MATH348.Spring2010.Syllabus
Lecture Slides
There are various lecture slides associated with the course. They were developed during the Spring of 2010 and are intended to deliver important bulk concepts while avoiding the need to write down 'every little thing.' Specifically, the slides address:
1. Definitions that are not useful for me to write and students to rewrite during lecture.
2. Derivations that will never need to be reproduced but need to be communicated quickly because they lead to important consequences.
3. Derivations that will need to be reproduced and have been recorded for clarity.
Listed in each slide set are:
Associated Section/Pages from EK.AEM
Associated Lecture Notes
Associated Homework Assignments
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00.LS.Introduction
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01.LS.Classical Vector Spaces
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02.LS.Geometry in R^n
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03.LS.KinematicsAndDynamics
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03.LS.KinematicsAndDynamics - Those Evil Natured Robots
Linear Algebra and its Applicationsby Peter D. Lax
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04.LS.Abstract Vector Spaces
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05.LS.Fourier Series to Fourier Integral to Fourier Transform - Update 4/5/2010
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06.LS.1D Heat Equation-Separation of Variables
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07.LS.The Acoustic Approximation and wave equations in 1D
Lecture Notes
There is a set of lecture notes associated with the course. They were developed during the Fall of 2008 through the Spring of 2009 and are intended to outline key-points, objectives and goals from the text in the order we cover them. Listed in each set are:
Associated Sections/Pages from EK.AEM
Suggested Problems from EK.AEM
Brief Outline of Lecture Talking Points
Lecture Objectives
Lecture Goals
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00.LN.Overview And Outline
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01.LN.LinearDefinitions : Updated 1.27.2010. Footnotes have been added referencing locations in the text where these definitions can be found.
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02.LN.Introduction To Linear Equations
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03.LN.Solving Linear Systems
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04.LN.Square Systems - Determinants and Matrix Inversion
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05.LN.Introduction to Linear Vector Spaces
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06.LN.Chapter 7 - Wrap Up
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07.LN.Eigenproblems
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08.LN.Diagonalization
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09.LN.Introduction to Fourier Series : Review of Periodic and Symmetric Functions
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10.LN.Complex Fourier Series
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11.LN.Fourier Integral to Fourier Transform
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12.LN.Fourier Transform
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13.LN.IntroToPDE
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14.LN.HeatEquation
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15.LN.WaveEquation
Assignments
The assignments for this course have reached a steady-state. Consequently, solutions are often available through students who have taken the course in the past. Since these resources might not be available to all students, I have drafted a set of solutions to these homework assignments which I make available through this site. These solutions were, more or less, finalized during the Spring of 2010 and represents the end of an evolution starting around 2006. Outside of the lecture itself, these homeworks and solutions represents some of the oldest parts of the course and many of the ancestors can be found on older ticc pages.
In the past the homeworks tended to have a good deal of discussion providing context to a problem so that both the mechanics and concepts could be gleaned. However, after talking with some students and course reviews I decided to move the commentary to the solutions in favor of a more streamlined problem statement. It is unclear whether this latest incarnation is 'better' than the past but what is clear is that they won't be regressing unless someone else wants to revamp them. If you want to see the previous versions then visit the older ticc pages. If you find any typos in these solutions then I would appreciate you letting me know. They are pretty clean but they could always be `cleaner.'
With that said, I must make emphasize the following point:
Caveat Emptor : We will work from these problems and since solutions are
readily available it is up to the individual user to make sure that they
are LEARNING the material. If you buy into a program of procrastination
followed by rapid and thoughtless recreation then you may find an
inadequate product, which cannot be returned.
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Homework0 - Due Jan. 18th by 5:00pm
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Homework0 - Solutions
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Homework1 - Due Feb. 3rd by 5:00pm - Note: Updated 1/19/2010, fixed a typo in problem 2 matrix 2, a_{22} = -3
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Homework1 - Solutions
Graphics for Homework 1
Geometry of Problem 2 System 1
Geometry of Problem 2 System 2
Geometry of Problem 2 System 3
Geometry of Problem 2 System 4
Geometry of Problem 2 System 5
Interpolated Parabolas of Problem 4 Set 1
Interpolated Parabolas of Problem 4 Set 2
Geometry of Least Squares Problem of Problem 4 Set 2
Interpolated Parabolas of Problem 4 Set 3
Fourier Transform
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Homework2 - Due Feb. 12th by 5:00pm : 1) Header Box Updated 2) Problem 4.2 \lambda = n^2
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Homework2 - Solutions : Update - There were a couple of typos, nothing major, corrected. 2/8/2010 : Updated again - One of the typos I corrected last time was not a typo at all (1.4). I have put it back in its place.
