To print a variable in your display on the command window, its place must be indicted by % in the format-string followed by the format of presentation (d, f, e, g).
%d: integer notation
%f: fixed point (decimal) notation
%e: exponential notation
%g: whichever is shorter, %f or %e
Basic Concepts of Algebra
R.1 R.2 R.3 R.4 R.5 R.6 R.7 The Real-Number System Integer Exponents, Scientific Notation, and Order of Operations Addition, Subtraction, and Multiplication of Polynomials Factoring Rational Expressions Radical Notation and Rational Exponents The Basics of Equation Solving
SUMMARY AND REVIEW TEST
A P P L I C A T I O N
ina wants to establish a college fund for her newborn daughter that will have accumulated $120,000 at the end of 18 yr.
Notations and Mathematical Preliminaries
1.1 NOTATIONS AND ABBREVIATIONS The notations and abbreviations used in the book are summarized here for ease of reference. D (α) f = f α (t) := d f α (t)/dt α f¯—complex conjugate of f ∞ fˆ := −∞ f (t)e−iωt dt, Fourier transform of f (t) ∞ 1 f (t) := 2π −∞ fˆ(ω)eiωt dω, inverse Fourier transform of fˆ(ω) f —norm of a function f ∗ g—convolution f, h := f (t)h(t) dt, inner product f n = O(n)-order of n, ∃C such that f n ≤ Cn C—complex N —nonnegative integers R—real number...
Combining sieve methods with automorphic form theory and techniques from -adic cohomology, we prove that the sign of Kloosterman sums Kl(1, 1; n) changes inﬁnitely often as n ranges over the squarefree integers having all their prime factors larger than n1/23.9 . 1. Introduction Soient a, b et n trois entiers, avec n 1. On rappelle que la somme de Kloosterman Kl(a, b; n) est d´ﬁnie par la formule e ax + bx Kl(a, b; n) = exp 2πi . n
x mod n (x,n)=1
(la notation x indique l’inverse de x modulo n). Rappelons que c’est un nombre r´el, qui,...
(start:increment:end) where start is the starting index, increment is the amount to add to each successive index, and end is the ending index, where start, increment, and end must be integers. The increment can be negative, but negative indices are not allowed to be generated. If the increment is to be 1, a shortened form of the notation may be used: (start:end) • 1:5 means “start with 1 and count up to 5.” x(1:5) ans = 0 0.3142 0.6283 0.9425 1.2566 • 7:end means “start with 7 and count up to the end of the vector.” x(7:end) ans...