Some derivatives...

Just testing out Latex on this blog.

$$\frac{d}{dx}f(g(x)) = f'(g(x))g'(x)$$
$$\frac{d}{dx}f(x)g(x) = f'(x)g(x) + f(x)g'(x)$$
$$\frac{d}{dx}\frac{f(x)}{g(x)} = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2}$$
$$\frac{d}{dx}b^x = b^x\ln b$$
$$\frac{d}{dx}\sec x = \sec x\tan x$$
$$\frac{d}{dx}\arctan x = \frac{1}{1 + x^2}$$

Looking good!

Microeconomics

Last quarter, I also took an introductory microeconomics course. Besides math, econ is my other favorite thing.

Here are the highlights of the class:

• Supply and demand
• The burden of a tax
• How consumers maximize their utility
• Cost curves of firms
• Market structures: perfect competition, monopolistic competition, oligopoly (my favorite because of the game theory involved), and monopoly
• The role of government
• Inefficiency in markets

This class was so much fun! The professor used really good (and funny!) examples to illustrate the concepts he taught. I am taking macro in the winter.

My grade for Calc 1

Grades were posted for my math class today.  I got an A for Calc 1, which is really deeply satisfying. :)

I am definitely looking forward to Calculus 2, and studying integration.

                                                            Photo Credit: fsymbols.com

Calculus 1

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. :(