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Mathematical and Computer Sciences Course Wikis

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 278

Office Phone : 303.384.2446

email : math348.spring2009@gmail.com

Course Calander

Classes Begin : January 7th, 2009

Meeting Days : Monday, Wednesday, Friday

Course Sections :

    Section B,  12:00pm-12:50pm, Alderson Hall 330
    Section C, 1:00pm-1:50pm, Green Center 211
    Section D, 2:00pm-2:50pm, Green Center 211

Class Holidays :

    February 16th, 2009 - Presidents Day
    March 9th-13th, 2009 - Spring Break
    April 2nd-4th, 2009 - E-Days

Classes End : April 30th, 2009

Important Dates :

   January  22nd - Last Day to Withdrawal  (Without a W)
   March 24th - Last Day to Withdrawal

Office Hours

Fixed Office Hours :

 M : 3-4pm
 W : 11-12pm
 F : 11-12pm

If you cannot meet during the previous office hours then please contact me to schedule another meeting time.

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

These downloads require Adobe Acrobat Reader

Course Documents

Handouts

A61.TrigIdentities

Special Angles and the Unit Circle

FS for f(x}=x, x \in (-\pi,\pi)

FS for f(x}=Exp(Abs(x)), x \in (-\pi,\pi)

Wikipedia - Sinc Function

Mathworld - Sinc Function

Wikipedia - Nyquist-Shannon Sampling Theorem

Mathworld - Convolution (Animation)

Convolution and Diffraction (Animations)

Wikipedia - Convolution (Animation)

Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125}

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 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 : $u 0 (x) = - tanh(x)$ : Red = Right Traveling, Blue=Left Traveling, Black = Superposition

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

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 :)

Millennium Bridge - Wikipedia

You Tube Video - Millennium Bridge Resonance

Lecture Slides

Syllabus

MATH348.Spring2009.Syllabus

Exams

Exam I will be held on February 13th in class there will be no class the following Wednesday. There will be no notecards or calculators. The exam will be five questions and contain material outlined in the following review:

Exam 1 - Review Sheet

Exam 1 - Fall2008

Exam 1 - Fall2008 Solutions

    Exam I -  Statistics
    Average = 39.69 = 79.38%
    Median = 41 = 82%
    A's = 27, B's = 31 , C's = 17 , D's = 16, F's =9, Total Number of Exams  = 100

Exam I - Spring2009

Exam I - Spring2009 Solutions

Exam II will be held on April 1st in class there will be no class the following Monday. There will be no notecards or calculators. The exam will be five questions and contain material outlined in the following review:

Exam 2 - Review Sheet

Exam 2 - Spring2009 Q + A

Exam 2 - Fall2008

Exam 2 - Fall2008 Solutions

Exam 2 - Fall2008 Q + A

    Exam II -  Statistics
    Average = 37.14 = 74.29%
    Median = 37 = 74%,
    A's = 9, B's = 25 , C's = 31 , D's = 23, F's =9, Total Number of Exams  = 97

Exam II - Spring2009 See Soln for problem 3 graph.

Exam II - Spring2009 Solutions

The final exam will be held on May 4th from 10:15am-12:15am. The classes will be split across rooms. Please go to the room assigned to the class you are enrolled in. There will be no notecards or calculators. The exam will be cumulative with an emphasis on PDE.

    MATH348B-BE241   Proctor: Ecklund
    MATH348C-BB201   Proctor: Bridgman
    MATH348D-BB204A  Proctor: Strong

Since, it is likely I won't see most of you at the exam -- Have a good summer and it was nice having class with you. :)

I will not be posting a practice exam, since it is policy to not disseminate final exams. I do have an old PDE only exam and I will post it below.

Final Exam - Review Sheet

OLD PDE EXAM - See Soln for the graph in problem 1

OLD PDE EXAM - SOLN

Assignments

MATH348.Spring2009.Homework1

MATH348.Spring2009.Homework1.Solutions

MATH348.Spring2009.Homework2

MATH348.Spring2009.Homework2Solutions

Picture of a Parallelepiped : [1]

MATH348.Spring2009.Homework3

MATH348.Spring2009.Homework3Solutions

MATH348.Spring2009.Homework4

MATH348.Spring2009.Homework4Solutions

MATH348.Spring2009.Homework5

MATH348.Spring2009.Homework5Solutions

MATH348.Spring2009.Homework6

NOTE : For the graphs you may want to consider using the eigenmath program posted below. Eigenmath Script for Example1 Results Feel free to post better scripts. I'm sure that this program could find the coefficients from their integral definitions.

