MATH-348 Advanced Engineering Mathematics - Fall 2009

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==Handouts==
 
==Handouts==
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{{PDF Table Item|filename=Math348_LAReview.fall2009.pdf|title= Linear Algebra Basics}}
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{{PDF Table Item|filename=Math348_planes.summer2009.pdf|title= Three Planes in Space}}
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{{PDF Table Item|filename=Unit_Circle.pd‎f|title=Special Angles and the Unit Circle}}
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{{PDF Table Item|filename=Example11.1.1.pdf|title=FS for f(x}=x, x \in (-\pi,\pi)}}
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{{PDF Table Item|filename=Example11.1.2.pdf|title=FS for f(x}=Exp(Abs(x)), x \in (-\pi,\pi)}}
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[http://en.wikipedia.org/wiki/Sinc_function Wikipedia - Sinc Function]
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[http://mathworld.wolfram.com/SincFunction.html Mathworld - Sinc Function]
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[http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem Wikipedia - Nyquist-Shannon Sampling Theorem]
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[http://mathworld.wolfram.com/Convolution.html Mathworld - Convolution (Animation)]
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[http://cnx.org/content/m13106/latest/  Convolution and Diffraction (Animations)]
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[http://cnx.org/content/m13106/latest/  Convolution and Diffraction (Animations)]
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[http://commons.wikimedia.org/wiki/File:Convolution_Animation_(Boxcar_and_Ramp).gif Wikipedia - Convolution (Animation)]
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{{PDF Table Item|filename=FreqResponseHO.pdf|title= Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125} }}
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[http://www.mines.edu/~sstrong/AEM_Materials/V.mp4 Heat Movie 1 - abs(x)]
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[http://www.mines.edu/~sstrong/AEM_Materials/parabola.mp4 Heat Movie 2 - parabola]
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[http://www.mines.edu/~sstrong/AEM_Materials/doubleV.mp4 Heat Movie 3 - Double V]
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[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 ]
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[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 ]
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[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Dirch_Triangle1.divx.ff.avi  Wave on a 1-D Sting with Fixed Endpoints]
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[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)]
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[http://www.mines.edu/~sstrong/AEM_Materials/Wave_Neumman_Triangle2.divx.ff.avi  Wave on a 1-D Sting with FLAT Endpoints from HW10]
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[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)]
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[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]
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[http://www.mines.edu/~sstrong/AEM_Materials/2DWave_Rec_BookEx1a.avi Rectangular Membrane Movie 1 -Text Example pg577]
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[http://www.mines.edu/~sstrong/AEM_Materials/2DWave_Rec_BookEx1b.avi Rectangular Membrane 2 -Text Example pg577]
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[http://www.falstad.com/membrane/ Applet - Pretty Cool]
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[http://hyperphysics.phy-astr.gsu.edu/Hbase/music/recmem.html Rectangular Membrane Modes]
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[http://www.kettering.edu/~drussell/Demos/MembraneSquare/Square.html Animations of Rectangular Membrane Modes - Pretty Good]
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[http://www.kettering.edu/~drussell/demos.html Animations done by Dr. Russell - All sorts of stuff! ]
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[http://music.nebrwesleyan.edu/wtt/index.html The Well-Tempered Timpani By Richard K. Jones]
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[http://www.mines.edu/~sstrong/AEM_Materials/Membrane1.mp4 Vibrating Membrane1 - 12.9.1 Example]
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[http://www.mines.edu/~sstrong/AEM_Materials/membrane2.mp4 Vibrating Membrane2 - 12.9.1 Example]
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[http://www.mines.edu/~sstrong/AEM_Materials/Mambrane3.mp4 Vibrating Membrane3 - 12.9.1 Example]
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[http://www.mines.edu/~sstrong/AEM_Materials/Mambrane4.mp4 Vibrating Membrane4 - 12.9.1 Example]
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[http://en.wikipedia.org/wiki/Shock_wave  Wikipedia Article on Shock Waves]
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[http://physics-animations.com/Physics/English/swa_txt.htm  Animation of Shock Wave Formation in Pressure Field]
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[http://www.youtube.com/watch?v=jZ3Hhdr8EjI&feature=PlayList&p=2AE42B05690BA5AD&playnext=1&playnext_from=PL&index=2  Shock Wave (Plane) - You Tube 1]
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[http://www.youtube.com/watch?v=QX04ySm4TTk&feature=PlayList&p=2AE42B05690BA5AD&index=3&playnext=2&playnext_from=PL Shock Wave (Plane) - You Tube 2]
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[http://www.youtube.com/watch?v=9r_2l5_FviU Shock Wave (Explosion) - You Tube 3]
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[http://www.youtube.com/watch?v=GvVQEl_q2ZM Shock Wave (Explosion) - You Tube 4 : Ignore The the cartoon bubble]
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[http://www.youtube.com/watch?v=pz7lcHN7GxQ Shock Wave (Simulation) - You Tube 5 : Notice the distortion of the expanding wave-front]
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[http://exploration.grc.nasa.gov/education/rocket/shock.html NASA - Shock Wave Simulator]
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[http://www.tfarchive.com/cartoons/wallpapers/shockwave17.jpg Shockwave :)]
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[http://en.wikipedia.org/wiki/Millennium_Bridge_(London) Millennium Bridge - Wikipedia]
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[http://www.youtube.com/watch?v=eAXVa__XWZ8 You Tube Video - Millennium Bridge Resonance]
  
