Embarking on Mathematics Self-Study

[Tee2612]

I will be attempting to self-study mathematics and I need some advice. I made a D in Calculus II this past semester. I will be retaking it along with Diff Equations and Mathematical statistics. I will also be sitting in Calculus I class with an instructor, although I don't need to take it since I made a B in the course. I just want to be refreshed in the material.

This semester I am taking Fundementals of Mathematics and the book we use is "Doing Mathematics: an introduction to proofs and problem-solving".

The book that is utilized in the calculus series(I-III) at my university is Anton Bivens Davis Calculus.

So far I have Spivak Calculus, Courant Calculus, Apostol and Piskunov as well as several Analysis Books.

I need to brush up on my Algebra and Trig so I have I.M. Gelfand's Algebra and Trigonometry. I also ordered "Fundementals of Freshman Mathematics" by Allendoerfer

I was going to start with my Algebra and Trig then brush up on my proofing techniques, which is a little difficult and new to me since this Fundamentals of math class is my first encounter with it, and then start with Spivak and go from there.

I will be graduating Spring '14 with a double major in Mathematics and Biology, but I don't think I'm as good at mathematics as I should be.

Any advice?

 

[micromass]

Getting a D in calculus II is not a good sign. It doesn't need to be fatal though, but it signals a deeper problem that needs to be addressed.

Can you explain why you got a D? Do you know what you did wrong? How are you preventing this from happening again?

 

[Tee2612]

The integration by parts tripped me up.

I have been studying the material and looking on youtube at examples and stuff.

 

[SolsticeFire]

How did you study exactly. Mathematics can't be studied like biology. You absolutely need to sit down with pen and paper and go over stuff. You just can't get a deep understanding by working some examples and YouTube. You need to go over theorems and think about what they try to convey. Get into habit of visualize things. Integration by parts is only a small part of calc II, you shouldn't have gotten a d because of that section alone. Also do a lot of problems. And exhaust each problem. Calc II is rich with good problems! Use that to your advantage.

Good Luck!

SolsticeFire

 

[micromass]

The integration by parts tripped me up.

I have been studying the material and looking on youtube at examples and stuff.

How did it trip you up? Did you solve enough exercises?
You can't just watch youtube and think you understand the topic. You actually need to work through it.

Integration by parts is not hard compared to things like analysis and abstract algebra. So if you're having troubles with integration by parts, then you need to find out what went wrong and you need to salvage it. Just saying "this part tripped me up" is not very useful until you know why exactly it did.

 

[Klungo]

Also knowing the motivation helps.

Why does integration by parts seem reasonable? Does it look like it works?

Ex:

On one hand,
int((uv)')=uv.
On the other, you have
int((uv)')=int(uv'+u'v)=int(uv')+int(u'v).

Put it together and it all begins makes sense.

The other half is practicing the concepts until you know how to effectively solve problems.

Ex. Knowing what to assign as U and dV in solving the antiderivatives of sin(x)*e^x, and ln(x) to make your computation easiest.