MATH-348 Advanced Engineering Mathematics - Spring 2010
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{{PDF Table Item|filename=Math348_syllabus.spring2010.pdf | title=MATH348.Spring2010.Syllabus}} | {{PDF Table Item|filename=Math348_syllabus.spring2010.pdf | title=MATH348.Spring2010.Syllabus}} | ||
+ | {{PDF Table Item|filename=Math235_hw2Edit1.pdf | title=MATH348.Spring2010.Syllabus}} | ||
==Lecture Slides== | ==Lecture Slides== | ||
+ | {{PDF Table Item|filename=Math348_s11.hw7.pdf | title=00.LS.Introduction }} | ||
+ | {{PDF Table Item|filename=Math348_s11.hw7Soln.pdf | title=00.LS.Introduction }} | ||
+ | {{PDF Table Item|filename=Math348_s11.hw8e.pdf | title=00.LS.Introduction }} | ||
+ | {{PDF Table Item|filename=Math348_s11.hw8Soln.pdf | title=00.LS.Introduction }} | ||
{{PDF Table Item|filename=Math348_LS.00.pdf | title=00.LS.Introduction }} | {{PDF Table Item|filename=Math348_LS.00.pdf | title=00.LS.Introduction }} | ||
{{PDF Table Item|filename=Math348_LS.01.pdf | title=01.LS.Classical Vector Spaces}} | {{PDF Table Item|filename=Math348_LS.01.pdf | title=01.LS.Classical Vector Spaces}} | ||
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{{PDF Table Item|filename=Math348_LS.04.pdf | title=04.LS.Abstract Vector Spaces}} | {{PDF Table Item|filename=Math348_LS.04.pdf | title=04.LS.Abstract Vector Spaces}} | ||
{{PDF Table Item|filename=Math348_LS.05.edit.pdf | title=05.LS.Fourier Series to Fourier Integral to Fourier Transform - Update 4/5/2010}} | {{PDF Table Item|filename=Math348_LS.05.edit.pdf | title=05.LS.Fourier Series to Fourier Integral to Fourier Transform - Update 4/5/2010}} | ||
+ | {{PDF Table Item|filename=Math348_LS.06.pdf | title=06.LS.1D Heat Equation-Separation of Variables}} | ||
+ | {{PDF Table Item|filename=Math348_LS.07.pdf | title=07.LS.The Acoustic Approximation and Wave Equations}} | ||
==Lecture Notes== | ==Lecture Notes== | ||
+ | {{PDF Table Item|filename=Math235_PE.pdf | title=??}} | ||
{{PDF Table Item|filename=Math348_LN.00.pdf | title=00.LN.Overview And Outline}} | {{PDF Table Item|filename=Math348_LN.00.pdf | title=00.LN.Overview And Outline}} | ||
{{PDF Table Item|filename=Math348_LN.01.update.pdf | title=01.LN.LinearDefinitions : Updated 1.27.2010. Footnotes have been added referencing locations in the text where these definitions can be found. }} | {{PDF Table Item|filename=Math348_LN.01.update.pdf | title=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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{{PDF Table Item|filename=Math348_LN.11.pdf | title=11.LN.Fourier Integral to Fourier Transform }} | {{PDF Table Item|filename=Math348_LN.11.pdf | title=11.LN.Fourier Integral to Fourier Transform }} | ||
{{PDF Table Item|filename=Math348_LN.12.pdf | title=12.LN.Fourier Transform }} | {{PDF Table Item|filename=Math348_LN.12.pdf | title=12.LN.Fourier Transform }} | ||
+ | {{PDF Table Item|filename=Math348_LN.13e.pdf | title=13.LN.IntroToPDE }} | ||
+ | {{PDF Table Item|filename=Math348_LN.14.pdf | title=14.LN.HeatEquation }} | ||
+ | {{PDF Table Item|filename=Math348_LN.15.pdf | title=15.LN.WaveEquation }} | ||
==Assignments== | ==Assignments== | ||
{{PDF Table Item|filename=Math348_HW.00.pdf | title=Homework0 - Due Jan. 18th by 5:00pm}} | {{PDF Table Item|filename=Math348_HW.00.pdf | title=Homework0 - Due Jan. 18th by 5:00pm}} | ||
