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3 credits - Ordinary differential equations, systems of ordinary differential equations, partial differential equations, Fourier series, complex analysis. Equations of heat conduction, wave propagation and Laplace.
Prerequisites
Prerequisites
MAP 2302 Elementary differential equations
EGM 3344 Introduction to numerical methods of engineering analysis
BS degrees in MAE (curricula, course catalog, etc.)
Textbook
Textbook
Kreyszig 2011, Advanced Engineering Mathematics, 10th edition, Wiley, New York.
You can get a hardcopy book if you like, but I do NOT require a hardcopy book. You can buy an e-book, which can be convenient to access anywhere with a computer, is cheaper, and much lighter (you don't have to carry the heavy book around). Exams are closed book, closed notes, with formula sheet allowed.
You have two options for an e-book of the Kreyszig 2011 text:
- Downloadable to the student’s machine
- Available without being connected to the internet
- $131.50
- Available online only, must be connected to the internet
- $106.50
Course objectives
Course objectives
In EGM 4313 the student will learn introductory analytical techniques for the solution of (mostly) linear differential systems commonly found in engineering analysis. Included in the analytical techniques are Fourier series, Fourier Transforms, solution of systems of ordinary differential equations by matrix methods, and solution of systems of ordinary differential equations by Laplace transform methods. Solution methods will also be learned for some partial differential equations of importance in engineering (Laplace, heat conduction, wave) by separation of variables and d’Alembert’s method as a special case of the method of characteristics. Complex variables and the Cauchy-Riemann conditions will be studied with particular attention paid to the connection between analytic functions and solutions to Laplace’s equation.
Topics
Topics
Below is a list of tentative topics and the corresponding sections in Kreyszig 2011.
Depth always takes precedence over breadth. So it is likely that not all of the tentative topics listed below would be covered, so a subset would be covered to some greater depth. The reason is the emphasis on the thought process and problem formulation, instead of shallow memorization of formulas.
You can find more info in the course wiki. In particular, that's where your team submit your archived reports.
ABET
ABET
Contribution of the course to meeting the professional component
Contribution of the course to meeting the professional component
This course contributes to the students becoming proficient in the analysis of engineering systems. In particular it supports several program outcomes enumerated in the Mission Statement of the Department of Mechanical and Aerospace Engineering, including
(A1) and (M1): Using knowledge of chemistry and calculus based physics with depth in at least one of them
(A2) and (M2): Apply knowledge of advanced mathematics through multivariate calculus and differential equations
(A3) and (M3): Apply statistics and linear algebra
Relationship of the course to the program outcomes
Relationship of the course to the program outcomes
(a) Apply knowledge of mathematics, science, and engineering – High coverage, 85% of course grade. (A2, M2, A3, M3)
(e) Identify, formulate, and solve engineering problems – Medium coverage, 15% of course grade. (A1, M1)
Home page: Loc Vu-Quoc
E-mail: vu-quoc AT ufl.eduMAE Department
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