An introduction to the mathematical foundations of advanced engineering analysis. The course prepares one for the further study of specific analytic techniques and begins with a survey of the mathematical fields and their applications to engineering analysis. Topics introduced in some detail include probability theory, statistics, Fourier analysis, solution of partial differential equations using methods including separation of variables, differential and vector calculus, and complex analysis. (Adapted from the course catalog.)
An introduction to the mathematical foundations of advanced engineering analysis. The course prepares one for the further study of specific analytic techniques and begins with a survey of the mathematical fields and their applications to engineering analysis. Topics introduced in some detail include probability theory, statistics, Fourier analysis, solution of partial differential equations using methods including separation of variables, differential and vector calculus, and complex analysis. (Adapted from the course catalog.)
(Kr) Erwin Kreyszig. Advanced Engineering Mathematics. Tenth Edition. Wiley, 2011. (Required. Old editions ok, but homework from Tenth.)
Everyone is required to join the messaging service called "Discord." We'll use it to communicate with each other during the semester. The Discord server you need to join is called drico. That's an invitation link. Be sure to join the channel #502.
A partial text (with fill-ins) I'm writing will be posted on the Engineering Mathematics site.
partial
I have posted videos of the lectures on my YouTube channel. The videos are also on the corresponding pages of the Engineering Mathematics site.
I recommend subscribing and familiarizing yourself with the playlist for this course:
The following schedule is tentative and will be updated as the course proceeds.
| Day | Date | Topics | Reading | Due |
|---|
Weekly homework will be due Sunday after the week it appears on the schedule. I will post solutions on Friday, you will correct your work, check off the completion of each problem, and submit your work on moodle.
Working in groups on homework is strongly encouraged, but the work you turn in should be your own.
Exams typically will be take-home. If you require any specific accommodations, please contact me.
Calculators will be allowed. Only ones own notes and the notes provided by the instructor will be allowed. No communication-devices will be allowed.
No exam may be taken early. Makeup exams require a doctor’s note excusing the absence during the exam.
The final exam will be cumulative.
Total grades in the course may be curved, but individual homework quizzes and exams will not be. They will be available on moodle throughout the semester.
Homework 40% Final Exam 60%
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In keeping with the standards of the Department of Mechanical Engineering, each course is evaluated in terms of its desired outcomes and how these support the desired program outcomes. The following sections document the evaluation of this course.
Upon completion of the course, the following course outcomes are desired:
Students will demonstrate the ability to use the fundamentals of advanced engineering analysis mathematics.
Students will demonstrate the ability to solve partial differential equations with the method of separation of variables.
Students will demonstrate the ability to use Fourier analysis.
Students will demonstrate the ability to use differential vector calculus.
Students will demonstrate an understanding of probability and statistics and how they relate to truth.
Students will demonstrate an understanding of the meaning of "truth" in the context of engineering analysis, with its foundations in mathematical, physical, and philosophical analysis.
Students will demonstrate the ability to use differential vector calculus.
Students will demonstrate an understanding of probability and statistics and how they relate to truth.
In accordance with ABET's student outcomes, our desired program outcomes are that mechanical engineering graduates have:
The following table correlates the desired course outcomes with the desired program outcomes they support.
| desired program outcomes | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | ||||||
| desired course outcomes | 1 | ✔ | ✔ | | | ✔ | ✔ | ✔ | ||||
| ✔ | ✔ | | | ✔ | ✔ | | ||||||
| ✔ | ✔ | | | ✔ | ✔ | | ||||||
| ✔ | ✔ | | | ✔ | ✔ | | ||||||
| ✔ | ✔ | | | ✔ | ✔ | | ||||||
| ✔ | ✔ | ✔ | | ✔ | ✔ | | ||||||
| ✔ | ✔ | ✔ | ✔ | ✔ | ✔ | ✔ | ||||||
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