Numerical Integration: Newton-Cotes Formulas

4 hours

Duration

Materials

Objectives

Session Overview

Comprehensive study of numerical quadrature including trapezoidal rule, Simpson's rules, and higher-order Newton-Cotes formulas. Composite rules, error analysis, and adaptive integration.

Learning Objectives

By the end of this session, you should be able to:

Derive trapezoidal and Simpson's rules using polynomial interpolation
Implement composite trapezoidal and Simpson's rules for improved accuracy
Understand Newton-Cotes formulas of various orders and their stability
Analyze quadrature errors and convergence rates
Apply Romberg integration for systematic error reduction
Implement adaptive quadrature methods with automatic error control

Course Materials

Download materials for offline study and reference

Quadrature Theory and Newton-Cotes Derivations (45 pages)

Available material

Composite Rule Implementations and Error Analysis

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Romberg Integration Algorithm and Examples

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Adaptive Integration Strategies

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Stability Analysis of High-Order Formulas

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Integration Project: Comprehensive Quadrature Package

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Performance Comparison Studies

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Engineering Application Examples

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