“Numerical Integration” Courseware
Course Materials Include:
- Courseware description
- 2 MATLAB live scripts
- 2 MATLAB live script solutions
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.
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