LECTURE 07 - Lecture 7 Lecture 7 MEEN 357 Engineering...

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Lecture 7 MEEN 357 Engineering Analysis for Mechanical Engineers 1 Lecture-07-MEEN357-2009.doc RMB Lecture 7 Possible Exam 1 Rules : EXAM 1 MEEN 357 February 17, 2009 Dr. Bowen Section: 502 Name: ____________________________________________ "Aggies do not lie, cheat, or steal, nor do they tolerate those who do." Aggie Code of Honor By my signature below I pledge that my conduct on this exam is consistent in every way with the Aggie Code of Honor: Signature: ____________________________________________ 1. This exam consists of ???? (?) problems that are weighted as shown below. 2. This is a open textbook ( Applied Numerical Methods with MATLAB ) open lecture note exam. a) The lecture notes are those posted on Vista Blackboard. 1. It is understood that you add incidental comments to your copies of these notes. b) You may also use graded homework solutions and the solutions posted on Vista Blackboard c) You may not use individual notes that you have created other than what you have added to the pages of the posted and printed class notes. 3. You may use handheld calculators unless the problem dictates otherwise. a) You may not use other computing devices. 4. Be sure to read the question carefully. 5. Be sure to show all work and calculations , and organize your solution procedure as clearly and systematically as possible. a) Example: Do not simply enter a string of numbers in your calculators and write down the answer. Write out the numbers in a mathematical formula and then show the answers obtained from doing the mathematical operations on your calculators. 6. Work problems in the space provided on the exam sheets. Clearly indicate continuation of the problem if you need extra pages. GRADE Problem ?: ________ / ?? % Problem ?: ________ / ??% Problem ?: ________ / ??% Problem ?: ________ / ??% TOTAL : ___________
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Lecture 7 MEEN 357 Engineering Analysis for Mechanical Engineers 2 Lecture-07-MEEN357-2009.doc RMB Roots to Nonlinear Equations Chapter 5 and 6 of the textbook. We are looking at various ways to find the roots of the equation ( ) 0 fx = (7.1) in some given interval of the real axis. As explained during Lectures 5 and 6, there are two methods that are used to find the roots of the function ( ) yfx = . Bracketing method: This method involves first establishing that the root lies within some interval and the use of an iteration scheme to find the root. o We discussed ± Bisection Method ± False Position Method Open method: An open method utilizes formulas that only require a single starting value or two starting values that do not necessarily bracket the root. o We discussed ± Newton-Raphson method ± Secant Method MATLAB Resources: 1. For the bisection method, the textbook provided, bisect.m. 2. For the false position method, we modified the bisect.m file and named it falsepos.m 3. For the Newton-Raphson method, the textbook provided newtraph.m . 4. The built in MATLAB command fzero can also be used. This command was discussed in Lecture 5. It is also discussed in Section 6.4 of the textbook.
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This note was uploaded on 02/23/2009 for the course MEEN 357 taught by Professor Anamalai during the Fall '07 term at Texas A&M.

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LECTURE 07 - Lecture 7 Lecture 7 MEEN 357 Engineering...

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