# UTPA STEM/CBI Courses/Circuits/Laplace Transform

Course Title: Circuit II

Lecture Topic: Laplace Transform

Instructor: Wenjie Dong

Institution: UTPA

## Backwards Design

[edit | edit source]**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

- In Class

- Homework (individual)
- Homework for Laplace transform of some signal functions
- Homework for analyzing linear circuits using Laplace transform

- Homework (individual)

**Summative Assessment**- Quiz
- Middle term test

## Legacy Cycle

[edit | edit source]**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**

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

**GO PUBLIC**

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

## Pre-Lesson Quiz

[edit | edit source]- Find the solution of y"(t)+10y'(t)+6y(t)=5.
- Find the current of RLC circuit.

## Test Your Mettle Quiz

[edit | edit source]- Find the current of RLC circuit with the aid of Laplace transforms
- Find the solutions to the differential equations y"
_{1}(t)+3y'_{2}(t)+2y_{2}(t)=4 and y"_{2}(t)+5y'_{1}(t)+3y_{2}(4)=6