Notes]]: I will post the notes from class here.
# [[Self-Assessment Questions]]: This will help you study for the midterm and the final exam.
# [[Exams]]: Information about the midterm and final exams.

Once you open a tiddler, you can close it by clicking on its link again. Alternatively you can use the close button over on the right. 

This page is experimental, and hopefully more services will be added as the course progresses, so come back often.

Homework will be assigned on Thursday, and will be collected at the beginning of the class on the following Thursday. ''@@color(red): Late homework will not be accepted. If you have a predictable absence, you will need to hand it in earlier@@''. 

''Assignments:''
#[[Homework 1|hw1.pdf]]: Due on October 8th, 2009. 
#[[Homework 2|hw2.pdf]]: Due on October 15th, 2009. [[Solutions|hw2_sol.pdf]], courtesy of Jordan Fisher.
#[[Homework 3|hw3.pdf]]: Due on October 22nd, 2009. [[Solutions|hw3_sol.pdf]], courtesy of Jordan Fisher.
#[[Homework 4|hw4.pdf]]: Due on October 29th, 2009.  [[Solutions|hw4_sol.pdf]], courtesy of Jordan Fisher.
#[[Homework 5|hw5.pdf]]: Due on November 5th, 2009. 
#[[Homework 6|hw6.pdf]]: Due on November 19th, 2009. 
#[[Homework 7|hw7.pdf]]: Due on December 3rd, 2009.

!Carlos J. ~García-Cervera.
South Hall, Room 6707.
Office Phone: (805) 893 3681
Office Fax: (805) 893 2385
Office Hours: Tuesday and Thursday, from 11:25am-12:25pm.
Main Website: http://www.math.ucsb.edu/~cgarcia

In this course we will study mostly second order linear ordinary differential equations of the form
ay' '+by'+cy = f(x).

Since the equation is linear, it turns out that the set of solutions forms a finite dimensional vector space, which explains why we study Linear Algebra in this course. 

These are the notes from class:

# [[Metric Spaces|LN/Metric Spaces (II).pdf]].
# [[Sequences and Series|LN/sequences and Series.pdf]].

Tuesday and Thursday, 12;30-1:45pm, GIRV 1116

[[Instructor]]
[[Teaching Assistant]]
[[Location]]
[[Syllabus]]
[[Weekly Readings]]
[[Homework]]
[[Lecture Notes]]
[[Self-Assessment Questions]]
[[Exams]]

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Try to answer the following questions without looking in the book. If you do not feel comfortable with them, please review the corresponding chapters in the book, and them attempt to solve them again.

# [[Self-Assessment Questions 1|sa1.pdf]].
# [[Self-Assessment Questions 2|sa2.pdf]].

Introduction to Real Analysis
Tuesday & Thursday, 12:30-1:45pm, GIRV 1116

Math 118A, Fall 2009

http://www.math.ucsb.edu/~cgarcia/Courses/Math118A_F09/

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''Textbook:'' //Principles of Mathematical Analysis//, by Walter Rudin, 3rd edition.

''Additional bibliography:''
# //Mathematical Analysis//, by T.M. Apostol.
# //Calculus//, by M. Spivak.
# //Introduction to Real Analysis//, by K. Stromberg.

''Course description:'' With this course, we begin an in-depth study of mathematical analysis. The objective of this part of the year-long course is to provide the student with a working knowledge of analysis of functions in one variable. The following concepts will be fundamental:
# Evaluation of limits of sequences, series, and functions.
# Continuity and differentiability.
# Extrema and convexity.
# Pointwise convergence and Uniform convergence.

I will not hand out //practice exams// or anything like that. As part of the course, you should develop the necessary skills to study this subject. In order to help you study, I will periodically post [[Self-Assessment|Self-Assessment Questions]] questions. You do not need to hand them in. Those questions will help you know whether you are studying effectively or not, and whether you need to review some parts of the material covered in class.

''Prerequisites:'' Math 8.

''Assignments and grading:'' Homework will be assigned on Thursday, and will be collected at the beginning of the class on the following Thursday.   ''@@color(red): Late homework will not be accepted. If you have a predictable absence, you will need to hand it in earlier. @@''

There will be a midterm and a final exam.  Your final grade
for the course will be decided according to the following scheme:

Final Grade = 20\% Homework + 30\% Midterm + 50\% Final.

''Syllabus:'' During this course we will try to follow the following
schedule. However, much like everything said earlier, this is subject
to change.
# ''Week 1:'' Real and Complex Numbers.
## Axiomatic definition of the real numbers. 
##Euclidean spaces: basic definitions.
# ''Weeks 2 & 3:'' Basic Topology.
## Metric Spaces.
## Compact Sets.
## Perfect Sets.
## Connected Sets.
# ''Weeks 4, 5, & 6:'' Sequences and Series.
## Accumulation points.
## Convergence of sequences.
## Subsequences. 
## Divergent sequences.
## Monotone sequences.
## Bounded sequences and the number {\it e}.
## Upper and Lower limits.
## ~Bolzano-Weierstrass' Theorem.
## Cauchy Theorem.
## Series: Convergence.
## Series with positive terms: Fundamental convergence criteria.
## Absolute convergence.
## Addition and multiplication of series.
## Methods to compute or estimate the sum of a series.
## Divergent series.
## Power Series: Radius of convergence.
# ''Weeks 7, & 8:''  Continuity.
## Definition of continuity.
## Continuous functions defined by power series.
## Classification of discontinuities.
## Weierstrass' theorem.
## Uniform continuity and the ~Heine-Borel theorem.
## Lipschitz Functions.
# ''Week 9:'' Sequences and Series of Functions.
## Definition of functional sequences and series: pointwise convergence and uniform convergence.
## Series of continuous functions: Weierstrass' M-criterion.
# ''Weeks 10, 11 & 12:'' Differentiability.
## Definition of derivative and geometric interpretation.
## Concept of differential.
## Rules of differentiation: product, quotient, and chain rules.
## Rolle's theorem and Mean Value Theorem. 
## Derivative of a functional series.
## Derivatives of high order and Leibniz's formula.
## L'Hospital's rule.
## Taylor's theorem.
## Extrema of functions. 
## Convex functions and Jensen's inequality.

!!Jordan Fisher.
South Hall, Room 6432M.
Office Hours: Wednesday 4-5pm;  ''Mathlab PM'' from 5-7pm on Monday.

# Week 2: ''Chapter 1, Chapter 2''
## Objectives for Chapter 1:
### Formal definition of the Real and Complex numbers.
### Euclidean space: Definition of norm and its properties.
### ~Cauchy-Schwarz inequality.
## Objectives for Chapter 2:
### Open sets, closed sets, and neighborhoods.
### Definition of metric spaces, and norm spaces.
### Compactness and Connectedness.
# Week 4: ''Chapter 3''
## Objectives for this chapter:
### Convergence of sequences in a metric space.
### Upper and lower limits, and subsequences.
### Cauchy sequences, and its relation to convergent sequences.
### Special sequences: Monotonicity.
### Series.
### The number e.