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Longhand

Lessons

One idea from each topic, in a figure you move. Guess before each step shows you, see why the method works, then try a question on paper.

23 lessons in the order the course teaches them, 15 of them also a short film. A slip that keeps catching you? Its page in Mistakes links the step that shows it.

Start with the first lesson

Before the midterm

  • Which power of x wins, near 0 and far away?

    Power functions and first sketches5 stepsFilm, 1:29

  • Why does a minus sign inside move a graph to the right?

    Functions, graphs and inverses5 steps

  • What does it mean for f(x) to approach L?

    Limits5 stepsFilm, 1:44

  • What does it take for a graph to have no break?

    Continuity5 steps

  • What is the slope of a curve at one point?

    The definition of the derivative5 stepsFilm, 1:42

  • Why does the product rule have two terms?

    Differentiation rules5 stepsFilm, 1:12

  • Why does calculus use e and radians?

    Exponential and trigonometric functions5 stepsFilm, 1:48

  • Why does the chain rule multiply?

    The chain rule and logarithms4 stepsFilm, 1:42

  • How do you find a slope without solving for y?

    Implicit differentiation and inverse trigonometric functions5 steps

  • Why does the top of a sliding ladder speed up?

    Related rates5 stepsFilm, 0:59

Before Quiz 2

Before the final

  • Where is the largest area, and why is the top flat?

    Optimization5 stepsFilm, 1:46

  • Why is a tangent line such a good estimate near its point?

    Linear approximation4 steps

  • Why does a Taylor polynomial divide by factorials?

    Taylor polynomials5 stepsFilm, 1:14

  • How does a tangent line find a root?

    Newton’s method5 stepsFilm, 1:44

  • What halves every few minutes as soup cools?

    Exponential growth and decay5 stepsFilm, 1:44

  • Why does Euler’s method drift off the solution?

    Slope fields and Euler’s method5 stepsFilm, 1:26

  • Where does a population end up?

    Logistic growth and phase lines5 stepsFilm, 1:47

  • What does a partial derivative measure?

    Functions of two variables and partial derivatives5 steps

  • Why is the best point on a budget line where a level curve touches it?

    Optimization in two variables and Lagrange multipliers5 steps

Not in the course

  • Must the speedometer ever read the average speed?

    The Mean Value Theorem4 stepsFilm, 1:32

  • Why does an antiderivative need a + C?

    Antiderivatives4 steps