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| MATH348D : 2:00pm Section : CO209 : Doug Poole | | 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. | | Since we will be in different rooms it is very important that you go to the room associated with your section. |
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| + | 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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| + | {{PDF Table Item|filename=Math348_fereview.Fall2009.pdf|title=Final Exam - Review Sheet}} |
| + | {{PDF Table Item|filename=Math348_ePDE.old.pdf|title=OLD PDE EXAM - See Soln for the graph in problem 1}} |
| + | {{PDF Table Item|filename=Math348_ePDESOLN.old.pdf|title=OLD PDE EXAM - SOLN}} |
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| =Other Materials= | | =Other Materials= |
Revision as of 15:21, 8 April 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
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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
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
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Homework6 - Due: April 12th
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Homework6 - 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 14th 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
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
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
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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)
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