MATLABTutorial Numerical Integration（MATLABTutorial数值积分）.pdf

MATLAB Tutorial – NUMERICAL INTEGRATION NUMERICAL INTEGRATION Numerical integration is a mathematical technique used to solve integrals. It can be done without taking calculus. Students who have not completed calculus should not be intimidated by this material. Most of it deals with calculating areas under curves, which should not be difficult for those who have not completed calculus. That being said, it is a good idea to learn how numerical integration is different from analytical integration. In the first semester of calculus, the average student will deal with limits and taking derivatives. The most important definition learned in the first calculus class is the following: ∆ lim ∆ ∆ This is the definition of a derivative. Graphically, it is the slope exactly at a point. An analytical solution (or exact solution) exists if this limit can be evaluated. The student will spend a large portion of their calculus course learning/memorizing many of these limits. For example, many students will memorize that the derivative of x2 is 2x or the derivative of ex is equal to itself. Once this material has been mastered the student moves on to Calculus II where they do a significant amount of integration. Integration involves taking the anti-derivative of an equation, which is basically differentiation in reverse. They will see the following equation very often: This is an indefinite integral. The answer will be the anti-derivative plus a constant. The student will spend a significant amount of time learning anti-derivatives of many functions. For example, the anti-deri