Apma midterm 1

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Calculus - Geometry

kipkogeibrxwzp Created by 6 mon ago

Cards in this deck(23)

= 1

= sec^2(x)

cosx

-sinx

cos^2x-sin^2x

2sinxcosx

-ln(cosx) or ln(secx)

ln|secx+tanx|+C

1/2(1+cos2x)

1/2(1-cos2x)

arctanx + C

1/2x - 1/4sin2x + C

1/2x + 1/4sin2x + c

Y=Ce^kt (walk through solution)

1. set solution equal to C 2. Find derivative of ye^-kt (with respect to y and t) (HINT: use given y'=ky to finish solution) 3. If derivative=0 then no other solutions is proved!

will either have constant coeffs, or coeffs will depend on t

Everything else

Homo f(t)=0 inhomo f(t)≠0 (homo/inhomo are only for linear ODEs)

The highest derivative

Make a table comparing y values and slopes. Plot the dashed slope lines along the horizontal y=whatever lines

Set f(y)=0

Graph moves in direction of y lines in bifurcation diagram

solve the ode (existence) prove no other solutions (uniqueness) Y'=f(y,t) and if f(y,t) and partial derivative of f with resp to y are continuous then there exists a unique solution

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Apma midterm 1

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