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# “Numerical Integration” Courseware

## Course Materials Include:

#### Numerical Integration

by Dr. Matthew Leineweber, San Jose State University.

This curriculum module contains interactive live scripts that teach two fundamental techniques for approximating definite integrals: the trapezoid rule and Simpson’s rules. These rules are derived from Lagrange interpolating polynomials and explored through interactive visualizations. Each lesson concludes with a guided activity in which students implement the discussed integration rule. These live scripts can be used as part of a lecture, as activities in an instructional setting, or as an interactive assignment to be completed outside of class.

Learning goals

TrapezoidRule.mlx (an interactive lesson that explores the trapezoid rule):

• Explain numerical quadrature and its relationship to the definite integral.
• Describe how the trapezoid rule is derived.
• Illustrate the trapezoid rule graphically.
• Compare integration of a continuous function with integration of tabulated data.
• Implement the trapezoid rule in MATLAB.

SimpsonsRules.mlx (an interactive lesson that explores Simpson’s rules):

• Describe how Lagrange interpolating polynomials can be used to derive integration rules.
• Illustrate Simpson’s 1/3 rule graphically.
• Explain the steps required to implement Simpson’s 1/3 rule.
• Compare the accuracy and limitations of Simpson’s 1/3 rule with those of Simpson’s 3/8 rule.
• Implement Simpson’s 3/8 rule in MATLAB.

Have any questions or feedback? Contact the MathWorks online teaching team.