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Revision as of 17:21, 27 March 2010
Course Information
MATH348: Advanced Engineering Mathematics - Introduction to partial differential equations, with applications to physical phenomena. Fourier series. Linear algebra, with emphasis on sets of simultaneous equations. Prerequisite: MATH 225 or equivalent.
Instructor Information
Instructor : Scott Strong
Office : Chauvenet Hall 266
Office Phone : 303.384.2446
email : math348.spring2010@gmail.com
Course Calendar
Classes Begin : January 13th, 2010
Lecture Days : Monday, Wednesday, Friday
Course Sections :
B : 11:00am-11:50am - Location: Coolbaugh Hall 131
C : 1:00pm-1:50pm - Location: Green Center 211
D : 2:00pm-2:50pm - Location: Alderson Hall 430
Last Day to Drop Without a W : January 28th
Last Day to Withdraw : March 30th
Classes End : May 14th, 2010
Important Dates :
February 14th : No Classes
March 15th-19th : Spring Break
April 8th-10th : E-Days
May 3th-7th : Dead Week
May 7th : Dead Day
Office Hours
Fixed Office Hours :
MWF : 12:00pm-12:50pm
Monday : 3:00pm-5:00pm
If you cannot meet during the previous office hours then please contact me to schedule another meeting time. Please see this google calender to see the times I am unavailable.
Textbook Information
Textbook : Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9
9th Edition Amazon : Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9
8th Edition Amazon (Used) : Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9
Course Materials
These downloads require Adobe Acrobat Reader
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
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
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
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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
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
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)
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