NOTE : A typo has been corrected. You should assume that E=\omega = 1 and L = \pi.

NOTE : Thanks to David Melton for Another Graphing Utility - Graphs Truncated FS

MATH348.Spring2009.Homework6Solutions

MATH348.Spring2009.Homework7

MATH348.Spring2009.Homework7Solutions

MATH348.Spring2009.Homework8

MATH348.Spring2009.Homework8Solutions

MATH348.Spring2009.Homework9

MATH348.Spring2009.Homework9Solutions

MATH348.Spring2009.Homework10

MATH348.Spring2009.Homework10Solutions

Course Links

Graphing Utilities

   Free Mathematica Like Program for Windows and Mac
   Eigenmath Manual

@@ Line 58: / Line 58: @@
 ==Handouts==
 {{PDF Table Item|filename=A61-TrigFormula.pdf|title=A61.TrigIdentities}}
 {{PDF Table Item|filename=Unit_Circle.pd‎f|title=Special Angles and the Unit Circle}}
@@ Line 77: / Line 78: @@
 {{PDF Table Item|filename=FreqResponseHO.pdf|title= Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125} }}
 [http://www.mines.edu/~sstrong/AEM_Materials/V.mp4 Heat Movie 1 - abs(x)]
 [http://www.mines.edu/~sstrong/AEM_Materials/parabola.mp4 Heat Movie 2 - parabola]
+[http://www.mines.edu/~sstrong/AEM_Materials/doubleV.mp4 Heat Movie 3 - Double V]
+[http://www.mines.edu/~sstrong/AEM_Materials/Heat_Dirch_Force.avi Heat Movie 4 - Forced Heat Equation with B.C. u(0,t)=u(L,t)=0 ]
+[http://www.mines.edu/~sstrong/AEM_Materials/Heat_Neumman_Forcing.avi Heat Movie 5 - Forced Heat Equation with B.C. u_{x}(0,t)=u_{x}(L,t)=0 ]
+[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Dirch_Triangle1.divx.ff.avi  Wave on a 1-D Sting with Fixed Endpoints]
+[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Dirch_Triangle2.divx.ff.avi  Wave on a 1-D Sting with Fixed Endpoints - Animated with first 5 Fourier Modes (Fundamental Mode in Red)]
+[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Neumman_Triangle2.divx.ff.avi  Wave on a 1-D Sting with FLAT Endpoints from HW10]
+[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Neumman_Triangle1.divx.ff.avi  Wave on a 1-D Sting with FLAT Endpoints from HW10 - Animated with first 5 Fourier Modes (Fundamental Mode in Red)]
+[http://www.mines.edu/~sstrong/AEM_Materials/Traveling%20Waves.divx.ff.avi  Traveling Wave :<math>u_{0}(x) = -\tanh(x)</math>: Red = Right Traveling, Blue=Left Traveling, Black = Superposition]
+[http://www.mines.edu/~sstrong/AEM_Materials/2DWave_Rec_BookEx1a.avi Rectangular Membrane Movie 1 -Text Example pg577]
+[http://www.mines.edu/~sstrong/AEM_Materials/2DWave_Rec_BookEx1b.avi Rectangular Membrane 2 -Text Example pg577]
+[http://www.falstad.com/membrane/ Applet - Pretty Cool]
+[http://hyperphysics.phy-astr.gsu.edu/Hbase/music/recmem.html Rectangular Membrane Modes]
+[http://www.kettering.edu/~drussell/Demos/MembraneSquare/Square.html Animations of Rectangular Membrane Modes - Pretty Good]
+[http://www.kettering.edu/~drussell/demos.html Animations done by Dr. Russell - All sorts of stuff! ]
@@ Line 93: / Line 125: @@
 [http://www.mines.edu/~sstrong/AEM_Materials/Mambrane4.mp4 Vibrating Membrane4 - 12.9.1 Example]
-[http://www.mines.edu/~sstrong/AEM_Materials/Mambrane5.mp4 Vibrating Membrane5 - 12.9.1 Example]
-[http://www.mines.edu/~sstrong/AEM_Materials/doubleV.mp4 Heat Movie 3 - Double V]
+[http://en.wikipedia.org/wiki/Shock_wave  Wikipedia Article on Shock Waves]
+[http://physics-animations.com/Physics/English/swa_txt.htm  Animation of Shock Wave Formation in Pressure Field]
+[http://www.youtube.com/watch?v=jZ3Hhdr8EjI&feature=PlayList&p=2AE42B05690BA5AD&playnext=1&playnext_from=PL&index=2  Shock Wave (Plane) - You Tube 1]
