# 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.
* Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
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.
Model of Knowledge
* Concept Map
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* Content Priorities
** Enduring Understanding
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** Important to Do and Know
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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:
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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.
* 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?
The idea is to lead them to a first-order approximation of instantaneous velocity.
$v_{instantaneous}\approx \Delta v/\Delta t$
RESEARCH & REVISE
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TEST YOUR METTLE
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GO PUBLIC
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## Test Your Mettle Quiz

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