This course is built in Ximera.

We explain how your work is scored.

Two young mathematicians think about limits.

Review methods of evaluating limits.

Two young mathematicians think about derivatives.

Review differentiation.

Two young mathematicians discuss linear approximation.

We use a method called “linear approximation” to estimate the value of a (complicated) function at a given point.

We give explanation for the product rule and chain rule.

Two young mathematicians discuss how to sketch the graphs of functions.

We use the language of calculus to describe graphs of functions.

Two young mathematicians discuss how to sketch the graphs of functions.

We will give some general guidelines for sketching the plot of a function.

Two young mathematicians discuss the standard form of a line.

In this section we differentiate equations that contain more than one variable on one side.

In this section we differentiate equations without expressing them in terms of a single variable.

Two young mathematicians think about derivatives and logarithms.

We use logarithms to help us differentiate.

Two young mathematicians think about trigonometric functions.

We review trigonometric functions.

Two young mathematicians think about the plots of functions.

We derive the derivatives of inverse trigonometric functions using implicit differentiation.

We see the theoretical underpinning of finding the derivative of an inverse function at a point.

Two young mathematicians discuss a circle that is changing.

Here we work abstract related rates problems.

Two young mathematicians discuss tossing pizza dough.

We solve related rates problems in context.

Two young mathematicians consider a way to compute limits using derivatives.

We use derivatives to give us a “short-cut” for computing limits.

Two young mathematicians consider a way to compute limits using derivatives.

We use derivatives to give us a “short-cut” for computing limits.

Two young mathematicians discuss a ‘Jeopardy!’ version of calculus.

We introduce antiderivatives.

We study a special type of differential equation.

Two young mathematicians discuss the idea of area.

We introduce the basic idea of using rectangles to approximate the area under a curve.

A dialogue where students discuss area approximations.

Two young mathematicians discuss cutting up areas.

Definite integrals arise as the limits of Riemann sums, and compute net areas.

Two young mathematicians discuss cutting up areas.

Properties of the definite integral

Two young mathematicians discuss what calculus is all about.

The rate that accumulated area under a curve grows is described identically by that curve.

Two young mathematicians discuss what calculus is all about.

The accumulation of a rate is given by the change in the amount.

At this point we have three “different” integrals.

Two young mathematicians discuss whether integrals are defined properly.

We give more contexts to understand integrals.

Two students consider substitution geometrically.

We learn a new technique, called substitution, to help us solve problems involving integration.

Two young mathematicians discuss how tricky integrals are puzzles.

We explore more difficult problems involving substitution.

Substitution is given a physical meaning.