- 103 Views
- Uploaded on

Engineering Computation. Lecture 0. Introduction. Objectives

Download Presentation
## Lecture 0

**An Image/Link below is provided (as is) to download presentation**

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript

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

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

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

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

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

- 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

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

Download Presentation

Connecting to Server..