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

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.

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.

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).

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

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.

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.

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

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.

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"

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.

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.

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).

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%

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

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