Sin ttulo de diapositiva

1
EngineeringComputation
Lecture 0
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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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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 ODEs. 5. Introduction
to numerical solutions of PDEs. 6. Introductory
probability statistics. 7. Curve-fitting,
regression, and cubic splines. 8. Numerical
integration and differentiation.
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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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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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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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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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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_at_unican.es Offic
e 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
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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_at_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

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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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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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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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Introduction

• Schedule
• Monday, Wednesday 830-1030 (2 sessions
  of 50 each) Lectures
• Friday 830-930 Computer Session (at
  the computer lab of the
  department of Applied Math. and Comput. Science).

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Contributions to the final grade Computer
Assignments (CA) 20 For 2 Prelims 40 Final
Exam 20 Attendance participation
various 20
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• 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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• and thats all for
  today!