Beginning Scientific Computing

Integration and Differentiation

Lecture 1

 

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NUMERICAL DIFFERENTIATION METHODS: From simple Taylor series expansions, the theory of numerical differentiation is developed.

 

MATLAB COMMANDS

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Supplementary Videos

 

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Mean Value Theorem

Lecture 2

 

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HIGHER-ORDER ACCURACY SCHEMES FOR DIFFERENTIATION AND INTEGRATION: The accuracy of the differentiation approximations is considered and new schemes are developed to lower the error. Integration is also introduced as a numerical algorithm.

 

MATLAB COMMANDS

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MATLAB CODE

 

Lecture 3

 

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HIGHER-ORDER INTEGRATION SCHEMES: Higher-order numerical integration schemes are considered along the classic schemes of trapezoidal rule and Simpson’s rule.

 

MATLAB COMMANDS

TRAPZ CUMTRAPZ QUAD

MATLAB CODE

 

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