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

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Presentation transcript:

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

Instructional Objective(s) with animation/simulation ITEM YOUR SPECIFICATIONS Numerical Analysis Topic Name URL of animation/simula tion 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 doWhat student will do Which visualization feature used, if any 13 Numerical Approximation and Errors. Understand different types of errors. Yes 29Solution of Algebraic and Transcendental Equation Understand the basic and able to solve algebraic and transcendental equation. Yes 39Solution of Linear EquationsStudent learn to solve linear system using matrices. Yes 47Numerical IntegrationIntegration can be solve by different adaptive methods. Yes 59Ordinary Differential Equations Help to solve differential equation more accurately. No 69Curve 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 IntegrationObjectives 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 doWhat student will do Which visualization feature used, if any 11Explain Integration Methods. Understand different types of errors. Yes 21Trapezoidal Rule.Understand the basic and able to solve integration. Yes 31Simpsons 1/3 & 3/8 RuleStudent learn to take proper method for accuracy Yes 41Boole’s Rule and Error.Integration can be solve by different adaptive methods. Yes 51Weddle Rule and Error.Help to solve integration equation more accurately. Yes 61Romberg Integration.Student learn to take proper method for accuracy Yes 71Gaussian Quadrature.Integration can be solve by different adaptive methods. Yes ‘Lesson Plan of Numerical Integration’

Repositories you can consult RepositoriesURL OSCARhttp://oscar.iitb.ac.in/availableanimati ons.do MIT-TEALhttp://web.mit.edu/8.02t/www/802TE AL3D/ National Science Digital Library (NSDL) SCRATCH-MIThttp://scratch.mit.edu/studios/73223/ Khan Academyhttps:// MERLOThttp:// tm Physics + Maths appletshttp:// tml Wisconsin Onlinehttp:// online.com/ListObjects.aspx