Problem Suppose that u and v are two vectors in R n. Let a = u + v b
... Solution: Let’s see what relations we would need p, q and r to obey. We want p~a + q~b + r~c = 0 Plugging in the expressions we have for (a, b, c), we get p(~u + ~v ) + q(2~u + 3~v ) + r(4~u + 7~v ) = 0 Expanding and regrouping, we want (p + 2q + 4r)~u + (p + 3q + 7r)~v = 0. The way to guarantee tha ...
... Solution: Let’s see what relations we would need p, q and r to obey. We want p~a + q~b + r~c = 0 Plugging in the expressions we have for (a, b, c), we get p(~u + ~v ) + q(2~u + 3~v ) + r(4~u + 7~v ) = 0 Expanding and regrouping, we want (p + 2q + 4r)~u + (p + 3q + 7r)~v = 0. The way to guarantee tha ...
Math 2
... functions, where students also begin to analyze functions in terms of transformations. ...
... functions, where students also begin to analyze functions in terms of transformations. ...
Systems of Equations
... two variables is the set of ordered pairs that satisfies each equation in the system. (There usually is only one!) ...
... two variables is the set of ordered pairs that satisfies each equation in the system. (There usually is only one!) ...
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.