#### How to use Ximera

This course is built in Ximera.

#### How is my work scored?

We explain how your work is scored.

#### Guess the Value

Two young mathematicians think about limits.

#### Review Limits.

Review methods of evaluating limits.

#### Review Derivatives BreakGround

Two young mathematicians think about derivatives.

#### Review Derivatives

Review differentiation.

#### Replacing curves with lines

Two young mathematicians discuss linear approximation.

#### Linear approximation

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

#### Explanation of the product and chain rules

We give explanation for the product rule and chain rule.

#### What’s the graph look like?

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

#### Concepts of graphing functions

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

#### Wanted: graphing procedure

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

#### Computations for graphing functions

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

#### Standard form

Two young mathematicians discuss the standard form of a line.

#### Implicit differentiation

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

#### Finding dx dy

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

#### Logarithmic differentiation

Two young mathematicians think about derivatives and logarithms.

#### Logarithmic differentiation

We use logarithms to help us differentiate.

#### Inv Trig Function BreakGround

Two young mathematicians think about trigonometric functions.

#### Inverse trigonometric functions

We review trigonometric functions.

#### Derivatives of inverse trigonometric functions BreakGround

Two young mathematicians think about the plots of functions.

#### Derivatives of inverse trigonometric functions

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

#### The Inverse Function Theorem

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

#### A changing circle

Two young mathematicians discuss a circle that is changing.

#### More than one rate

Here we work abstract related rates problems.

#### Pizza and calculus, so cheesy

Two young mathematicians discuss tossing pizza dough.

#### Applied related rates

We solve related rates problems in context.

#### A limitless dialogue

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

#### L’Hopital’s rule

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

#### Indeterminate mutterings

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

#### L’Hopital’s rule for other forms

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

#### Jeopardy! Of calculus

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

#### Basic antiderivatives

We introduce antiderivatives.

#### Falling objects

We study a special type of differential equation.

#### What is area?

Two young mathematicians discuss the idea of area.

#### Approximating area with rectangles

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

#### So many rectangles.

A dialogue where students discuss area approximations.

#### Computing areas

Two young mathematicians discuss cutting up areas.

#### The definite integral

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

#### Computing areas

Two young mathematicians discuss cutting up areas.

#### Properties of the definite integral

Properties of the definite integral

#### What’s in a calculus problem?

Two young mathematicians discuss what calculus is all about.

#### The First Fundamental Theorem of Calculus

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

#### A secret of the definite integral

Two young mathematicians discuss what calculus is all about.

#### The Second Fundamental Theorem of Calculus

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

#### A tale of three integrals

At this point we have three “different” integrals.

#### What could it represent?

Two young mathematicians discuss whether integrals are defined properly.

#### Applications of integrals

We give more contexts to understand integrals.

#### Geometry and substitution

Two students consider substitution geometrically.

#### The idea of substitution

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

#### Integrals are puzzles!

Two young mathematicians discuss how tricky integrals are puzzles.

#### Working with substitution

We explore more difficult problems involving substitution.

#### The Work-Energy Theorem

Substitution is given a physical meaning.