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[edit | edit source]
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 and 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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- Enduring Understanding
Assessment of Learning
- Formative Assessment
- In Class (groups)
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- Homework (individual)
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- In Class (groups)
- Summative Assessment
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Legacy Cycle[edit | edit source]
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.
RESEARCH & REVISE
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TEST YOUR METTLE
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GO PUBLIC
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Pre-Lesson Quiz[edit | edit source]
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Test Your Mettle Quiz[edit | edit source]
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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