− | {{PDF Table Item|filename= | + | {{PDF Table Item|filename=MHW2_edit2.pdf | title=Homework0 - Solutions}} |
{{PDF Table Item|filename=Math348_HW.01.edit1.pdf | title=Homework1 - Due Feb. 3rd by 5:00pm - Note: Updated 1/19/2010, fixed a typo in problem 2 matrix 2, a_{22} = -3 }} | {{PDF Table Item|filename=Math348_HW.01.edit1.pdf | title=Homework1 - Due Feb. 3rd by 5:00pm - Note: Updated 1/19/2010, fixed a typo in problem 2 matrix 2, a_{22} = -3 }} | ||
{{PDF Table Item|filename=Math348_HW.01.Soln.pdf | title=Homework1 - Solutions }} | {{PDF Table Item|filename=Math348_HW.01.Soln.pdf | title=Homework1 - Solutions }} | ||
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[http://ticc.mines.edu/csm/wiki/images/a/a4/Math348_HW.1.4.2.2.lsp.Plot.pdf Geometry of Least Squares Problem of Problem 4 Set 2] | [http://ticc.mines.edu/csm/wiki/images/a/a4/Math348_HW.1.4.2.2.lsp.Plot.pdf Geometry of Least Squares Problem of Problem 4 Set 2] | ||
[http://ticc.mines.edu/csm/wiki/images/8/86/Math348_HW.1.4.2.3.Plot.pdf Interpolated Parabolas of Problem 4 Set 3] | [http://ticc.mines.edu/csm/wiki/images/8/86/Math348_HW.1.4.2.3.Plot.pdf Interpolated Parabolas of Problem 4 Set 3] | ||
− | + | Fourier Transform | |
{{PDF Table Item|filename=Math348_HW.02.edit2.pdf | title=Homework2 - Due Feb. 12th by 5:00pm : 1) Header Box Updated 2) Problem 4.2 \lambda = n^2}} | {{PDF Table Item|filename=Math348_HW.02.edit2.pdf | title=Homework2 - Due Feb. 12th by 5:00pm : 1) Header Box Updated 2) Problem 4.2 \lambda = n^2}} | ||
{{PDF Table Item|filename=Math348_HW.02..edit2.Soln.pdf | title=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.}} | {{PDF Table Item|filename=Math348_HW.02..edit2.Soln.pdf | title=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.}} | ||
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{{PDF Table Item|filename=Math348_HW.06.pdf | title=Homework6 - Due: April 12th }} | {{PDF Table Item|filename=Math348_HW.06.pdf | title=Homework6 - Due: April 12th }} | ||
{{PDF Table Item|filename=Math348_HW.06.soln.pdf | title=Homework6 - Solutions }} | {{PDF Table Item|filename=Math348_HW.06.soln.pdf | title=Homework6 - Solutions }} | ||
+ | {{PDF Table Item|filename=Math348_HW.07e3.pdf | title=Homework7 - Due April 28 - Last edits (minor) at 4:31pm. }} | ||
+ | {{PDF Table Item|filename=Math348_HW.07e2.soln.pdf | title=Homework7 - Solutions - Last edits (minor) at 4:31pm : Note at a step in problem 1.1 I use quantities like I1 and I2. By these I mean l1 and l2. }} | ||
+ | {{PDF Table Item|filename=Math348_HW.08.pdf | title=Homework8 - Due May 3 }} | ||
+ | {{PDF Table Item|filename=Math348_HW.08.soln.pdf | title=Homework8 - Solutions }} | ||
==Exams== | ==Exams== | ||
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{{PDF Table Item|filename=Math348_e2.summer2009.pdf|title=Exam II - Summer2009 }} | {{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}} | {{PDF Table Item|filename=Math348_e2Soln.summer2009.pdf|title=Exam II - Summer2009 Solutions}} | ||
+ | {{PDF Table Item|filename=Math348_e2.fall2009.pdf|title=Exam II - Fall2009 }} | ||
+ | {{PDF Table Item|filename=Math348_e2Soln.Fall2009.pdf|title=Exam II - Fall2009 Solutions - Graphs Included}} | ||
+ | |||
Exam II - Statistics | Exam II - Statistics | ||
− | Mean = | + | Mean = 36.5 (72.5%) |
