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Engineering Computation. Lecture 0. Introduction. Objectives

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Lecture 0

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EngineeringComputation

Lecture 0

E. T. S. I. Caminos, Canales y Puertos

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 Puertos

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 Puertos

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 Puertos

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 Puertos

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 Puertos

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 Puertos

Introduction

Instructors:Prof. Amparo Gil

Departamento de Matemática Aplicada y CC. De la Computación

Escuela de Ingenieros de Caminos

e-mail: amparo.gil@unican.es

Office Hours: by appointment via e-mail.

Visiting Prof. Sarah Hallerberg

Departamento de Matemática Aplicada y CC. De la Computación

Escuela de Ingenieros de Caminos

E. T. S. I. Caminos, Canales y Puertos

Introduction
• Course computing framework:
• – Microsoft Excel.
• Numerical Languages
• – MATLAB
• Electronic Communication by e-mail:
• Computer assignments will be submitted as attachments via e-mail: amparo.gil@unican.es
• Text files, Excel & MATLAB documents as attachments.
• documents will be distributed via the ENGCOMP web page. http://personales.unican.es/gila/UC-Cornell

E. T. S. I. Caminos, Canales y Puertos

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 Puertos

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 Puertos

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 Puertos

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 Puertos

• Computer Assignments (CA) 20%
• For 2 Prelims 40%
• Final Exam 20%
• Attendance & participation & various 20%

E. T. S. I. Caminos, Canales y Puertos

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 Puertos

… and that’s all for today!

E. T. S. I. Caminos, Canales y Puertos