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UTPA STEM/CBI Courses/Circuits/Laplace Transform

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Course Title: Circuit II

Lecture Topic: Laplace Transform

Instructor: Wenjie Dong

Institution: UTPA

Backwards Design

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Course Objectives

  • Primary Objectives- By the next class period students will be able to:
    • Calculate Laplace transform for a given function
    • Apply Laplace transform to analyze circuits
  • Sub Objectives- The objectives will require that students be able to:
    • Convert a signal from time domain to s domain
  • Difficulties- Students may have difficulty:
    • Remembering the definition of a Laplace transform
    • Calculating Laplace transforms
  • Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
    • Solve differential equations
    • Analyze linear systems
    • Analyze linear circuits

Model of Knowledge

  • Concept Map
    • Signal in time domain
    • Integral transform
    • Signal in 's' domain
  • Content Priorities
    • Enduring Understanding
      • Laplace transform
    • Important to Do and Know
      • Differential equations
      • Basic laws for circuit analysis
      • Calculus
    • Worth Being Familiar with
      • Linear algebra


Assessment of Learning

  • Formative Assessment
    • In Class
      • Quiz for calculating Laplace transform of a simple signal function
    • Homework (individual)
      • Homework for Laplace transform of some signal functions
      • Homework for analyzing linear circuits using Laplace transform
  • Summative Assessment
    • Quiz
    • Middle term test

Legacy Cycle

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OBJECTIVE

By the next class period, students will be able to:

  • Apply Laplace transforms to analyze circuits

The objectives will require that students be able to:

  • Calculate Laplace transforms for some signals


THE CHALLENGE

For a circuit with many meshes, how do you find the current for each mesh?

GENERATE IDEAS

Provide the challenge and ask for opinions from the students

MULTIPLE PERSPECTIVES

The students work for 10 minutes and come up with ideas

RESEARCH & REVISE

The teacher introduces the definition of a Laplace transform and explains some key points in the definition. Then, the teacher give several examples on how to find Laplace transforms for several typical functions in the time domain.

TEST YOUR METTLE

  1. Students do an example.
  2. Instructors ask questions in order for students to explain their solutions and understanding of concepts.
  3. Answer the questions in the homework.


GO PUBLIC

  1. Students demonstrate to the instructor and other students how to calculate Laplace transform.
  2. Students turn in their solutions.

Pre-Lesson Quiz

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  1. Find the solution of y"(t)+10y'(t)+6y(t)=5.
  2. Find the current of RLC circuit.

Test Your Mettle Quiz

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  1. Find the current of RLC circuit with the aid of Laplace transforms
  2. Find the solutions to the differential equations y"1(t)+3y'2(t)+2y2(t)=4 and y"2(t)+5y'1(t)+3y2(4)=6
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