Schaums outline of calculus 6th edition pdf free download

To set up a linear coordinate system on a given line: 1 select any point of the line as the origin and let. If x is a positive number, find the point cor-. If x is negative,. The number assigned to a point by a coordinate system is called the coordinate of that point. We often. Divide by. So, by 1. See Fig. Multiplying or dividing an equality by a negative number reverses the inequality. The reasoning here is similar to that for. Let P and P be points on the line having coordinates x and x.

We shall use the term open interval and the notation a, b also for all the points between the points with coordinates a and b on a line. Notice that the open interval a, b does not contain the endpoints. As in the case of open intervals, we extend the terminology and notation to points. Notice that the closed interval [ a, b ] contains both endpoints a and b.

By a half-open interval we mean an open interval a, b together with one of its endpoints. To solve an inequality means to determine the corresponding interval of numbers that satisfy the inequality. Recall that dividing by a negative number reverses an inequality. By property 1. This defines the open interval 2, 4. This is equivalent to saying that the distance between x and 2 is less than.

Note that it is negative when. The result is called the. Dividing by 4, we obtain 1 8 3 8. Thus, this case yields no solutions. The inequality contains all numbers greater than or equal to 5or less than or equal to In interval notation it can be written as unionof the intervals Draw the number line as: Here the end points -5 and 5 are included in the number line asit is closed at -5 and 5.

The inequality contains all numbers greater than and less than. In interval notation it can be written as Draw the number line as: Here the end points are not included in the number line as it is open interval. Take the negation of the inequality is This can be written as: The inequality contains all numbers greater than 4 or less than2.

In overall plan the book divides roughly into a first half which develops the calculus principally the differential calculus in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

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