How do we perform first order differential equations?
Most problems will have the form: Q' + P(x)Q = W(x) In this case, we will have to make an integrating factor using P(x), where exp(int(P(x)) is the intergrating factor y. We will multiply y to both sides of the equation: Q'y + P(x)Qy = W(x)y You can simplify the left side to: (Q*y)', since P(t)y = y'. Now the equation is: (q*y)' = W(x)*y then you integrate and divide by y to get: Q = 1/y int(W(x)*y)
How do you do integration by parts?
Since integration by parts has the form uv - int(vdu), its best to make the portion of the equation that will terminate when a derivative is taken as your u value. (This is especially important with problems using trig functions because they never end...no matter how many derivative you take). For example, if we had the equation: int(xcosx) dx we would proceed as follows: u = x du = dx dv = cosx dx v = sinx giving us: xsinx - int(cosx)dx then we take the integral: xsinx - sinx + C
How do you complete addition in binary?
When you add in the decimal system, anything larger than 10 carries the 1 to the next value. In binary, 2 and larger carries to the next value. For example, when adding 13+9, 2 and 9 makes 12, so the '1' gets carried so you finally get 22. When adding those numbers in binary, you get: 1101 + 1001 = 10110.