5.7 Euler`s Marvelous Formula (slides, 4-to-1)
... By simple laws of exponents, (eiz )n = einz and so Euler’s equation explains DeMoivre formula. This explains the “coincidence” we noticed with the complex number z = cos π6 + i sin π6 which is one-twelfth of the way around the unit circle; raising z to the twelfth power will simply multiply the angl ...
... By simple laws of exponents, (eiz )n = einz and so Euler’s equation explains DeMoivre formula. This explains the “coincidence” we noticed with the complex number z = cos π6 + i sin π6 which is one-twelfth of the way around the unit circle; raising z to the twelfth power will simply multiply the angl ...
a < b
... What is the distance between you and your partner? If your partner lived 20 miles WEST off I-4 what would the distance be? If a and b are any two points on a real number line, then the distance between a and b is given by |a – b| or |b – a| Show how we could write the above using integers and absolu ...
... What is the distance between you and your partner? If your partner lived 20 miles WEST off I-4 what would the distance be? If a and b are any two points on a real number line, then the distance between a and b is given by |a – b| or |b – a| Show how we could write the above using integers and absolu ...
Dynamical systems: Multiply recurrent points
... In this section, we study the notion of a multiply recurrent point in a dynamical system. Unless for the notion of (uniformly) recurrent points, we can show existence of such points only under additional conditions on a dynamical system. 12.1. Definition Let X be a dynamical system over S and e a su ...
... In this section, we study the notion of a multiply recurrent point in a dynamical system. Unless for the notion of (uniformly) recurrent points, we can show existence of such points only under additional conditions on a dynamical system. 12.1. Definition Let X be a dynamical system over S and e a su ...
Geometric mean
... Is the geometric mean (when it exists) always between the two numbers? When you have one positive and one negative number there is a problem with this, but what if both numbers are negative? What if one number is zero? ...
... Is the geometric mean (when it exists) always between the two numbers? When you have one positive and one negative number there is a problem with this, but what if both numbers are negative? What if one number is zero? ...
Ch3
... reversible. For example, it is all right to complement both sides of the equation, but it is not permissible to multiply both sides of the equation by the same expression. (Multiplication is not reversible because division is not defined for Boolean algebra.) Similarly, it is not permissible to add ...
... reversible. For example, it is all right to complement both sides of the equation, but it is not permissible to multiply both sides of the equation by the same expression. (Multiplication is not reversible because division is not defined for Boolean algebra.) Similarly, it is not permissible to add ...
6.3 Solving Quadratic Equations by Factoring
... 6.3 Solving Quadratic Equations by Factoring Write a quadratic equation with given roots ...
... 6.3 Solving Quadratic Equations by Factoring Write a quadratic equation with given roots ...
QED - Rose
... for S to give a specific fraction a terminating expansion is that it contains the factors of the denominator of r. Thus an appropriate choice of S to make all fractions have terminating expansions would be one in which all possible factors where included. Once we have selected such a base, the above ...
... for S to give a specific fraction a terminating expansion is that it contains the factors of the denominator of r. Thus an appropriate choice of S to make all fractions have terminating expansions would be one in which all possible factors where included. Once we have selected such a base, the above ...
