Calculus teacher is incompetent; need help self-instructing

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So my Cal B teacher is an idiot. In the last 5 classes Ive attended hes been able to solve less then 20% of the homework problems that he assigns, and he is frequently unable to apply the material in the most basic manner possible.

We literally spent one and a half hours on the same problem last class. The remaining 30 minutes of class was 20 minutes of "new material" and 10 minutes of break. Unfortunately, I am one of the two most outspoken and competent members of the class, so the teacher frequently relies on my insight to solve homework problems.

The problem with this is that I don't do the homework and still have an A in the class, because he gives us a list of 30 questions, 15 of which will comprise the entirety of the test. I simply spend about 5-10 hours before each test (4 tests / semester) studying and the rest warming my seat because attendance is mandatory. The material in this class is new to everyone in the class, myself included.

This has resulted in me getting VERY f*****g BORED and a bit unnerved because the teacher spends half the class looking at me and expecting me to lead him on how to solve types of problems Ive never seen before.

So, I need to devise a method of studying that allows me to go beyond the class. Preferably a book, collection of books, online tutorials, a structured list of topics to explore in order, that sort of thing. Because simply following my book is boring (god, math texts really do a good job of sucking the fun out of it) and sticking with the class is a waste of my time.

Therefor, I do not care about what I learn in so long as its new to me, and fun. I particularly enjoy math puzzles, but prefer a guide through the infinite wilderness of mathematics (else wise I tend to fruitlessly reinvent the wheel).

Right now we are going over series & summations, and we just finished integrating solids rotated about an axis and polar calculus. I haven't looked ahead but I believe that double integrals and a further investigation of 3 dimensional solids are next.

Funny story: Last class period I used basic programming for loops as self-obviating inspiration to solve a series using triple nested sums (it being the only problem we solved that period), despite this not being present anywhere in our book and being a process my teacher, who claims to have a Master's in Mathematics, was unfamiliar with. The measure of admiration I gained was unfounded; all I did was apply an elementary concept from a closely related field. Id like to put forth the effort so that next time I impress the class I feel like I actually deserve the admiration.

wow. and i thought my calculus teacher was bad.

Schaums Outlines are my favorites tbh. The advanced calculus textbooks are the best. But tbh, learning from your peers is the way forward, not your lecturers (I don't even bother going to a whole truckload of mine). Also MIT do video lectures (Denis Auroux does an amazing course on multivariate calculus).

Out of curiosity, could you stick up some of the problems you got stuck with.

Put up a notice asking for a tutor?

Go to MIT OCW or, better yet, UC Berkeley's webcasts if you need calculus lectures. There are dozens of free calculus textbooks you can download off the internet. Here is one list of math books you could try. I always found learning out of a book was better in math than lectures ever were.

Examples of problems that he could not solve:

A cow is tied by a r*pi length rope to a cylindrical silo of radius r. How much grazing area is available for the cow?

Suppose that a microphone has an optimal pickup area defined by 8+8sin(theta). This microphone is placed near a large, deep, rectangular theatrical stage so that the stage is nearest (4 units distant) at theta=pi/2. How much area is available to the troupe to perform on stage, in the microphone's optimal pickup area? (he spent an entire class period trying to solve this one)

And basically any series/summation problem we have covered. We are almost done with that chapter and hes only solved three problems other then the one I solved for him. Ive decided since then that my time is better spent on meditating, doodling, reading ahead, or solving unrelated problems, so I am not actively involved in the class any more.

And.... pretty much the entire chapter on area between curves. That one was really embarrassing. It had him insisting that there was a finite amount of area between y<|x|, y>-|x| and x<f(x). Where f(x) was some right-opening parabola inside of y<|x|, y>-|x| and which never intersected y=|x|.

Oh, yeah, and my teacher loves word problems. He completely skips covering easier more straight forward problems in favor of s**t he doesn't understand.

Write a threatening letter to the head of the Math Department. Are you paying for this education?

He works at the nearby military base doing missile defense work (comforting, I know). He apparently has a Master's in Mathematics.

He has a post-graduate degree in Mathematics.

Ya know, getting a PhD seems easier and easier every day.

Could it be that you've simply been placed in the wrong math class? Maybe you should be at the next level up.