iit bombay january, 2015 ‘numerical analysis’ with visualization by rasik r. shah
TRANSCRIPT
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I I T B O M B AYJ A N U A RY, 2 0 1 5
‘Numerical Analysis’ with Visualization
byRasik R. Shah
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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)
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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’
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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.
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Numerical Integration
Basic Issues in Integration Objectives
Key concepts
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Newton’s Cotes Integration
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Trapezoidal Rule
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Simpson’s 1/3 rule
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Simpson’s 3/8 rule
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Key Notes
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Comparisons of Method
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Romberg Integration
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Taking different value of a
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Continue…..
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Gaussian Quadrature
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Example:
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Comparison of Romberg & Gauss Quad.
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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’
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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