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I struggled with Math a lot when I was young, until I began to see the beauty of the topic, thanks to a Metal band of all things. I googled "Tesseract" one day, and found the wikipedia page for the Four-Dimensional analogue to the cube. That absolutely blew my mind. "Math can describe things that human beings can't even imagine?" The next step was seeing the film "Interstellar", and seeing the blackboards full of equations. That made me want to study math and physics until I could understand those equations.

Now, I'm pursuing my Master's degree, doing research on resonance phenomena in epidemiological equations. I've taught tutorials in Linear Algebra, Complex and Real Analysis, and Calculus, in addition to being a private tutor working with high school students as well as university students.

Write an equation that expresses the fact that a function $ f $ is continuous at the number 4.

(a) Use a computer algebra system to draw a direction field for the differential equation. Get a printout and use it to sketch some solution curves without solving the differential equation.(b) Solve the differential equation.(c) Use the CAS to draw several members of the family of solutions obtained in part (b). Compare with the curves from part (a).$ y' = y^2 $

(a) Use a computer algebra system to draw a direction field for the differential equation. Get a printout and use it to sketch some solution curves without solving the differential equation.(b) Solve the differential equation.(c) Use the CAS to draw several members of the family of solutions obtained in part (b). Compare with the curves from part (a).$ y' = xy $

Find the orthogonal trajectories of the family of curves. Use a graphing device to draw several members of each family on a common screen.$ y^2 = kx^3 $

An integral equation is an equation that contains an unknown function $ y(x) $ and an integral that involves $ y(x). $ Solve the given integral equation. [Hint: Use an initial condition obtained from the integral equation.]$ y(x) = 2 + \int^x_2 [t - ty(t)] dt $

Find a function $ f $ such that $ f(3) = 2 $ and $ (t^2 + 1)f'(t) + [f(t)]^2 + 1 = 0 t \neq 1 $