MATH 2370 Lecture Notes - Lecture 1: Trapezoidal Rule, Gaussian Function, Matlab
25 Nov 2020
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In calculus, one computes a "definite integral" of a function f(x) to find the exact area under f(x) (if f(x)>0), above the x axis and between 2 vertical lines x=a and x=b. In calculus, the symbol for this exact area is: that an event occurs, sometimes we need the area under: We need the area under the curves in many fields, including statistics. Where and are position constants; this is called the gaussian function ("bell curve") In calculus, the fundamental theorem tells us how to compute the exact area, possible to find this we must approximate. Trapezoidal rule - one of many algorithms to approximate the area under f(x) We are finding the area under a linear spline. Assume n trapezoids between x=a and x=b of equal width, Can implement in matlab with a for loop and running sum. Simpson"s rule: another algorithm to approximate the area. It finds the area under a quadratic spline rather than a linear.