 
==Lecture Slides==
 
==Lecture Slides==
  
 
{{PDF Table Item|filename=Math348_Lect01.fall2009.pdf|title= Lecture 1}}
 
{{PDF Table Item|filename=Math348_Lect01.fall2009.pdf|title= Lecture 1}}
−
 
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{{PDF Table Item|filename=Math348_Lect02.fall2009.pdf|title= Lecture 2}}
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{{PDF Table Item|filename=Math348_Lect03.fall2009.pdf|title= Lecture 3}}
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{{PDF Table Item|filename=Math348_Lect04.fall2009.pdf|title= Lecture 4}}
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{{PDF Table Item|filename=Math348_Lect05.fall2009.pdf|title= Lecture 5}}
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{{PDF Table Item|filename=Math348_Lect06.fall2009.pdf|title= Lecture 6}}
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{{PDF Table Item|filename=Math348_Lect07.fall2009.pdf|title= Lecture 7}}
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{{PDF Table Item|filename=Math348_Lect08.summer2009.pdf|title= Lecture 8}}
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{{PDF Table Item|filename=Math348_Lect09.summer2009.pdf|title= Lecture 9}}
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{{PDF Table Item|filename=Math348_Lect10.summer2009.pdf|title= Lecture 10}}
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{{PDF Table Item|filename=Math348_Lect11.fall2009.pdf|title= Lecture 11}}
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{{PDF Table Item|filename=Math348_Lect12.fall2009.pdf|title= Lecture 12}}
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{{PDF Table Item|filename=Math348_ODEReview.fall2009.pdf|title= Review of Ordinary Differential Equations (DRAFT - 11/16/09)}}
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{{PDF Table Item|filename=Math348_Lect13.spring2009.pdf|title= Lecture 13}}
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{{PDF Table Item|filename=Math348_Lect14.fall2009.pdf|title= Lecture 14}}
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{{PDF Table Item|filename=Math348_Lect15.fall2009.pdf|title= Lecture 15}}
  
