Engineering
Computation
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 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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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: [email protected]
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
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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: [email protected]
• 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: BrooksCole, cop.
– Gil, A., Segura, J., Temme, NM, “Numerical Methods
for Special Functions”, 2007, SIAM.
– Kincaid D., Cheney W., “Análisis Numérico”. AddisonWesley 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:
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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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 that’s all for today!
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Numerical Methods for Engineers