Lecture 10

Question 1

What is the definition of an integral?

Answer 1

Question 2

What is the quadrature rule?

Answer 2

Question 3

How are Quadrature rules formulated? What are its weights? When is it open or closed?

Answer 3

Question 4

How accurate are the Quadrature rules? Give a bound. How to improve the accuracy?

Answer 4

Question 5

What are proggressive quadrature rules?

Answer 5

Question 6

How stable are quadrature rules?

Answer 6

Question 7

What is the Newton-Cores quadrature? Name three examples (no formulas).

Answer 7

Question 8

What is the midpoint rule (integration)?

Answer 8

Question 9

What is the Trapezoid rule (integration)?

Answer 9

Question 10

What is Simpson’s rule?

Answer 10

Question 11

How do you transform a quadrature rule to a new interval?

Answer 11

Question 12

What is a composite quadrature rule?

Answer 12

Question 13

What is the degree of exactness (integration)?

Answer 13

Question 14

What is the error estimate from integration based on r?

Answer 14

Question 15

How do you improve the accuracy of integration (quadrature)?

Answer 15

Question 16

What is the Clenshaw-Curtis Quadrature?

Answer 16

Question 17

What is a Gaussian Quadrature?

Answer 17

Question 18

What is polynomial division?

Answer 18

Question 19

How to change the interval for a Gaussian Quadrature?

Answer 19

Question 20

What is adaptive integration?

Answer 20

Question 21

How to do differentiation? What is a better alternative?

Answer 21