− | Median = | + | Median = 37.5 (75%) |
− | A's = | + | A's = 9, B's = 32, C's = 38, D's = 19, F's = 16, Total Number of Exams = 114 |
+ | A's = 8%, B's = 28%, C's = 33%, D's = 17%, F's = 14 % | ||
+ | |||
+ | {{PDF Table Item|filename=Math348_e2.spring2010.pdf|title=Exam II - Spring2010 }} | ||
+ | {{PDF Table Item|filename=Math348_e2Soln.Spring2010.pdf|title=Exam I - Spring2010 Solutions}} | ||
===Final Exam=== | ===Final Exam=== | ||
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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: | 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= | + | {{PDF Table Item|filename=Math235_hw2.pdf|title=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. | 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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===Three Planes in Space=== | ===Three Planes in Space=== | ||
{{PDF Table Item|filename=Math348_planes.summer2009.pdf | title=Three Planes in Space - Four Different Ways}} | {{PDF Table Item|filename=Math348_planes.summer2009.pdf | title=Three Planes in Space - Four Different Ways}} | ||
+ | {{PDF Table Item|filename=MATH235-EI-Reading2.pdf | title=Three Planes in Space - Four Different Ways}} | ||
'''Legend for the Animations''' | '''Legend for the Animations''' | ||
Red = First Plane Equation | Red = First Plane Equation | ||
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===Ordinary Differential Equations=== | ===Ordinary Differential Equations=== | ||
{{PDF Table Item|filename=Math348_ODEReview.fall2009.pdf|title= Review of Ordinary Differential Equations (DRAFT - 11/16/09)}} | {{PDF Table Item|filename=Math348_ODEReview.fall2009.pdf|title= Review of Ordinary Differential Equations (DRAFT - 11/16/09)}} | ||
+ | [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] | ||
===Heat Equation=== | ===Heat Equation=== | ||
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===Wave Equation=== | ===Wave Equation=== | ||
+ | ====1D Wave Equation==== | ||
+ | [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] | ||
+ | |||
+ | ====2D Wave Equation Rectangular and Polar==== | ||
+ | |||
+ | [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! ] | ||
+ | |||
+ | |||
+ | [http://music.nebrwesleyan.edu/wtt/index.html The Well-Tempered Timpani By Richard K. Jones] | ||
+ | |||
+ | [http://www.mines.edu/~sstrong/AEM_Materials/Membrane1.mp4 Vibrating Membrane1 - 12.9.1 Example] | ||
+ | |||
+ | [http://www.mines.edu/~sstrong/AEM_Materials/membrane2.mp4 Vibrating Membrane2 - 12.9.1 Example] | ||
+ | |||
+ | [http://www.mines.edu/~sstrong/AEM_Materials/Mambrane3.mp4 Vibrating Membrane3 - 12.9.1 Example] | ||
+ | |||
+ | [http://www.mines.edu/~sstrong/AEM_Materials/Mambrane4.mp4 Vibrating Membrane4 - 12.9.1 Example] | ||
+ | |||
+ | |||
+ | |||
+ | ====Nonlinear Wave Phenomenon==== | ||
+ | |||
+ | [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://www.break.com/index/explosion-shock-waves-in-slow-motion.html Shockwave Slowmo] | ||
+ | |||
+ | [http://exploration.grc.nasa.gov/education/rocket/shock.html NASA - Shock Wave Simulator] | ||
− | + | [http://www.tfarchive.com/cartoons/wallpapers/shockwave17.jpg Shockwave :)] |
Latest revision as of 14:24, 20 April 2011
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.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