Evgeni Dimitrov

advanced integrals and applications, series, sequences,

Quite a bit. We had homeworks every week, which took a while but varied (5-10 hours, maybe). We also had two midterms, which were incredibly stressful for me, at least. And of course a final. Grade weights respectively 25%, 2 x 20%, and 35%.

Solving differential equations and which techniques to use in different contexts. Learnt Laplace Transformations which were so cool.

In Calculus 2 I learned numerous integration methods including integration by parts, trigonometric substitution, trigonometric integrals, Euler's formula to represent fundamental trigonometric functions using complex numbers, and partial fraction decomposition. We studied improper integrals with the concepts of convergence and divergence. We also studied seperable and linear differential equations of first order. We studied applications of integrals to finding areas, volumes of exotic geometric shapes, changes of variables and associated differentiation and integration. We covered mathematical induction and its application to proving certain types of propositions. We studied sequences and series with the associated concepts of convergence of divergence, and numerous tests to make such a determination including the ratio and root tests, comparison tests, and integral test. We finally covered power series, and Taylor/Maclaurin series. Overall I gained a great appreciation for the depth of mathematics and desire to further study math at a higher level.

General appeal to CU math professors: Please, please, please, please, *please* stop teaching analysis as simply Rudin, expanded. Please. I believe that there are good ways to use Rudin, but they are not to plunge us into Rudin and hold our heads down. There is very little of the beauty of math in this process; it retains its purity in the sense that it is true and very little is assumed, but not its elegance, as it has no meaning; it is just words (prove [this statement]) that expand into more words (ok, so [this statement] means [this expansion of this statement] which means [stuff with epsilons and deltas] then we can apply a theorem which means very little to us although we vaguely remember proving it so we suppose it's true and which seemingly came out of nowhere to get more different epsilons and deltas, and then TA-DA! QED) as a logical or memorization game. If you _do_ assign Rudin (please don't!!!), please explain what these things mean--- as pictures, or intuitions, or explanations of the desires mathematicians have for their definitions--- in class instead of simply following the damn book. Also, please give us a reference text, as I have not been able to find one that isn't just completely different. The homeworks were fine. (A little long, but that's to be expected in this sort of math class.) I wish the tests were not repeats of the practice tests, as this means i…

I learned many techniques for how to solve any order linear differential equations.

Calculus II, nothing new in perspectives, I just learned more math. Integrals, sequences, series

) that expand into more words (ok, so [this statement] means [this expansion of this statement] which means [stuff with epsilons and deltas] then we can apply a theorem which means very little to us although we vaguely remember proving it so we suppose it's true and which seemingly came out of nowhere to get more different epsilons and deltas, and then TA-DA! QED) as a logical or memorization game. \r\n\r\nIf you _do_ assign Rudin (please don't!!!), please explain what these things mean--- as pictures, or intuitions, or explanations of the desires mathematicians have for their definitions--- in class instead of simply following the damn book. Also, please give us a reference text, as I have not been able to find one that isn't just completely different. \r\nThe homeworks were fine. (A little long, but that's to be expected in this sort of math class.)\r\n\r\nI wish the tests were not repeats of the practice tests, as this means it is not at all valuable to try to actually understand the concepts and methods of analysis and instead is important to train ourselves on the practice exams and more or less memorize the answers given by the professor. As a result, people for whom rote memorization or test-training is incredibly hard (yes, this includes myself) do poorly. What are we testing, here? Speed? Memorization? I may be biased, but am I not right? \r\n\r\nSometimes I close my…

I learned how to solve Ordinary Differential Equations - including solving linear systems, incidial equations, higher order ODEs, Laplace transformations, etc.

I learned how to calculate more intergrals and some more ways and techniques of solving mathematical problems.