 
==Assignments==
 
==Assignments==
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{{PDF Table Item|filename=Math348_hw0.fall2009.pdf|title=MATH348.Fall2009.Homework0}}
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{{PDF Table Item|filename=Math348_hw1.fall2009.pdf|title=MATH348.Fall2009.Homework1}}
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{{PDF Table Item|filename=Math348_hw1.soln.fall2009.pdf|title=MATH348.Fall2009.Homework1-Solutions}}
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{{PDF Table Item|filename=Math348_hw2.fall2009.pdf|title=MATH348.Fall2009.Homework2}}
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{{PDF Table Item|filename=Math348_hw2.soln.fall2009.pdf|title=MATH348.Fall2009.Homework2-Solutions}}
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{{PDF Table Item|filename=Math348_hw3.fall2009.pdf|title=MATH348.Fall2009.Homework3}}
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{{PDF Table Item|filename=Math348_hw3.soln.summer2009.pdf|title=MATH348.Summer2009.Homework3 - Solutions}}
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{{PDF Table Item|filename=Math348_hw4.fall2009.pdf|title=MATH348.Fall2009.Homework4}}
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{{PDF Table Item|filename=Math348_hw4.soln.summer2009.pdf|title=MATH348.Summer2009.Homework4 - Solutions}}
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{{PDF Table Item|filename=Math348_hw5.fall2009.pdf|title=MATH348.Fall2009.Homework5}}
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{{PDF Table Item|filename=Math348_hw5.soln.spring2009.pdf|title=MATH348.Summer2009.Homework5 - Solutions}}
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{{PDF Table Item|filename=Math348_hw6.fall2009.pdf|title=MATH348.Fall2009.Homework6}}
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{{PDF Table Item|filename=Math348_hw6.soln.summer2009.pdf|title=MATH348.Summer2009.Homework6 - Solutions}}
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{{PDF Table Item|filename=Math348_hw7.fall2009.pdf|title=MATH348.Fall2009.Homework7}}
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{{PDF Table Item|filename=Math348_hw7.soln.summer2009.pdf|title=MATH348.Fall2009.Homework7 - Solutions}}
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{{PDF Table Item|filename=348.Hw5.s08Soln.pdf|title=Homework Assignment 5 - Solutions (2008) - This is contains the solution to problem 5.}}
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{{PDF Table Item|filename=Math348_hw8.fall2009.pdf|title=MATH348.Fall2009.Homework8}}
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{{PDF Table Item|filename=Math348_hw8.soln.spring2009.pdf|title=MATH348.Fall2009.Homework8 - Solutions}}
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{{PDF Table Item|filename=Math348_hw9.fall2009.pdf|title=MATH348.Fall2009.Homework9}}
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{{PDF Table Item|filename=Math348_hw9.soln.spring2009.pdf|title=MATH348.Fall2009.Homework9 - Solutions}}
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{{PDF Table Item|filename=Math348_hw10.fall2009.pdf|title=MATH348.Fall2009.Homework10}}
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{{PDF Table Item|filename=Math348_hw10.soln.spring2009.pdf|title=MATH348.Fall2009.Homework10 - Solutions}}
  
