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E. T. S. I. Caminos, Canales y Puertos1 Lecture 0 Engineering Computation

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E. T. S. I. Caminos, Canales y Puertos2 Introduction Objectives 1. Introduction (quite ambitious!) to numerical methods for engineering as a general and fundamental tool for all engineering disciplines. We plan to cover (almost) the main topics of numerical analysis and basic concepts of probability & statistics. 2. Programming will be essential; we will use commercial software widely used in science and engineering: MATLAB and Excel. 3. We will illustrate and discuss how numerical methods are used in practice. We will consider examples from Engineering.

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E. T. S. I. Caminos, Canales y Puertos3 Introduction ENGCOMP Course overview 1. Approximation, errors, and precision. 2. Finding roots of functions of one variable. 3. Simultaneous linear equations: - tri-diagonal, LU decomposition, iterative solutions; - norms, condition number, operation counting. 4. Numerical methods for ODE’s. 5. Introduction to numerical solutions of PDE’s. 6. Introductory probability & statistics. 7. Curve-fitting, regression, and cubic splines. 8. Numerical integration and differentiation.

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E. T. S. I. Caminos, Canales y Puertos4 Introduction Why are Numerical Methods so widely used in Engineering? Engineers use mathematical modeling (equations and data) to describe and predict the behavior of systems. Closed-form (analytical) solutions are only possible and complete for simple problems (geometry, properties, etc.). Computers are widely available, powerful, and (relatively) cheap. Powerful software packages are available (special or general purpose).

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E. T. S. I. Caminos, Canales y Puertos5 Introduction A few applications of Numerical Methods in Engineering: Structural/mechanical analysis, design, and behavior. Communication/power Network simulation Train and traffic networks Computational Fluid Dynamics (CFD): Weather prediction Groundwater & pollutant movement

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E. T. S. I. Caminos, Canales y Puertos6 Introduction Why study Numerical Methods? Numerical Analysis is a Discipline: Need to understand concepts and theory - Know what problems can be solved. - Know what problems cannot be solved, or when problems will be troublesome. Need to understand methods and techniques - Know why methods work, or judge when they are working. - Be able to create or modify tools (software) as needed. - Evaluate errors, convergence, and stability of arithmetic approximations.

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E. T. S. I. Caminos, Canales y Puertos7 Introduction Why study Numerical Methods? (continued) Use of Numerical Methods is an Art: Numerical methods are approximate. The most appropriate method(s) is not always obvious. Evaluating precision and accuracy is an essential part of the process.

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E. T. S. I. Caminos, Canales y Puertos8 Introduction Instructors: Prof. Amparo Gil Departamento de Matemática Aplicada y CC. De la Computación Escuela de Ingenieros de Caminos Universidad de Cantabria Office Hours: by appointment via . Visiting Prof. Sarah Hallerberg Departamento de Matemática Aplicada y CC. De la Computación Escuela de Ingenieros de Caminos Universidad de Cantabria

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E. T. S. I. Caminos, Canales y Puertos9 Introduction Course computing framework: Spreadsheets – Microsoft Excel. Numerical Languages – MATLAB Electronic Communication by Computer assignments will be submitted as attachments via Text files, Excel & MATLAB documents as attachments. documents will be distributed via the ENGCOMP web page.

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E. T. S. I. Caminos, Canales y Puertos10 Introduction ENGCOMP Course Materials Required Textbook and Notes: Chapra & Canale, Numerical Methods for Engineers, 4th Ed., 2002 Computer sessions (recommended texts): Palm, Introduction to MATLAB for Engineers. The MathWorks, The Student Edition of MATLAB. Pratap, Getting Started with MATLAB. Additional material will be available at the course website, e.g.: "Introduction to Spreadsheets: Using Microsoft EXCEL" "Primer on MATLAB"

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E. T. S. I. Caminos, Canales y Puertos11 Selected bibliography –Datta, NB, “Numerical linear algebra and applications”, 1995, Pacific Grove, California: Brooks- Cole, cop. –Gil, A., Segura, J., Temme, NM, “Numerical Methods for Special Functions”, 2007, SIAM. –Kincaid D., Cheney W., “Análisis Numérico”. Addison- Wesley Iberoamericana,1994. –Lambert, J.D., “Numerical Methods for Ordinary Differential Equations”, 1973, John Wiley & Sons. –Mitchell, A.R., Griffiths, D.F., “The Finite Difference Method in Partial Differential Equations”, 1980, Wiley, London. –Schwartz, H.R., “Finite Element Methods”, 1998, Academic Press, London.

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E. T. S. I. Caminos, Canales y Puertos12 Introduction Weekly Assignments Problem Sets (PS) - teams of 3; work together, check each other - teams to be formed at the end of September. Computer Assignments (CA) due Friday -teams of 3; work together, learn from each other -submit electronically Assignment submissions must follows the standards described on the course web page.

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E. T. S. I. Caminos, Canales y Puertos13 Introduction Schedule: Monday, Wednesday: 8:30-10:30 (2 sessions of 50’ each) Lectures Friday: 8:30-9:30 Computer Session (at the computer lab of the department of Applied Math. and Comput. Science).

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E. T. S. I. Caminos, Canales y Puertos14 Contributions to the final grade: Computer Assignments (CA)20% For 2 Prelims 40% Final Exam 20% Attendance & participation & various20%

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E. T. S. I. Caminos, Canales y Puertos15 Preliminary exams: Prelim 1: To be announced (most probably at the end of October). Prelim 2: To be announced. Final exam To be announced

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E. T. S. I. Caminos, Canales y Puertos16 … and that’s all for today!

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