Application of Differentiation and Integration: Creating ...

1 Application of Differentiation and integration : Creating RC circuits and using function generator in MyDAQ to analyze the functions Step-Up Lesson Plan 2015 Santhi Prabahar, Math Teacher Johns Creek High School Georgia Title: Application of Differentiation and integration function in engineering field. Creating RC Circuits to generate functions using function generator NI MyDAQ and then analyze the functions using Calculus. Problem: Do we use calculus in everyday life? What is the relationship between electrical circuit and calculus? What are differentiator and Integrator circuits?

2 Abstract: High School calculus students often ask the question When do we ever use this calculus in our lives? This lesson shows them how the electrical signal changing from Differentiation to integration and integration to Differentiation . The concept of understanding integrating a differential function gives the original function is very hard for a high school student. This lesson basically explains when you send a function through the function generator it will show the Differentiation function and Integrated function. State and National Standards: According to College Board, students who are enrolled in AP Calculus AB are expected to Understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

3 Learn the concept of derivative as a function as in applications , and computations. Learn the concept of Integrals and its applications TAG- Talented and Gifted Standards: The student uses a variety of multi-media and innovative technology to create illustrations, models, charts, tables, and graphs as tools for communication.(ACS) The student develops and uses systematic procedures for recording and organizing information(ARS) The student questions accepted practices, rules, and existing principles to discover new knowledge.(CPCTS) The student designs, applies, evaluates, and adapts a variety of innovative strategies to when problem solving ( , recognizes problems, defines problems, identifies possible solutions, selects optimal solution, implements solution, and evaluates solution).

4 (CPCTS) The student asks probing, insightful, and relevant questions. The student responds to questions with supporting information that reflects in-depth knowledge of a topic The student identifies and illustrates basic principles and the foundational concepts that are central to understanding the essence of a field of study. Objectives: Students will learn the applications of derivative and Integrals in engineering field. Students will learn to graph both derivative and integral of a function on the same plane. Students will recognize the given graph of f(x) draw graphs of f (x) and f (x) Students will learn from given graph of f (x) to find where the function is increasing, decreasing, max, min, points of inflection, and concavity Students will learn the connection to physics by learning Ohm s law Students will learn to create an RC circuit and use NI MyDAQ to analyze the graphs.

5 Students should be able to communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems. Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral. Students should be able to use technology to help solve problems, experiment, interpret results, and verify conclusions. Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement. Anticipated Learner Outcomes: Students are able to understand the Application of Differentiation and integration .

6 Students will be able to state Ohm s law = . Where V = voltage , I = Current ,and R = resistance Students will be able to know that the Current is the derivative of Voltage and Voltage is the integral of the current. , = ,-,. =56 where C is the capacitor which is always a constant. Students will be able to make simple RC circuits. Students will able to graph both Differentiation and integral of a function using oscilloscope in MI myDAQ equipment Students will be able to relate that calculus is used in electric signals. Students will able to analyze the input and output of the graphs.

7 Students will be able to connect with antiderivative of the functions Student will be able to connect with velocity, acceleration and position of the function Assessment and Rubric: This project is done by group of 2. The following documents need to be submitted for a test grade. Each group submits one document with both names written on each document. (No name no gradeJ ) 1. Completed applications of Integral worksheet.(10 points) 2. LAB 1 worksheet with calculations.(30 points) 3. LAB 2, Part A and Part B with pictures and screenshots copy pasted on a word document and labeled correctly Make sure you write your names on the top with period and date.

8 (40 points) 4. Complete the applications of integrals worksheet 2 problems.(20 points) Background Knowledge: Students should have learned the derivatives unit and antiderivatives. This lesson and labs can be done right after the introduction of integrals. If the students know about Ohm s law and the simple circuit you can directly jump into the LAB 1 and LAB 2 Materials Needed: Day1 Application of Integrals WS1 Day2 and Day 3 LAB assignments packets Day 4 Application of Integrals WS 2 Computer with NI myDAQ software installed. It is available on line. It is easy to use the CD that comes with the myDAQ, but you may also download it from the National Instruments website at: NI myDAQ equipment with all the attachments.

9 Lesson Plan: Day 1: Warm-up: Introduce the Ohm s law. Explain the relationship between Voltage, Current, and resistance . Opening: Explain the Ohm s law and the relationship between the differential and Integral equations of Ohm s law Ohm s law states that the electrical difference between the two points on a circuit Voltage (V) is the product of the current between those two points (I) and the resistance (R) between all electrical devices between those two points. = , = , = , = , The current BF 6 HIEJD @ABCCDEDFGD BF.

10 BKD L ----------- (1) The charge = ------ (2) Differentiating the equation (2) we get ,-,. ----- (3) Substituting (1) in (3), we get, = ,-,. ------- (4) Integrating equation (4) we get = This implies =56 ----- (5) From equation (4) and (5) we can see that Current is the derivative of the voltage and Voltage is integral of the current. Solve the following problems: 1. Find Voltage if the current I = A and R = 5 k . Answer: V= (5) = volts 2. Find the Current in Amp if V= 12V and R = 2k . Answer: I= V/R = 12/2 = 6mA 3.