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Calculus II: Numerical Integration | Simpson's Rule | Week 1 Math Notes

by: Shellinator

Calculus II: Numerical Integration | Simpson's Rule | Week 1 Math Notes Math 150B

Marketplace > California State University - Fullerton > Mathematics (M) > Math 150B > Calculus II Numerical Integration Simpson s Rule Week 1 Math Notes
Cal State Fullerton
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About this Document

Briefly goes over integrals, left-endpoint approximation, right-endpoint approximation, midpoint approximation, and trapezoidal approximation. There is an example on the Simpson's Rule and how it's...
Calculus II
Adam Glesser
Class Notes
Math, Calculus, calculus II, calculus 2, Numerical Integration, Integrals, Antiderivative, Approximation, Simpson's Rule




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This 7 page Class Notes was uploaded by Shellinator on Saturday January 30, 2016. The Class Notes belongs to Math 150B at California State University - Fullerton taught by Adam Glesser in Spring 2016. Since its upload, it has received 33 views. For similar materials see Calculus II in Mathematics (M) at California State University - Fullerton.

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Date Created: 01/30/16
NUMERICS AL INTEGR ATION CONTENTS CLASS ANNOUNCEMENTS WHAT IS AN INTEGRAL? LEFT-ENDPOINT APPROXIMATION RIGHT-ENDPOINT APPROXIMATION MIDPOINT APPROXIMATION TRAPEZOIDAL APPROXIMATION SIMPSON’S RULE APPROXIMATION CLASS ANNOUNCEMENTS - review syllabus - homework is due everyWednesday - must use custom csuf textbook for homework - section 6.5 and worksheet due wednesday WHAT IS AN INTEGRAL? You can compute the area using an integral. An integral is also known as an antiderivative. Let’s sketch out x This shaded area is x a b WHAT IS AN INTEGRAL? What if the curve goes below the x-axis? x x If that’s the case, = - ENDPOINT APPROXIMATIONS Assume each endpoint has an equal distance from the endpoint next to it. sarthere end here LEFT-ENDPOINT end here start here RIGHT-ENDPOINT use midpoint MIDPOINT ENDPOINT APPROXIMATIONS Assume each endpoint has an equal distance from the endpoint next to it. statheeee end here TRAPEZOIDAL (straight line from one point to another) SIMPSON’S RULE It’s the most efficient and accurate method to compute because it uses parabolas instead of rectangles and trapezoids. x Example: Use Simpson’s Rule to approximate with n=4


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