MATH348 Advanced Engineering Mathematics
(New page: {{Start Hierarchy|link=Main Page|title=Main Page}} {{Hierarchy Item|link=Mathematics_Course_Wikis|title=Mathematical and Computer Sciences Course Wikis}} {{End Hierarchy}} =Course Informat...) |
|||
| Line 13: | Line 13: | ||
Office Phone : 303.384.2446 | Office Phone : 303.384.2446 | ||
| − | email : math348 | + | email : math348@gmail.com |
| − | == | + | ==Textbook Information== |
| − | + | ||
| − | + | Textbook : [http://www.wiley.com/WileyCDA/WileyTitle/productCd-0471488852.html Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9] | |
| + | 9th Edition Amazon : [http://www.amazon.com/Advanced-Engineering-Mathematics-Textbook-Solutions/dp/0470084847/ref=sr_1_4?ie=UTF8&s=books&qid=1231462860&sr=1-4 Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9] | ||
| + | 8th Edition Amazon (Used) : [http://www.amazon.com/gp/offer-listing/0471154962/ref=dp_olp_1 Advanced Engineering Mathematics - Erwin Kreyszig, ISBN 978-0-471-48885-9] | ||
| − | Course | + | =Course Materials= |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ==Syllabus== | |
| + | {{PDF Table Item|filename=Math348_syllabus.spring2010.pdf | title=MATH348.Spring2010.Syllabus}} | ||
| + | ==Lecture Slides== | ||
| − | + | There are various lecture slides associated with the course. They were developed during the Spring of 2010 and are intended to deliver important bulk concepts while avoiding the need to write down 'every little thing.' Specifically, the slides address: | |
| − | + | 1. Definitions that are not useful for me to write and students to rewrite during lecture. | |
| − | + | 2. Derivations that will never need to be reproduced but need to be communicated quickly because they lead to important consequences. | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | 3. Derivations that will need to be reproduced and have been recorded for clarity. | |
| − | + | Listed in each slide set are: | |
| − | + | ||
| − | + | ||
| − | + | Associated Section/Pages from EK.AEM | |
| + | Associated Lecture Notes | ||
| + | Associated Homework Assignments | ||
| − | + | *[[MATH-348 Advanced Engineering Mathematics - Lecture Slides |MATH 348 : Advanced Engineering Mathematics - Lecture Slides ]] | |
| − | + | ==Lecture Notes== | |
| − | + | ||
| − | + | ||
| − | + | There is a set of lecture notes associated with the course. They were developed during the Fall of 2008 through the Spring of 2009 and are intended to outline key-points, objectives and goals from the text in the order we cover them. Listed in each set are: | |
| − | + | ||
| − | + | Associated Sections/Pages from EK.AEM | |
| − | + | Suggested Problems from EK.AEM | |
| − | + | Brief Outline of Lecture Talking Points | |
| − | + | Lecture Objectives | |
| − | + | Lecture Goals | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | *[[MATH-348 Advanced Engineering Mathematics - Lecture Notes |MATH 348 : Advanced Engineering Mathematics - Lecture Notes ]] | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
==Assignments== | ==Assignments== | ||
| − | |||
| − | |||
| − | |||
| − | |||
| − | + | The assignments for this course have reached a steady-state. Consequently, solutions are often available through students who have taken the course in the past. Since these resources might not be available to all students, I have drafted a set of solutions to these homework assignments which I make available through this site. These solutions were, more or less, finalized during the Spring of 2010 and represents the end of an evolution starting around 2006. Outside of the lecture itself, these homeworks and solutions represents some of the oldest parts of the course and many of the ancestors can be found on older ticc pages. | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| + | In the past the homeworks tended to have a good deal of discussion providing context to a problem so that both the mechanics and concepts could be gleaned. However, after talking with some students and course reviews I decided to move the commentary to the solutions in favor of a more streamlined problem statement. It is unclear whether this latest incarnation is 'better' than the past but what is clear is that they won't be regressing unless someone else wants to revamp them. If you want to see the previous versions then visit the older ticc pages. If you find any typos in these solutions then I would appreciate you letting me know. They are pretty clean but they could always be `cleaner.' | ||
| + | With that said, I must make emphasize the following point: | ||
| + | Caveat Emptor : We will work from these problems and since solutions are | ||
| + | readily available it is up to the individual user to make sure that they | ||
| + | are LEARNING the material. If you buy into a program of procrastination | ||
| + | followed by rapid and thoughtless recreation then you may find an | ||
| + | inadequate product, which cannot be returned. | ||
| − | + | ||
| − | + | *[[MATH-348 Advanced Engineering Mathematics - Assignments |MATH 348 : Advanced Engineering Mathematics - Assignments ]] | |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
==Exams== | ==Exams== | ||
| Line 200: | Line 148: | ||
{{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_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}} | {{PDF Table Item|filename=Math348_ePDESOLN.old.pdf|title=OLD PDE EXAM - SOLN}} | ||
| + | |||
=Other Materials= | =Other Materials= | ||
Revision as of 20:49, 27 April 2010
| 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@gmail.com
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
Syllabus
|- |MATH348.Spring2010.Syllabus
Lecture Slides
There are various lecture slides associated with the course. They were developed during the Spring of 2010 and are intended to deliver important bulk concepts while avoiding the need to write down 'every little thing.' Specifically, the slides address:
