Calculus 1 is all about differentiation. We started the quarter with limits, and the limit definition of a derivative. Next, we learned how to differentiate various functions. We studied the power rule, the product rule, the quotient rule, and the chain rule, as well as the derivatives of trig and inverse trig functions, logs, and exponentials. In addition, we learned implicit and logarithmic diff to help us differentiate more complicated functions. We applied the concept of derivatives to solve related rates problems. We learned what the first and second derivative can tell us about a function: its intervals of increasing/decreasing, its intervals of concavity (concave up/concave down), and its extrema. Then we solved some optimization problems. Finally, we started studying antiderivatives, to help prepare us for the central topic of Calculus 2, integration.
I loved this class, and learned so, so much. The professor was excellent and inspired me to decide to major in math. The class was over too soon. :(
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