 
==Exams ==
 
==Exams ==
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===Exam I===
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Exam I will be held on September 30th in class. There will be no notecards or calculators. The exam will have five required questions and contain material outlined in the following review:
 +
 +
{{PDF Table Item|filename=Math348_E1review.pdf|title=Exam 1 - Review Sheet - UPDATED}}
 +
 +
The following exams with solutions are posted for your review.
 +
 +
{{PDF Table Item|filename=Math348_e1.fall2008.pdf|title=Exam 1 - Fall2008 }}
 +
{{PDF Table Item|filename=Math348_e1Soln.fall2008.pdf|title=Exam 1 - Fall2008 Solutions}}
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{{PDF Table Item|filename=Math348_e1.spring2009.pdf|title=Exam I - Spring2009 }}
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{{PDF Table Item|filename=Math348_e1Soln.spring2009.pdf|title=Exam I - Spring2009 Solutions}}
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{{PDF Table Item|filename=Math348_e1.summer2009.pdf|title=Exam I - Summer2009 }}
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{{PDF Table Item|filename=Math348_e1Soln.summer2009.pdf|title=Exam I - Summer2009 Solutions}}
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 +
    Exam I -  Statistics
 +
    Mean = 80.5%
 +
    Median = 82&
 +
    A's = 35, B's = 40, C's = 32, D's = 18, F's = 4, Total Number of Exams  = 129
 +
 +
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{{PDF Table Item|filename=Math348_e1.fall2009.pdf|title=Exam I - Fall2009 }}
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{{PDF Table Item|filename=Math348_e1Soln.Fall2009.pdf|title=Exam I - Fall2009 Solutions}}
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 +
 +
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===Exam II===
 +
Exam I will be held on November 13th in class. There will be no notecards or calculators. The exam will have five required questions and contain material outlined in the following review:
 +
 +
{{PDF Table Item|filename=Math348_E2review.pdf|title=Exam II - Review Sheet}}
 +
 +
The following are the results of Q+A's from previous semesters:
 +
 +
{{PDF Table Item|filename=Math348_e2QA.Spring2009.pdf|title=Exam 2 - Spring2009 Q + A}}
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{{PDF Table Item|filename=Math348_e2QA.fall2008.pdf|title=Exam 2 - Fall2008 Q + A}}
 +
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The following exams with solutions are posted for your review.
 +
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{{PDF Table Item|filename=Math348_e2.fall2008.pdf|title=Exam II - Fall2008 }}
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{{PDF Table Item|filename=Math348_e2Soln.fall2008.pdf|title=Exam II - Fall2008 Solutions}}
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{{PDF Table Item|filename=Math348_e2.spring2009.pdf|title=Exam II - Spring2009 }}
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{{PDF Table Item|filename=Math348_e2Soln.spring2009.pdf|title=Exam II - Spring2009 Solutions}}
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{{PDF Table Item|filename=Math348_e2.summer2009.pdf|title=Exam II - Summer2009 }}
 +
{{PDF Table Item|filename=Math348_e2Soln.summer2009.pdf|title=Exam II - Summer2009 Solutions}}
 +
 +
    Exam II -  Statistics
 +
    Mean = 36.8
 +
    Median = 38
 +
    A's = 12, B's = 40, C's = 37, D's = 20, F's = 20, Total Number of Exams  = 129
 +
 +
{{PDF Table Item|filename=Math348_e2.fall2009.pdf|title=Exam II - Fall2009 }}
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{{PDF Table Item|filename=Math348_e2Soln.Fall2009.pdf|title=Exam I - Fall2009 Solutions - Graphs Included}}
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==Final Exam==
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The final exam will be held on December 14th in Brown Building 201 and 204.
 +
    11:00am Section : BB204A : Proctor = Strong
 +
    1:00pm Section : BB204A - If there is no room then go to BB201 : Proctor = Strong or Ott
 +
    2:00pm Section : BB201 : Proctor = Ott
 +
There will be no notecards or calculators. The exam will have ten required questions and contain material outlined in the following review:
 +
 +
{{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}}
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{{PDF Table Item|filename=Math348_ePDESOLN.old.pdf|title=OLD PDE EXAM - SOLN}}
  
 
==Course Links==
 
==Course Links==

Latest revision as of 23:21, 9 December 2009

Main Page > Mathematical and Computer Sciences Course Wikis

Contents

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.fall2009@gmail.com

Course Calendar

Classes Begin : August 25th, 2009

Meeting Days : Monday, Wednesday, Friday

Course Sections : 

  C : 11:00am-11:50am & Location: Green Center 210 South 
  D : 1:00pm-1:50pm & Location: Green Center 265 
  E : 2:00pm-2:50pm & Location: Coolbaugh Hall 131

Last Day to Drop Without a W : September 9th

Last Day to Withdraw : November 3rd

Classes End : December 9th, 2009

Important Dates : 

   September 9th : Last Day to Withdrawal  (Without a W)
   October 19th-20th : Fall Break
   November 3rd : Last Day to Withdrawal
   November 25th-27th : Thanksgiving Break

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.

