What is the Substitution Rule?

When I learned the following basic formula of indefinite integrals in the calculus,at that time I was a teenager,the strange ideas had jump out my head.I would be a great girl in math if I can change all the ? in the following formula to the real functions     

What is the Euler’s Method? (1)

In mathematics and computational science,the Euler’s Method,named after Leonhard Euler,is a first-order numerical procedure for solving ordinary differential equations (ODEs) with     

What is the Euler’s Method?(2)

Solution: Since we know y=f(x)=x2+x-1, so get the initial value at x=1, which is f(1)=1,and also we can get y’=2x+1.     

How to find derivative of a parametric function?

When a particle moves on the plane,it can be described uncounted points corresponding to coordinates in a Cartesian coordinate system with the same unit on the each axis.However,not all the processes are convenient to express y in terms x.At times a relationship between x and y in terms of a third variable which is a various time t,is mexessary.     

What is continuity?

A continuous process is a person who draws the curve without a break,or,takes place gradually without interruption. Those are a daily language in continuity. However,in calculus,we notice that the limit of a function as x approaches a can often be found simply by calculating the value of the function at a. It means a continuous function     

What is the limit of an infinite sequence？

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What is the basic integration rule?

<正>In this paper you will learn the basic integration rule from the basic differentiation rule.Last time we have learned anti-derivative,indefinite integral,and the power rule in integration.Let us recall what the power rule in differentiation is.If n is a real number,and y=xn,then y'=nxn-1.Proof:Let y=xn,we get ln|y|=ln|xn|,Since ln|xn|=n ln|x|,so we get ln|y|=n ln|x|.Take differentiation for both side above:y'y=n x.     

How to use the method of the improvising differentiation?

<正>We know the Substitution Rule,which is based on the following identity in differentiation.∫f(g(x))g′(x)dx=∫f(u)du(where u=g(x)).Now,we'll talk about how to use the method of the improvising differentiation,and give some examples by using basic     

The definite integral

1. What does the definite integral mean？
The definite integral off（x） from a to b is defined the limit of the sum as n→∞.