IIT BOMBAY JANUARY, 2015 ‘Numerical Analysis’ with Visualization by Rasik R. Shah.

I I T B O M B AYJ A N U A RY, 2 0 1 5

‘Numerical Analysis’ with Visualization

byRasik R. Shah

Instructional Objective(s) with animation/simulation

ITEM YOUR SPECIFICATIONS

•Numerical AnalysisTopic Name

•http://www.hegartymaths.com/•http://www.falstad.com/mathphysics.html •http://nsdl.org/browse/collections/All

URL of animation/simu

lation

•Understand the basic algorithms to solve non-linear equations, Linear algebraic equations, Interpolation and Curve fitting, Numerical Integration and ordinary differential equation.

Learning objective(s)

Step No.

Time(Hrs.)

What teacher will do What student will do Which visualization feature used, if any

1 3 Numerical Approximation and Errors.

Understand different types of errors.

Yes

2 9 Solution of Algebraic and Transcendental Equation

Understand the basic and able to solve algebraic and transcendental equation.

Yes

3 9 Solution of Linear Equations

Student learn to solve linear system using matrices.

Yes

4 7 Numerical Integration Integration can be solve by different adaptive methods.

Yes

5 9 Ordinary Differential Equations

Help to solve differential equation more accurately.

No

6 9 Curve Fitting and Interpolation

Understand the concept of interval and how to fit the curve.

Yes

‘Lesson Plan’

Process to follow for creating ‘Lesson Plan of Numerical Integration’ with visualization

4

Step 1• Objectives to solve Integration

examples by numerical solution.

Step 2• Apply Trapezoidal rule, Simpson’s

rule, Romberg Integration, etc to solve Integration.

Step 3• Comparisons of all method for

better accuracy.

Numerical Integration

Basic Issues in Integration Objectives

Key concepts

Newton’s Cotes Integration

Trapezoidal Rule

Simpson’s 1/3 rule

Simpson’s 3/8 rule

Key Notes

Comparisons of Method

Romberg Integration

Taking different value of a

Continue…..

Gaussian Quadrature

Example:

Comparison of Romberg & Gauss Quad.

Step No.

Time(Hrs.)

What teacher will do What student will do Which visualization feature used, if any

1 1 Explain Integration Methods.

Understand different types of errors.

Yes

2 1 Trapezoidal Rule. Understand the basic and able to solve integration.

Yes

3 1 Simpsons 1/3 & 3/8 Rule Student learn to take proper method for accuracy

Yes

4 1 Boole’s Rule and Error. Integration can be solve by different adaptive methods.

Yes

5 1 Weddle Rule and Error. Help to solve integration equation more accurately.

Yes

6 1 Romberg Integration. Student learn to take proper method for accuracy

Yes

7 1 Gaussian Quadrature. Integration can be solve by different adaptive methods.

Yes

‘Lesson Plan of Numerical Integration’

Repositories you can consult

Repositories URL

OSCAR http://oscar.iitb.ac.in/availableanimations.do 

MIT-TEAL http://web.mit.edu/8.02t/www/802TEAL3D/ 

National Science Digital  Library (NSDL) 

http://nsdl.org/browse/collections/All

SCRATCH-MIT http://scratch.mit.edu/studios/73223/ 

Khan Academy https://www.khanacademy.org/ 

MERLOT http://www.merlot.org/merlot/index.htm 

Physics + Maths applets http://www.falstad.com/mathphysics.html 

Wisconsin Online http://www.wisc-online.com/ListObjects.aspx