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Learn Calc 1 & 2 (and AP) Fast
(from someone who can actually explain it)
Chris is a Stanford-educated tutor with over 10 years experience tutoring Calc 1 & 2 (and AP) to students of all abilities, from students struggling to get from a C to a B, to go-getters trying to move an A- up to an A, to struggling students just hoping to pass. In that time he got a lot of experience learning how to explain this stuff in a way it actually makes sense to normal people. Through his videos he has helped countless students, and he can do the same for you.
Whether you're in high school or college, AP or regular, AB or BC, "Calculus for Business" or "Calculus for Science & Engineering," calculus classes always cover basically the same topics, in the same order. The only difference comes in whether certain topics are skipped and how hard the problems are. So no matter what school you're in, if you're in calculus, this page is for you!
We sometimes get the question of where Calc 1 ends and Calc 2 begins... It's different by school, but since everyone goes in roughly the same order, just look for where your class is now.
The videos in this chapter cover the more conceptual side of limits. In the first video we cover what limits are, and give an overview of the various types of limit problems you'll see in calculus. The rest of the videos cover analyzing graphs for limits, figuring out if the limit "exists", and finding the limits of piecewise functions.
These are your classic "big mess of algebra" limit problems, which happen when a limit is "indeteriminate" (plugging in results in 0/0 or infinity/infinity). This chapter covers finding limits of "giant fractions" (i.e. rational expressions) containing polynomials and roots & radicals.
If a limit has a sine or cosine, this chapter covers it. Besides knowing your unit circle so you can plug in, this chapter has a couple special formulas and strategies. Also covered are special limits like sinx/x and cosx/x.
These videos introduce the limit definition of derivatives, which every class covers and then forgets about. It's the one where you have to find f(x+h), then somehow plug in h and take the limit as h approaches zero.
A tangent line is the equation of a line that's tangent to a function at a particular point, and you find it by using derivatives. This line is important because it's slope is the "rate of change" of the function at that point. Just to make things awesome, we'll also review point-slope form of lines since that's the easiest way to find a tangent line.
This chapter covers the formulas for taking the derivatives of exponents, polynomials, powers of x, trig functions (sin, cos, tan, cot, sec, csc), exponentials, and radicals. As long as you don't need chain rule.
In this lengthy chapter we'll re-learn all the derivative formulas, except this time using the Chain Rule too: exponents (power rule), roots & radicals, trig functions, inverse trig functions, exponentials, and natural logs. A must-watch for Calculus students!
This chapter is a grab bag of graphical analysis. Intervals of increase and decrease, how to find critical values, how to sketch the derivative of a function just from the sketch of the original function, and a general intro to relative extrema (maxima and minima).
This chapter introduces concavity, points of inflection and the second derivative test, then reviews asymptotes, relative extrema, and how to find intercepts so you'll have the tools for graphing functions calculus-style.
In this chapter we'll approximate area using left-hand sums, right-hand sums, midpoint, upper bounds, lower bounds, and trapezoidal rules. Collectively, these are called "Riemann Sums" or "approximation integration".
In this chapter we use The Fundamental Theorem of Calculus and definite integrals (the ones with little numbers on the integral sign) to find the area under curves, negative area, and integral properties.
This chapter covers kinematics projectile motion problems as you would see in Pre-Calculus or Algebra 2 math classes. This topic is covered in more depth on the physics page. One-dimensional and two-dimensional gravity problems, range, vector components of velocity, etc.
Everything you could possibly need to know about convergence and divergence of infinite series is all in this one chapter because otherwise it would be really confusing. In addition to the topics listed to the left, there's a free overview of series convergence, as well as more obscure topics like the remainder (error) of an alternating series approximation.
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)