MATH348.Spring2010.Syllabus
Lecture Slides
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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
Lecture Notes
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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
Assignments
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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 26 - Last edits (minor) at 4:31pm.
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Homework7 - Solutions - Last edits (minor) at 4:31pm
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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 = xx
Median = xx
A's = x, B's = x, C's = x, D's = x, F's = x, Total Number of Exams = xx
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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
Other Materials
Linear Algebra
Three Planes in Space
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Three Planes in Space - Four Different Ways
Legend for the Animations
Red = First Plane Equation
Orange = Second Plane Equation
Yellow = Third Plane Equation
Green = Column Space of A (AKA the set of all linear combination of the pivot columns of A)
Blue = Right Hand Side for non-homogeneous problem.
Animation : Ax=0 with oo-many solutions that form a line in space.
Animation : Ax=b with oo-many solutions that form a line in space.
Animation : Ax=b with a single solution
Animation : Ax=b with no solutions
Linear Algebra Software
Linear Algebra Toolkit
Fourier Methods
Review of Functions
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Special Angles and the Unit Circle
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A61.TrigIdentities
Odd and Even Functions (Wikipedia) : (see Also 09.LN)
Periodic Functions (Wikipedia) : (See Also 09.LN)
Fourier Series
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FS for f(x}=x, x \in (-\pi,\pi)
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FS for f(x}=Exp(Abs(x)), x \in (-\pi,\pi)
Fourier Series - Wikipedia
Gibbs Phenomenon - Wikipedia
Fourier Transform
Fourier Transform - Wikipedia
Wikipedia - Sinc Function
Mathworld - Sinc Function
Wikipedia - Nyquist-Shannon Sampling Theorem
Mathworld - Convolution (Animation)
Convolution and Diffraction (Animations)
Convolution and Diffraction (Animations)
Wikipedia - Convolution (Animation)
Green's Function - Wikipedia
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Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125}
Partial Differential Equations
Ordinary Differential Equations
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Review of Ordinary Differential Equations (DRAFT - 11/16/09)
Millennium Bridge - Wikipedia
You Tube Video - Millennium Bridge Resonance
Heat Equation
Heat Movie 1 - abs(x)
Heat Movie 2 - parabola
Heat Movie 3 - Double V
Heat Movie 4 - Forced Heat Equation with B.C. u(0,t)=u(L,t)=0
Heat Movie 5 - Forced Heat Equation with B.C. u_{x}(0,t)=u_{x}(L,t)=0
Wave Equation
1D Wave Equation
Wave on a 1-D Sting with Fixed Endpoints
Wave on a 1-D Sting with Fixed Endpoints - Animated with first 5 Fourier Modes (Fundamental Mode in Red)
Wave on a 1-D Sting with FLAT Endpoints from HW10
Wave on a 1-D Sting with FLAT Endpoints from HW10 - Animated with first 5 Fourier Modes (Fundamental Mode in Red)
Traveling Wave :u0(x) = − tanh(x): Red = Right Traveling, Blue=Left Traveling, Black = Superposition
2D Wave Equation Rectangular and Polar
Rectangular Membrane Movie 1 -Text Example pg577
Rectangular Membrane 2 -Text Example pg577
Applet - Pretty Cool
Rectangular Membrane Modes
Animations of Rectangular Membrane Modes - Pretty Good
Animations done by Dr. Russell - All sorts of stuff!
The Well-Tempered Timpani By Richard K. Jones
Vibrating Membrane1 - 12.9.1 Example
Vibrating Membrane2 - 12.9.1 Example
Vibrating Membrane3 - 12.9.1 Example
Vibrating Membrane4 - 12.9.1 Example
Nonlinear Wave Phenomenon
Wikipedia Article on Shock Waves
Animation of Shock Wave Formation in Pressure Field
Shock Wave (Plane) - You Tube 1
Shock Wave (Plane) - You Tube 2
Shock Wave (Explosion) - You Tube 3
Shock Wave (Explosion) - You Tube 4 : Ignore The the cartoon bubble
Shock Wave (Simulation) - You Tube 5 : Notice the distortion of the expanding wave-front
NASA - Shock Wave Simulator
Shockwave :)
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