“Numerical Integration” Courseware
Download the free mathematics courseware module using MATLAB.
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.
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.