Slide 1
... In the notation ƒ(x), ƒ is the name of the function. The output ƒ(x) of a function is called the dependent variable because it depends on the input value of the function. The input x is called the independent variable. When a function is graphed, the independent variable is graphed on the horizontal ...
... In the notation ƒ(x), ƒ is the name of the function. The output ƒ(x) of a function is called the dependent variable because it depends on the input value of the function. The input x is called the independent variable. When a function is graphed, the independent variable is graphed on the horizontal ...
Full text
... A positive integer n is a triangular number if there is another positive integer k such that n - Y2k(k +1). n is a square number if there is a positive integer I such that n = t2, and n is a nearly square number if there is a positive integer I such that n = 1(1+ X) (see [1], [4]). More generally, l ...
... A positive integer n is a triangular number if there is another positive integer k such that n - Y2k(k +1). n is a square number if there is a positive integer I such that n = t2, and n is a nearly square number if there is a positive integer I such that n = 1(1+ X) (see [1], [4]). More generally, l ...
Divide-and
... • Why this recursive algorithm takes so much time? – Building out the recursion tree for F(n), we can see that there are lots of common subtrees. – Too many duplications that waste time ...
... • Why this recursive algorithm takes so much time? – Building out the recursion tree for F(n), we can see that there are lots of common subtrees. – Too many duplications that waste time ...
Hahn-Banach theorems
... Convex sets can be separated by linear functionals. Second, continuous linear functionals on subspaces of a locally convex [1] topological vectorspace have continuous extensions to the whole space. These assertions are proven first for real vectorspaces. The complex-linear versions are corollaries. ...
... Convex sets can be separated by linear functionals. Second, continuous linear functionals on subspaces of a locally convex [1] topological vectorspace have continuous extensions to the whole space. These assertions are proven first for real vectorspaces. The complex-linear versions are corollaries. ...
Full text
... Putting r= 1, s = 0, we obtain the generating function for the Fibonacci sequence (see [3] and Riordan [6]). Putting r = 2, s = -1, we obtain the generating function for the Lucas sequence (see [3] and Carlitz [1]). Other results in Riordan [6] carry over to the //-sequence. The //-sequence (and the ...
... Putting r= 1, s = 0, we obtain the generating function for the Fibonacci sequence (see [3] and Riordan [6]). Putting r = 2, s = -1, we obtain the generating function for the Lucas sequence (see [3] and Carlitz [1]). Other results in Riordan [6] carry over to the //-sequence. The //-sequence (and the ...
4.3 Powerpoint
... In the same way, both the range of an exponential function and the domainof a logarithmic function are the set of all positive real numbers, so logarithms can be found for positive numbers only. ...
... In the same way, both the range of an exponential function and the domainof a logarithmic function are the set of all positive real numbers, so logarithms can be found for positive numbers only. ...
Mathematics of radio engineering
The mathematics of radio engineering is the mathematical description by complex analysis of the electromagnetic theory applied to radio. Waves have been studied since ancient times and many different techniques have developed of which the most useful idea is the superposition principle which apply to radio waves. The Huygen's principle, which says that each wavefront creates an infinite number of new wavefronts that can be added, is the base for this analysis.