UTPA STEM/CBI Courses/Numerical Methods and Statistics/Taylor Series

Course Title: MECE 2450 Numerical Methods and Statistics

Lecture Topic: Using the Taylor Series

Instructor: Javier A. Kypuros, Ph.D.

Institution: UTPA

Backwards Design
Course Objectives


 * Primary Objectives- By the next class period students will be able to:
 * use the Taylor series to approximate 1st- and 2nd-order derivatives.


 * Sub Objectives- The objectives will require that students be able to:
 * flow chart or pseudocode,
 * program "For" and "Do" loops,
 * program "if-then-else" statements,
 * numerically approximate derivatives.


 * Difficulties- Students may have difficulty:
 * translating a problem into logic and numerical algorithms,
 * understanding flowchart/pseudocode syntax, and
 * learning MATLAB.

The Taylor-Series is used through-out engineering to approximate complex functions that model physical phenomena. Non-linear functions like $$\sin {t}$$ and $$e^t$$ which appear in many areas of engineering can be approximated using the Taylor Series.
 * Real-World Contexts- There are many ways that students can use this material in the real-world, such as:

Model of Knowledge


 * Concept Map
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 * Content Priorities
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 * Worth Being Familiar with
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Assessment of Learning


 * Formative Assessment
 * In Class (groups)
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 * Homework (individual)
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 * Summative Assessment
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Legacy Cycle
OBJECTIVE

By the next class period, students will be able to: The objectives will require that students be able to:
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THE CHALLENGE

How can you estimate the instantaneous velocity and acceleration of a vehicle during the course of a drag race if the instrument panel does not function?

GENERATE IDEAS


 * You can use a stop watch and the odometer (if it functions) to measure distance traveled at various intervals.


 * Use GPS to track position at various time intervals.


 * Alternatively you can use markers on the side of the track that are at known distances and a stop watch.

MULTIPLE PERSPECTIVES

The professor will lead a discussion asking students probing questions. The idea is to lead them to a first-order approximation of instantaneous velocity. $$ v_{instantaneous} \approx \Delta v / \Delta t $$
 * If you travel to San Antonio from Edinburg and it takes you 4 hours, what is your average speed?
 * On interstates there are markers on the side of the road. If you have a watch, how might you estimate your current velocity?
 * How can you improve your velocity estimates?

RESEARCH & REVISE

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TEST YOUR METTLE

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GO PUBLIC

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Pre-Lesson Quiz

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Test Your Mettle Quiz
Saldivar.jess 04:50, 6 February 2010 (UTC)Don't forget to include the concept map and objective of this course
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