MATH348 Advanced Engineering Mathematics

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*[[MATH-348 Advanced Engineering Mathematics - Lecture Notes |MATH 348 : Advanced Engineering Mathematics - Lecture Notes ]]
 
*[[MATH-348 Advanced Engineering Mathematics - Lecture Notes |MATH 348 : Advanced Engineering Mathematics - Lecture Notes ]]
  
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==Assignments==
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==Homework Assignments==
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Students learn by doing problems. Consequently, a course's assignments are critically important and is where the majority of student learning takes place. So, this raises an important question, "how should the assignments for a course like AEM be structured?" This is a tough question and to arrive at my 'answer,' we need some background.
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First, while the majority of students (>90%) in AEM are engineers their skill-sets are highly inhomogeneous. Specifically, you have all had two-years of post-secondary mathematics at different difficulty levels, pace and success. So, there isn't a standard assumption I can use about what you have seen, how well you remember it and, most importantly, how comfortable you are manipulating "it." Moreover, it is unclear where you are going from here. Some of you will find yourself in industry and some in academia, which means that your needs from the material are different. Clearly, any [http://en.wikipedia.org/wiki/Curve_fitting line of best fit] through the material will be poor. 
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Second, everyone in this course needs to understand that they have an '''fairly extensive''' mathematical background. Seriously, how many students do you know that will have had six semesters of course work, outside of their discipline, when they graduate? Those that do are typically awarded a [http://mcs.mines.edu/Academic_Programs/mathminor.shtml minor] in the field. The point is, you are moving past [http://en.wikipedia.org/wiki/Computer plug-and-chug] mathematics and into the conceptual framework of [http://en.wikipedia.org/wiki/Linear_algebra finite] and [http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node2.html infinite] dimensional [http://en.wikipedia.org/wiki/Linear_system linear theory]. Finally, we address the question
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      How should the assignments for a course like AEM be structured?
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Based on the diverse background of the student audience and the growing sophistication of the material homework, assignments should be constructed to highlight both the algorithmic procedures and conceptual framework of linear mathematics. For quick practice skills the recommended homework problems and examples in the text should suffice. However, a student should only do this after replicating the work from class and deciding they wish to have more practice.
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On the other hand, the homework assignments are made to provide a deeper understanding of the course material and often take the student past a first-calculation and into a deeper concept. For example, using the power-series representation for the exponential function is a first-calculation, while using this power-series to show the deep connection between exponential functions and sinusoids is uses multiple pieces of math to arrive at a deeper concept. All students should be able to handle the first-calculations in the homework and at the same time the more advanced students are still challenged by the deeper concepts present in many of the problems.  This is the goal of the homework assignments. 
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===Homework Assignments===
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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 [[MATH-348 Advanced Engineering Mathematics - Archive | older ticc pages ]].
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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 [[MATH-348 Advanced Engineering Mathematics - Archive | 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.'
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With that said, I must make emphasize the following point:
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      Caveat Emptor : We will work from these problems and since solutions are
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      readily available it is up to the individual user to make sure that they
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      are LEARNING the material. If you buy into a program of procrastination
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      followed by rapid and thoughtless re-creation then you may find yourself with an
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      inadequate product that cannot be returned.
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Homework is an essential part of any course. We will only have class/lecture roughly 48 hours in one semester. While this sounds like a lot it really isn't a ton. Here are some comparisons.
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48 Hours is the same as:
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  1. One and one-fifth works weeks.
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  2. Four months of average daily facebooking (or so I've read)
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  3. Six weeks of average video gameplay.
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  4. Seven days of average phone usage
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  5. Thirty-two days of average texting.
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  6. Two and one-half weeks of average driving.
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I guess the point I'm trying to make is that some of these things are what people do everyday and we do them b/c we deem them important. That's fine, but when deciding what you do everyday, remember that this course is about $1000-important to whomever is paying for it. A majority of student learning occurs outside of class, which is spent largely doing homework. The homeworks for this course are meant to guide/focus this time and your homework will primarily reflect the time and effort spent with them. I encourage you to work every day with the goal of spending six-hours outside of class per week on AEM material.
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*[[MATH-348 Advanced Engineering Mathematics - Assignments |MATH 348 : Advanced Engineering Mathematics - Assignments ]]
 
*[[MATH-348 Advanced Engineering Mathematics - Assignments |MATH 348 : Advanced Engineering Mathematics - Assignments ]]

Revision as of 23:19, 9 January 2012

Main Page > Mathematical and Computer Sciences Course Wikis
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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 : Stratton Hall 205

Office Phone : 303.384.2446

email : math348@gmail.com

Textbook Information

I do not require a textbook for this course as the lecture notes should suffice. However, owning a post Calc/DiffEQ textbook may be useful. I provide some options below.

Kreyszig Abridged edition

The bookstore sells an abridged version of the Kreyszig text, which is now in its tenth edition -- all previous CSM abridged editions will be acceptable for this course. The abridged version contains the seven chapters and an appendix:

1. Chapter 5: Power Series Solutions to ODE and Frobenius method

2. Chapter 7: Systems of Linear Algebraic Equations

3. Chapter 8: Eigenvalues and Eigenvectors

4. Chapter 11: Fourier Series

5. Chapter 12: Introduction to Linear Partial Differential Equations

6. Chapter 20: Numerical Methods in Linear Algebra

7. Chapter 21: Numerical Methods in Differential Equations


While this will meet out needs, if you plan to continue in mathematics for a minor or area of special interest or seek an advanced degree in your field then you are advised to get the unabridged edition.

Texts on Fourier Series

Texts on PDE

Texts on Linear Algebra

Continued use of your Differential Equations (MATH225) text

Course Materials

The following outlines materials specific to this course. The materials, as indicated, have been developed over time and have achieved a steady-state. An archive of older ticc pages is available. The ticc websites pick up at Spring 2008 when I started presenting linear algebra first.

Syllabus

MATH348.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 desire 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

Homework Assignments

Homework is an essential part of any course. We will only have class/lecture roughly 48 hours in one semester. While this sounds like a lot it really isn't a ton. Here are some comparisons. 

48 Hours is the same as:
 1. One and one-fifth works weeks.
 2. Four months of average daily facebooking (or so I've read)
 3. Six weeks of average video gameplay.
 4. Seven days of average phone usage
 5. Thirty-two days of average texting.
 6. Two and one-half weeks of average driving.

I guess the point I'm trying to make is that some of these things are what people do everyday and we do them b/c we deem them important. That's fine, but when deciding what you do everyday, remember that this course is about $1000-important to whomever is paying for it. A majority of student learning occurs outside of class, which is spent largely doing homework. The homeworks for this course are meant to guide/focus this time and your homework will primarily reflect the time and effort spent with them. I encourage you to work every day with the goal of spending six-hours outside of class per week on AEM material.


Exams

Previous exams going back through Fall2008 and review sheets are available for studying via the following link.


Student Feedback

MATH348.PostVSSurvey.Fall2011

Supplemental Materials
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