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Engineering Computation. Lecture 0. Introduction. Objectives

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EngineeringComputation

Lecture 0

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

introduction
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

introduction1
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

introduction2
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

introduction3
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

introduction4
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

introduction5
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

introduction6
Introduction

Instructors:Prof. Amparo Gil

Departamento de Matemática Aplicada y CC. De la Computación

Escuela de Ingenieros de Caminos

Universidad de Cantabria

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

Universidad de Cantabria

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

introduction7
Introduction
  • Course computing framework:
    • Spreadsheets
      • – 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

introduction8
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
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

introduction9
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

introduction10
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

slide14

Contributions to the final grade:

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

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

slide15

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

slide16

… and that’s all for today!

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