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 Documents

Pdf.png These downloads require Adobe Acrobat Reader

Syllabus

MATH348.fall2009.Syllabus

Handouts

Linear Algebra Basics
Three Planes in Space
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)

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 :u0(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

Lecture 1
Lecture 2
Lecture 3
Lecture 4
Lecture 5
Lecture 6
Lecture 7
Lecture 8
Lecture 9
Lecture 10
Lecture 11
Lecture 12
Review of Ordinary Differential Equations (DRAFT - 11/16/09)
Lecture 13
Lecture 14
Lecture 15

Assignments

MATH348.Fall2009.Homework0
MATH348.Fall2009.Homework1
MATH348.Fall2009.Homework1-Solutions
MATH348.Fall2009.Homework2
MATH348.Fall2009.Homework2-Solutions
MATH348.Fall2009.Homework3
MATH348.Summer2009.Homework3 - Solutions
MATH348.Fall2009.Homework4
MATH348.Summer2009.Homework4 - Solutions
MATH348.Fall2009.Homework5
MATH348.Summer2009.Homework5 - Solutions
MATH348.Fall2009.Homework6
MATH348.Summer2009.Homework6 - Solutions
MATH348.Fall2009.Homework7
MATH348.Fall2009.Homework7 - Solutions
Homework Assignment 5 - Solutions (2008) - This is contains the solution to problem 5.
MATH348.Fall2009.Homework8
MATH348.Fall2009.Homework8 - Solutions
MATH348.Fall2009.Homework9
MATH348.Fall2009.Homework9 - Solutions
MATH348.Fall2009.Homework10
MATH348.Fall2009.Homework10 - Solutions

Exams

Exam I

Exam I will be held on September 30th in class. There will be no notecards or calculators. The exam will have five required questions and contain material outlined in the following review:

Exam 1 - Review Sheet - UPDATED

The following exams with solutions are posted for your review.

Exam 1 - Fall2008
Exam 1 - Fall2008 Solutions
Exam I - Spring2009
Exam I - Spring2009 Solutions
Exam I - Summer2009
Exam I - Summer2009 Solutions 
    Exam I -  Statistics
    Mean = 80.5%
    Median = 82&
    A's = 35, B's = 40, C's = 32, D's = 18, F's = 4, Total Number of Exams  = 129


Exam I - Fall2009
Exam I - Fall2009 Solutions



Exam II

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

Exam II - Review Sheet

The following are the results of Q+A's from previous semesters:

Exam 2 - Spring2009 Q + A
Exam 2 - Fall2008 Q + A

The following exams with solutions are posted for your review.

Exam II - Fall2008
Exam II - Fall2008 Solutions
Exam II - Spring2009
Exam II - Spring2009 Solutions
Exam II - Summer2009
Exam II - Summer2009 Solutions 
    Exam II -  Statistics
    Mean = 36.8
    Median = 38
    A's = 12, B's = 40, C's = 37, D's = 20, F's = 20, Total Number of Exams  = 129
Exam II - Fall2009
Exam I - Fall2009 Solutions - Graphs Included

Final Exam

The final exam will be held on December 14th in Brown Building 201 and 204. 

   11:00am Section : BB204A : Proctor = Strong
   1:00pm Section : BB204A - If there is no room then go to BB201 : Proctor = Strong or Ott
   2:00pm Section : BB201 : Proctor = Ott

There will be no notecards or calculators. The exam will have ten required questions and contain material outlined in the following review:

Final Exam - Review Sheet
OLD PDE EXAM - See Soln for the graph in problem 1
OLD PDE EXAM - SOLN

Course Links

Graphing Utilities

   Free Mathematica Like Program for Windows and Mac
   Eigenmath Manual
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