+[http://www.youtube.com/watch?v=QX04ySm4TTk&feature=PlayList&p=2AE42B05690BA5AD&index=3&playnext=2&playnext_from=PL Shock Wave (Plane) - You Tube 2]
+[http://www.youtube.com/watch?v=9r_2l5_FviU Shock Wave (Explosion) - You Tube 3]
+[http://www.youtube.com/watch?v=GvVQEl_q2ZM Shock Wave (Explosion) - You Tube 4 : Ignore The the cartoon bubble]
+[http://www.youtube.com/watch?v=pz7lcHN7GxQ Shock Wave (Simulation) - You Tube 5 : Notice the distortion of the expanding wave-front]
+[http://exploration.grc.nasa.gov/education/rocket/shock.html NASA - Shock Wave Simulator]
+[http://www.tfarchive.com/cartoons/wallpapers/shockwave17.jpg Shockwave :)]
+[http://en.wikipedia.org/wiki/Millennium_Bridge_(London) Millennium Bridge - Wikipedia]
+[http://www.youtube.com/watch?v=eAXVa__XWZ8 You Tube Video - Millennium Bridge Resonance]
 ==Lecture Slides==
@@ Line 111: / Line 167: @@
 {{PDF Table Item|filename=Math348_Lect11.spring2009.pdf|title= Lecture Eleven}}
 {{PDF Table Item|filename=Math348_Lect12.spring2009.pdf|title= Lecture Twelve}}
+{{PDF Table Item|filename=Math348_Lect13.spring2009.pdf|title= Lecture Thirteen}}
+{{PDF Table Item|filename=Math348_Lect14.spring2009.pdf|title= Lecture Fourteen}}
+{{PDF Table Item|filename=Math348_Lect15.spring2009.pdf|title= Lecture Fifteen}}
 ==Syllabus ==
@@ Line 140: / Line 199: @@
       Exam II -  Statistics
       Average = 37.14 = 74.29%
-      Median = 37 = 74%
+      Median = 37 = 74%,
       A's = 9, B's = 25 , C's = 31 , D's = 23, F's =9, Total Number of Exams  = 97
 {{PDF Table Item|filename=Math348_e2.spring2009.pdf|title=Exam II - Spring2009 }} See Soln for problem 3 graph.
 {{PDF Table Item|filename=Math348_e2Soln.spring2009.pdf|title=Exam II - Spring2009 Solutions}}
+The final exam will be held on May 4th from 10:15am-12:15am. The classes will be split across rooms. Please go to the room assigned to the class you are enrolled in. There will be no notecards or calculators. The exam will be cumulative with an emphasis on PDE.
+     MATH348B-BE241   Proctor: Ecklund
+     MATH348C-BB201   Proctor: Bridgman
+     MATH348D-BB204A  Proctor: Strong
+Since, it is likely I won't see most of you at the exam -- Have a good summer and it was nice having class with you. :)
+I will not be posting a practice exam, since it is policy to not disseminate final exams. I do have an old PDE only exam and I will post it below.
+{{PDF Table Item|filename=Math348_fereview.spring2009.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}}
 ==Assignments==
@@ Line 170: / Line 246: @@
 {{PDF Table Item|filename=Math348_hw8.soln.spring2009.pdf|title=MATH348.Spring2009.Homework8Solutions}}
 {{PDF Table Item|filename=Math348_hw9.spring2009.pdf|title=MATH348.Spring2009.Homework9}}
+{{PDF Table Item|filename=Math348_hw9.soln.spring2009.pdf|title=MATH348.Spring2009.Homework9Solutions}}
+{{PDF Table Item|filename=Math348_hw10.spring2009.pdf|title=MATH348.Spring2009.Homework10}}
+{{PDF Table Item|filename=Math348_hw10.soln.spring2009.pdf|title=MATH348.Spring2009.Homework10Solutions}}
 {{End PDF Table}}

MATH-348 Advanced Engineering Mathematics - Spring 2009

Latest revision as of 00:45, 30 April 2009

Contents

Course Information

Instructor Information

Course Calander

Office Hours

Textbook Information

Course Documents

Handouts

Lecture Slides

Syllabus

Exams

Assignments

Course Links

Graphing Utilities

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