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 1^st- and 2^nd-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
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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