By Michel Herve
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Additional info for Analytic and plurisubharmonic functions in finite and infinite dimensional spaces. Course given at the University of Maryland, Spring 1970
A1x + a0 Note that every term in a polynomial is x raised to the power of a nonnegative integer, multiplied by a real-number coefficient. Here are a few examples of polynomials: f(x) = x3 – 4x2 + 2x – 5 f(x) = x12 – 3 x7 + 100x – π 4 f(x) = (x2 + 8)(x – 6)3 Note that in the last example, multiplying the right side of the equation will change the polynomial to a more recognizable form. Polynomials enjoy a special status in math because they’re particularly easy to work with. For example, you can find the value of f(x) for any x value by plugging this value into the polynomial.
2 x x=1 5 Area =1∫ x 2 dx x=5 19 20 Part I: Introduction to Integration Untangling a hairy problem by using rectangles The earlier section “Checking out the Area” tells you how to write the definite integral that represents the area of the shaded region in Figure 1-9: 5 #x 2 dx 1 Unfortunately, this definite integral — unlike those earlier in this chapter — doesn’t respond to the methods of classical and analytic geometry that I use to solve the problems earlier in this chapter. ), you can approximate it by slicing the shaded region into two pieces, as shown in Figure 1-10.
Distinguishing sequences and series A sequence is a string of numbers in a determined order. For example: 2, 4, 6, 8, 10, ... 1, 1 , 1 , 1 , 1 , ... 2 4 8 16 1 1, , 1 , 1 , 1 , ... 2 3 4 5 Sequences can be finite or infinite, but calculus deals well with the infinite, so it should come as no surprise that calculus concerns itself only with infinite sequences. You can turn an infinite sequence into an infinite series by changing the commas into plus signs: 2 + 4 + 6 + 8 + 10 + ... 1 + 1 + 1 + 1 + 1 + ...
Analytic and plurisubharmonic functions in finite and infinite dimensional spaces. Course given at the University of Maryland, Spring 1970 by Michel Herve