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- Catalog Description
- 548 Engineering Analysis II. (Crosslisted with EMA 548.) II; 3 cr (P-I). Function of complex
variable, series solution of different equations, partial differential equations. P: A yr of math beyond
calculus.
- Course Prerequisite(s)
- Two of Math 319, 321, 322, 340 or equivalents
- One course in numerical methods for solving engineering problems
- Prerequisite knowledge and/or skills
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Differential and integral calculus of one variable
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Elements of vector calculus, complex variables, linear analysis and matrix algebra
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Basics of solving ordinary and partial differential equations
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Experience in solving engineering problems on computers
- Textbook(s) and/or other required material
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G. Strang, "Introduction to Applied Mathematics," Wellesley-Cambridge Press, 1986.
- Course objectives
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The primary objectives of this applications-oriented course are to:
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Expose engineering students to the most important areas of applied mathematics and numerical methods that are useful in graduate level engineering problem solving.
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Provide experience in developing analytical and computational solutions of relevant partial differential equations for wave propagation, potential theory and diffusion for key engineering problems in Newtonian mechanics, fluid mechanics and heat diffusion.
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Whet graduate students appetite for taking advanced mathematics and numerical methods courses in key specialty areas relevant to their thesis research.
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Desired student outcomes are:
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An understanding of how contemporary applied mathematics and numerical methods are used in conjunction with physical principles to develop detailed models for describing the key physical processes governing engineering applications.
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Basic competence in using a mix of analytical and numerical techniques to solve key graduate level engineering problems.
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Graduate students appreciate areas where they need additional backgound in applied mathematics and/or numerical methods, and they take relevant Mathematics and Computer Science Department courses.
- Topics covered
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Numerical solutions of ordinary differential equations -- initial and boundary value, iteration methods
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Perturbation techniques -- regular and singular, boundary layers
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Partial differential equations -- classification, methods of solution, boundary conditions
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Inversion of large matrices -- LU decomposition, tridiagonal, sparse
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Numerical solutions of partial differential equations -- elliptic, parabolic, hyperbolic
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Numerical determination of eigenvalues, eigenvectors
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Numerical solution of integral equations
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Other computing considerations -- machine parameters, FFTs/filtering, random numbers, solution verification, arbitrary precision
- Class/laboratory schedule
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EMA/NEEP 548 meets twice a week in conventional 75-minute class periods, with some class periods held in a computer-equipped classroom.
- Contribution of course to meeting the professional component
- This course contributes primarily to the students' knowledge of engineering topics, but does not provide design experience.
The following statement indicates which of the following considerations are included in this course: economic, environmental, ethical, political, societal, health and safety, manufacturability, sustainability.
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This optional course contributes only indirectly to meeting the professional component in that it provides an opportunity for exposure to graduate level mathematical and computational techniques for engineering analysis.
- Relationship of course to undergraduate degree program objectives and outcomes
- This course primarily serves students in the department. The information below describes how the course contributes to the undergraduate program objectives.
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This optional course supports the program objectives of the undergraduate EMA and NE degrees in that it provides an intellectual challenge and broadening for mathematically and computationally inclined undergraduate students, and an introduction to graduate level thinking and coursework for students planning to go on to graduate school.
- Assessment of student progress toward course objectives
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50% Homework (8 to 10 sets -- half analytic and half numerical)
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25% Mid-term exam
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25% Numerical project
- Person(s) who prepared this description