1. Definitions that are not useful for me to write and students to rewrite during lecture.
2. Derivations that will never need to be reproduced but need to be communicated quickly because they lead to important consequences.
3. Derivations that will need to be reproduced and have been recorded for clarity.
Listed in each slide set are:
Associated Section/Pages from EK.AEM Associated Lecture Notes Associated Homework Assignments
Lecture Notes
There is a set of lecture notes associated with the course. They were developed during the Fall of 2008 through the Spring of 2009 and are intended to outline key-points, objectives and goals from the text in the order we cover them. Listed in each set are:
Associated Sections/Pages from EK.AEM Suggested Problems from EK.AEM Brief Outline of Lecture Talking Points Lecture Objectives Lecture Goals
Assignments
The assignments for this course have reached a steady-state. Consequently, solutions are often available through students who have taken the course in the past. Since these resources might not be available to all students, I have drafted a set of solutions to these homework assignments which I make available through this site. These solutions were, more or less, finalized during the Spring of 2010 and represents the end of an evolution starting around 2006. Outside of the lecture itself, these homeworks and solutions represents some of the oldest parts of the course and many of the ancestors can be found on older ticc pages.
In the past the homeworks tended to have a good deal of discussion providing context to a problem so that both the mechanics and concepts could be gleaned. However, after talking with some students and course reviews I decided to move the commentary to the solutions in favor of a more streamlined problem statement. It is unclear whether this latest incarnation is 'better' than the past but what is clear is that they won't be regressing unless someone else wants to revamp them. If you want to see the previous versions then visit the older ticc pages. If you find any typos in these solutions then I would appreciate you letting me know. They are pretty clean but they could always be `cleaner.'
With that said, I must make emphasize the following point:
Caveat Emptor : We will work from these problems and since solutions are
readily available it is up to the individual user to make sure that they
are LEARNING the material. If you buy into a program of procrastination
followed by rapid and thoughtless recreation then you may find an
inadequate product, which cannot be returned.
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:
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 - Fall2009 |- |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 %
|- |Exam I - Spring2010 |- |Exam I - Spring2010 Solutions
Exam II
Exam II will be held on April 16th in class. There will be no notecards or calculators. The exam will have five required questions and contain material outlined in the following review:
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 - Spring2009 See Soln for problem 3 graph. |- |Exam II - Spring2009 Solutions |- |Exam 2 - Fall2008 |- |Exam 2 - Fall2008 Solutions |- |Exam II - Summer2009 |- |Exam II - Summer2009 Solutions |- |Exam II - Fall2009 |- |Exam I - Fall2009 Solutions - Graphs Included
Exam II - Statistics
Mean = 36.5 (72.5%)
Median = 37.5 (75%)
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 %
|- |Exam II - Spring2010 |- |Exam I - Spring2010 Solutions
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:
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.
|- |OLD PDE EXAM - See Soln for the graph in problem 1 |- |OLD PDE EXAM - SOLN
Other Materials
Linear Algebra
Three Planes in Space
|- |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
Fourier Methods
Review of Functions
|- |Special Angles and the Unit Circle |- |A61.TrigIdentities Odd and Even Functions (Wikipedia) : (see Also 09.LN)
Periodic Functions (Wikipedia) : (See Also 09.LN)
Fourier Series
|- |FS for f(x}=x, x \in (-\pi,\pi) |- |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 |- |Frequency Response Graph for a Harmonic Oscillator m=k=1, Gamma = {1,.5,.25,.125}
Partial Differential Equations
Ordinary Differential Equations
|- |Review of Ordinary Differential Equations (DRAFT - 11/16/09) Millennium Bridge - Wikipedia
You Tube Video - Millennium Bridge Resonance
Heat Equation
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 Equation
1D Wave Equation
Wave on a 1-D Sting with Fixed Endpoints
Wave on a 1-D Sting with FLAT Endpoints from HW10
Traveling Wave :u0(x) = − tanh(x): Red = Right Traveling, Blue=Left Traveling, Black = Superposition
2D Wave Equation Rectangular and Polar
Rectangular Membrane Movie 1 -Text Example pg577
Rectangular Membrane 2 -Text Example pg577
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
Nonlinear Wave Phenomenon
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
.gif){kind=link}
