College of Engineering and Computer ScienceMechanical Engineering DepartmentMechanical Engineering 501ASeminar in Engineering AnalysisFall 2004 Number: 17472 Instructor: Larry CarettoCourse OutlineCatalog Description for ME 501AB, Seminar in Engineering AnalysisAnalytic and numerical methods applied to the solution of engineering problems at an advanced level. Solution methods are demonstrated on a wide range of engineering topics, including structures, fluids, thermal, thermal energy transport, and mechanical systems. ME 501A and 501B form an integrated, two semester sequence.A. Emphasizes physical phenomena that can be described by systems of ordinary differential equations.B. Emphasizes physical phenomena that can be described by partial differential equations.Instruction informationName Larry CarettoEmail address [email protected] EA 1333Phone 818.677.6448Fax 818.677.7062Office hours Monday and Wednesday, 3:15 to 3:45 pm and Tuesday and Thursday 4:45 to 5:15 pm, also by email, drop-in, or appointmentCourse InformationCourse number 17472Class hours Tuesday – Thursday, 5:30 – 6:45 pmClass location Oviatt Library 5Web site http://www.csun.edu/~lcaretto/me501aExpanded DescriptionAs noted in the catalog description, this is the first course in a two-course sequence in engineering analysis. The one-year course deals with the analysis of these problems using classical mathematical solutions and applying techniques of numerical analysis to the problems.While emphasizing “physical phenomena that can be described by systems of ordinary differentialequations,” the introductory 501A course also provides a common set of concepts that will be used throughout the one-year sequence. These concepts generalize the usual notion of two-dimensional and three-dimensional vectors that students have seen in courses from high-school physics to their engineering mechanics courses. In the general case, a “vector” may have an arbitrary number of components. In addition, the concept of two vectors being perpendicular (or orthogonal) so that their dot product vanishes is extended to integrals of functions. Similarly, the notion that vectors can be represented in terms of their basic components is extended to representing functions in terms of a set of basis functions.Engineering Building Room 1333 Mail Code Phone: 818.677.6448E-mail: [email protected] 8348 Fax: 818.677.7062Although there are no formal prerequisites for this course, 500-level courses are designed primarily for graduate students, but allow the enrollment of advanced undergraduates. All students in the course are expected to have a background in mathematics and numerical analysisthat is equivalent to a graduate in mechanical engineering or other engineering discipline. This includes mathematics courses through ordinary differential equations and some familiarity with matrices and with numerical analysis. (This would be equivalent to the completion of Mathematics 280 and Mechanical Engineering 309 at CSUN.) This expected background material will be reviewed at appropriate times during the course.TextbooksThe two texts listed below that will be used during the one-year 501AB course. The text by Kreyszig will be extensively used during both 501A and 501B. It covers the traditional mathematical analysis topics and has introductory material on numerical analysis that is almost sufficient for the 501A course. Readings will be assigned from the text by Hoffman in both 501A and 501B. Its main use, however, will be in 501B.Erwin Kreyszig, Advanced Engineering Mathematics, (eighth edition) Wiley, 1999. (ISBN: 0-471-15496-2)Joe D. Hoffman, Numerical Methods for Engineers and Scientists, (second edition) Marcel Dekker, 2001. (ISBN: 0-824-70443-6)Course ConductCourse Objectives – This course has three basic goals: (1) enhance students ability to perform more complex mathematical analyses of engineering problems and get actual answers to those problems; (2) improve students’ understanding of how mathematical applications are defined, derived and related, and (3) give students the ability to read and understand publications in their field that make use of advanced concepts in engineering analysis. This course will address all these goals.In particular, students should be able to achieve the following goals by completing this course.- Understand that seemingly disparate concepts such as vectors and function expansions have common vocabulary and that an understanding of one will strengthen the understanding of the other.- Understand publications of applied engineering analysis that involve simultaneous linear equations, matrices, eigenvalues, ordinary differential equations, special functions such as Bessel functions, orthogonal functions, eigenfunction expansions.- Be familiar with algorithms and software packages for solving simultaneous linear equations, matrix eigenvalue problems, and the numerical integration of systems of ordinary differential equations and understand the limitations of these approaches.- Analyze engineering problems that require systems of simultaneous equations, obtain solutions to those problems where solutions are possible, and understand why unique solutions may not be possible. - Perform manipulations of matrices when this is appropriate for the analysis of engineering systems.- Understand the role that eigenvalues and eigenvectors play in engineering analysis, obtain these quantities in simple cases, and use software to obtain them in systems that are more complex.- Understand when solutions to ordinary differential equations are possible and obtain solutions in those cases.Engineering Building Room 1333 Mail Code Phone: 818.677.6448E-mail: [email protected] 8348 Fax: 818.677.7062- Obtain power series solutions to ordinary differential equations.- Obtain solutions to ordinary differential equations that involve special functions such as Bessel functions.- Be familiar with the use of Laplace transforms for solving ordinary differential equations and be able to use a transform table to get such solutions in simple cases.- Use various algorithms for solving systems of ordinary differential equations and understand the approaches used to keep the accuracy to the solution within the bounds desired by the user. This ability should apply to initial value problems, boundary value problems, and eigenvalue problems.Class participation – Learning engineering subjects is a difficult task that