Homework 3 - Note : I have just noticed a pesky typo. Equation (2) from the assignment, (26) from the solutions, should read l_1 u(a) + k_1 u'(a) = 0 and NOT l_1 u(a) + k_1 u'(b) = 0
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Homework3 - Due Feb. 22th by 5:00pm : Update - There were multiple things going on here. Once I updated the assignment with an old copy that was missing problems.... Ugh, it's all fixed up now. :)
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Homework3 - Solutions
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Homework4 - Due: March 12th
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Homework4 - Solutions
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Homework5 - Due: March 31st
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Homework5 - Solutions
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Homework6 - Due: April 12th
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Homework6 - Solutions
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Homework7 - Due April 28 - Last edits (minor) at 4:31pm.
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Homework7 - Solutions - Last edits (minor) at 4:31pm : Note at a step in problem 1.1 I use quantities like I1 and I2. By these I mean l1 and l2.
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Homework8 - Due May 3
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Homework8 - Solutions
Exams
Exam I
Exam I will be held on March 1st in class. There will be no notecards or calculators. The exam will have five required questions and contain material outlined in the following review:
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Exam 1 - Review Sheet
The following exams with solutions are posted for your review.
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Exam 1 - Fall2008
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Exam 1 - Fall2008 Solutions
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Exam I - Spring2009
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Exam I - Spring2009 Solutions
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Exam I - Summer2009
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Exam I - Summer2009 Solutions
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Exam I - Fall2009
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Exam I - Fall2009 Solutions
Exam I - Statistics
Mean = 37.15 (74,31%)
Median = 38 (76%)
Mode = 47 (94%)
A's = 34, B's = 17, C's = 24, D's = 18, F's = 25, Total Number of Exams = 118
A's = 29%, B's = 14%, C's = 20%, D's = 15%, F's = 21 %
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Exam I - Spring2010
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Exam I - Spring2010 Solutions
Exam II
Exam II will be held on April 16th in class. There will be no notecards or calculators. The exam will have five required questions and contain material outlined in the following review:
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Exam 2 - Review Sheet
The following are the results of Q+A's from previous semesters:
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Exam 2 - Spring2009 Q + A
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Exam 2 - Fall2008 Q + A
The following exams with solutions are posted for your review.
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Exam II - Spring2009 See Soln for problem 3 graph.
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Exam II - Spring2009 Solutions
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Exam 2 - Fall2008
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Exam 2 - Fall2008 Solutions
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Exam II - Summer2009
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Exam II - Summer2009 Solutions
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Exam II - Fall2009
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Exam I - Fall2009 Solutions - Graphs Included
Exam II - Statistics
Mean = 36.5 (72.5%)
Median = 37.5 (75%)
A's = 9, B's = 32, C's = 38, D's = 19, F's = 16, Total Number of Exams = 114
A's = 8%, B's = 28%, C's = 33%, D's = 17%, F's = 14 %
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Exam II - Spring2010
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Exam I - Spring2010 Solutions
Final Exam
The final exam will be held Saturday May 8th from 7:00pm-9:00pm. The classes will be testing in the following rooms:
Class : Meeting Time : Testing Room : Proctor
MATH348B : 11:00am Section : Petroleum Hall : Jennifer Strong
MATH348C : 1:00pm Section : CT 102 : Scott Strong
MATH348D : 2:00pm Section : CO209 : Doug Poole
Since we will be in different rooms it is very important that you go to the room associated with your section.
There will be no notecards or calculators. The exam will have ten required questions and contain material outlined in the following review:
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Final Exam - Review Sheet
The following is an old 50 minute PDE exam, which should give you some idea of the content and structure of the PDE portion of the exam.
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OLD PDE EXAM - See Soln for the graph in problem 1
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OLD PDE EXAM - SOLN
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