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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>>
<<option chkSaveBackups>> SaveBackups
<<option chkAutoSave>> AutoSave
<<option chkRegExpSearch>> RegExpSearch
<<option chkCaseSensitiveSearch>> CaseSensitiveSearch
<<option chkAnimate>> EnableAnimations

----
Also see AdvancedOptions

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We will have a ''@@color(red):Midterm exam on Tuesday, February 12th, 2008@@''. The ''@@color(red):Final exam will be on Wednesday, March 19th, 2008, from 8-11am@@''.

Welcome to the Math 5A 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 or more ~TAs 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 Tuesdays, and will be due the following Tuesday. @@Late homework will not be accepted@@.

We will be using [[WebWork|http://hw.math.ucsb.edu/webwork/math3c-01-W08/]] this quarter. 

# [[Homework 2|hw2.pdf]]: To be handed in on Thursday, January 24th 2008, in class (in addition to the assignment on WebWork, which is due on the same day). The ''@@color(red):solutions@@'' can be found [[here|hw2_sol.pdf]].

!Carlos J. ~García-Cervera.
South Hall, Room 6707.
Office Phone: (805) 893 3681
Office Fax: (805) 893 2385
Office Hours: Tuesday & Thursday, 11am-12:30pm. 
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:

# [[Matrices|LN/3.1.- Matrices - Sums and products.pdf]]
# [[Linear Systems of Equations|LN/3.2.- Linear Systems of Equations.pdf]]
# [[The Inverse of a Matrix|LN/3.3.- The Inverse of a Matrix.pdf]] 
# [[Determinants and Cramer's Rule|LN/3.4.- Determinants and Cramer's rule.pdf]]
# [[Vector spaces and subspaces|LN/3.5.- Vector spaces and Subspaces.pdf]]
# [[Basis and Dimension|LN/3.6.- Basis and Dimension.pdf]]
# [[Differential Equations|LN/1.- Differential Equations.pdf]]
# [[Separation of Variables|LN/1.3.- Separation of Variables.pdf]]
# [[Linearity and Nonlinearity|LN/2.- Linearity and Nonlinearity.pdf]]
# [[Linearization|LN/Linearization.pdf]]

Tuesday, & Thursday, 9:30-10:45am, MUSIC Lotte Lehmann Concert Hall

[[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.

# [[Sections 3.1-3.4|SelfAssessment/sa1.pdf]]
# [[Self Assessment 2|SelfAssessment/sa2.pdf]]

Differential Equations and Linear Algebra
Tuesday & Thursday, 9:30-10:45am, MUSIC Lotte Lehmann Concert Hall

Math 3C, Winter 2008

http://www.math.ucsb.edu/~cgarcia/Courses/Math3C_W08/

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''Textbook'': //Differential Equations and Linear Algebra//, by Jerry Farlow, James E. Hall, Jean Marie ~McDill, and Beverly H. West.

''Course description'' This is the first part of the undergraduate course on Differential Equations and Linear Algebra. In this first part, we will dedicate the first few weeks to the study of fundamental concepts in Linear Algebra, such as vector spaces, basis, matrices, etc.  In the remainder of the course we will cover first order linear differential equations, and we will see some applications and examples of the concepts of Linear Algebra discussed at the beginning of the course, in the context of differential equations. By the end of the course, the following will be expected:
#A working knowledge of Linear Algebra: 
##How to solve linear systems of equations.
##How to determine if a given set is a vector space.
##How to determine the dimension of a vector space, and how to find a basis.
##To be able to determine whether a matrix has an inverse, and to be able to compute such inverse.
##To be able to operate with matrices, i.e., perform additions and multiplications.
#To be able to solve first order linear differential equations.
#To be able to determine whether a given function is a solution to a given differential equation.

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.

''Assignments and Grading Policy'': Homework will be assigned on Thursdays, and will be due the following week. We will be using [[WebWork|http://hw.math.ucsb.edu/webwork/math3c-01-W08/]], with which you will need to familiarize yourselves. There may be some handwritten assignments to hand in during the quarter. ''@@color(red):Late homework will not be accepted.@@''

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

    Final Grade = 40% Homework + 25% Midterm + 35% 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:
#Matrices: Sums and Products.
#Systems of Linear Equations.
!!!Week 2:
#The Inverse of a Matrix.
#Determinants and Cramer's Rule.
#Vector Spaces and Subspaces.
!!!Week 3:
#Vector Spaces and Subspaces (cont.).
#Basis and Dimension.
!!!Week 4:
#Dynamical Systems: Modeling.
#Solutions and Directions Fields: Qualitative Analysis.
#Separation of Variables.
!!!Week 5:
#Separation of Variables (cont.).
#Approximation Methods: Numerical Analysis.
!!!Week 6:
#''@@color(red):Midterm Exam.@@''
#Approximation Methods: Numerical Analysis (cont.).
!!!Week 7:
#Picard's Theorem.
#Linear Equations: The Nature of Their Solutions.
!!!Week 8:
#Solving the ~First-Order Linear Differential Equation.
#Growth and Decay Phenomena.
!!!Week 9:
#Linear Models: Mixing and Cooling.
#Nonlinear Models: Logistic Equation.
!!!Week 10:
#Nonlinear Models (cont.).
#Systems of Differential Equations.

!!Rena Levitt
South Hall, Room 6431D.
Office Hours: Monday 2-3pm.
Mathlab Hours: Wednesday 3-5pm.

!!Joules Nahas
South Hall, Room 6431L.
Office Hours: Friday 11am-12pm.
Mathlab Hours : Wednesday 2-3pm; Thursday 3-4pm.

!!Jarrod Pickens
South Hall, Room 6431K.
Office Hours: Wednesday 12-1pm. 
Mathlab Hours: Wednesday 2-4pm.

# Week 1 & 2: ''Sections 3.1, and 3.2''.
## Objectives for Section 3.1: 
### Become familiar with matrices, and their operations: addition and subtraction, multiplication, and transposition.
## Objectives for Section 3.2:
### To be able to solve a linear system of equations of any size.
### To be able to determine whether a given system of equations has a solution or not. In case the system has solutions, to be able to determine whether the solution is unique, or whether there are more than one solutions. If there are more than one solutions, to be able to find all of them.
# Week 3: ''Section 3.3 and 3.4''
## Objectives for Section 3.3:
### Introduce the inverse of a matrix with respect to the product of matrices.
### Properties of the inverse of a matrix.
### To be able to determine the inverse of a matrix.
## Objectives for Section 3.4:
### To introduce the concept of determinant, and its basic properties.
### Cramer's rule: How to solve a linear system of equations, and how to compute the inverse of a matrix using determinants.
# Week 4: ''Section 3.5 and 3.6''
## Objectives for Section 3.5:
### Introduction of the notion of vector space, as an abstract mathematical structure.
### To be able to determine whether a given set is a vector space or not.
## Objectives for Section 3.6:
### To be able to determine whether a set of vectors is linearly independent, and what their linear span is.
### Given a vector space, to be able to find a basis, and determine its dimension.
### Relation between the rank of a matrix, and the linear span of its columns.
### To be able to determine whether a given set of functions are linearly independent: The Wronskian.
### Connection between solving a system of equations and the linear span of the columns of the coefficient matrix.