Recent content by Akorys

I had similar goals to yours going into university. Primarily to learn math, to learn some more of physics and programming, and to learn French. Attending university pushed me further along than I had expected. You can still do some self study, especially regarding German, while taking courses.

Hey Radic, I am not far along in my studies, so take anything I say with that in mind, but I used Apostol's book to study single variable calculus and plan to continue with his second volume. That being said, I can relate to many of the issues you've been facing, as this was the first textbook I...

Micromass, you say that physics helps in understanding the motivation for certain math fields, of which I've no doubt. However, studying mathematics already gives you a large number of courses to choose from, and additionally the recommended stat courses. If one wants to be a math major, surely...

If you like both subjects, the best way to decide (assuming you have sufficient background knowledge, as the above questions are trying to deduce) would be to take a more difficult book from each of the fields and try to work through the problem sets. If you find that doing hours of work for...

Exactly, similar triangles can be used to find the areas, which I believe was a hint from SteamKing and not myself. Also, as far as I can see, E does not need to be the midpoint of AC.

The sides not being equal are not what I meant. When labeling a shape, the order in which you label describes the sides that are present. Usually, you want to label the shape clockwise or counterclockwise. So for ex. ABCD has sides AB, BC, CD, and DA. I was pointing out that your image, as...

I do not know if the diagram you provide is your interpretation of a problem or the diagram given in a problem. However, as drawn, ACBD would not be a square, since the name implies that its sides are AC, CB, BD, and DA. Also, do you mean that you need the area of FGKJ?

The "Relevant equations" section has enough information to simplify the left side without any circularity, and as SammyS has pointed out, that is all that was used. May I ask how you use the product rule to prove the exponent rule for logarithms?

Hellmut1956, I have read your advice and I both appreciate and make use of it! I have watched almost all of the lectures for single variable calculus, barring those for series and sequences which I would like to first study through my text. I find MIT resources very helpful, and often refer to...

Thank you for checking it!

Homework Statement I wanted to ask anyone willing to check my proofs to two problems, so that I may know if I am making any mistakes or assumptions. Let the function f be continuous and strictly monotonic on the positive real axis and let g denote the inverse of f. If a_1\lt a_2\lt...\lt a_n...

I would like to expand a bit in case you wanted to know about how you would find the solution to \int f(x)dx for some function f. It does not have a formula, as a derivative would have in the form of a limit of a secant, which makes evaluating integrals generally more complicated. There are...

I have two questions related to self study, so instead of starting a new thread I assume it is ok to simply ask them here! First of all, I am a bit confused about when "Advanced Calculus" by Loomis and Sternberg would be best studied. Is it a first text in multivariable calculus? I saw posts on...

Then I'd appreciate any criticism you may have of it. We are given the relation 1-\frac{1}{x} \leq \log x \leq x-1 , for x \gt 0. Moreover, the equality only holds for x=1 (this was proved in another question). Then we can substitute x by (x+1) and attain; 1-\frac{1}{x+1} \leq \log (x+1)...

Oh yes I meant if you take (log x)' then that's (1/x). Then when x = 1, the derivative is 1. Using this fact, you can use the definition of the derivative as [log(1+x) - log(1)]/x as x tends to 0. Log(1) = 0, so you're left with the expression I was trying to work with: [log(x+1)]/x as x tends...