A Guide to AP Calculus AB

This video provides an introduction to limits, a preliminary topic necessary for understanding more complex topics in calculus.

This video covers the graphical evaluation of limits. In these examples, we consider how different discontinuities affect limits.

Here we study the relationship between limits and continuity, establishing rules for continuity as well as enumerating how different discontinuities impact limits.

In this video, we go through several examples using the algebraic evaluation of limits, suppressing the previous dependence on graphs.

In this video, we consider an example of the famous piecewise function question where you must find the values of certain constants to make the function continuous.

In this video, we go over three special trig limits that are important to remember.

In this video, we make several generalizations about functions at infinity and negative infinity. These generalizations can be used to study various functions' end behavior.

In this video, we introduce two important theorems regarding limits: the Algebraic Limit Theorem and the Squeeze Theorem.

Here I have attached a test on Limits and Continuity Test; using this test, you can practice the topics covered in this chapter.

In this video, we consider the first major problem in calculus, the tangent line problem. The limit definition of a derivative is also introduced.

This video covers a simple shortcut for taking the derivative of polynomials. Using the Power Rule, we avoid the tedious nature of the limit definition of a derivative.

Here we introduce three more rules for differentiation. These three rules, along with the power rule, are the simplest rules for differentiation.

This video covers a simple way to take the derivative of a product of two functions.

Here we cover a shortcut for taking the derivative of quotients of two functions.

In this video, we cover trigonometric derivatives as well as other special derivatives.

In this video, we cover the rule for taking the derivative of compositions of functions.

Here we cover the final rule for taking derivatives, implicit differentiation. This rule covers scenarios where one variable cannot be explicitly expressed in terms of the other variable.

Here we go through an example using implicit differentiation.

Here we cover another example using several differentiation rules.

In this video, we cover higher order derivatives. In previous videos, we have only considered the first derivative of functions; here, we extend differentiation rules to higher order derivatives.

Here I have attached a short test on differentiation, so you can practice the techniques taught in this section.

In this video, we cover the first major application of differentiation, the mean value theorem.

In this video, we cover a special case of the mean value theorem: Rolle's Theorem.

Here we consider another theorem of importance: the Intermediate Value Theorem.

The Extreme Value Theorem is an important theorem that will provide a basis for the next few videos.

Here we consider the difference between two types of extrema: local/relative and absolute.

In this video, we go over a technique used to find and classify extrema on an interval.

In this video, we cover an example of finding extrema using the first derivative test.

In this video, we cover another way to classify extrema: the Second Derivative Test.

In this video, we cover an example involving extrema and inflection points.

Here we cover another example involving extrema.

Here we revisit the previous example using the second derivative test to verify the classifications made previously.

In this video, we introduce another application of differentiation: Related Rates.

In this video, we cover an example involving related rates.

Here we cover a famous problem in related rates: the Ladder Problem.

Here we cover another famous related rates problem: the Shadow Problem.

Here we consider a basic application of differentiation: writing equations for tangent lines.

Slope fields are a minor application of differentiation but will become important later in this course.

Here I have attached a short test on the applications of differentiation, so you can practice the different differentiation techniques covered in this section.

In this video, we introduce the second major problem in calculus: the Area Problem.

Here we cover a technique used to approximate the area under a curve: the Left Riemann Sum.

In this video, we consider another method for estimating the area under a curve: the Right Riemann Sum.

Here we cover another technique for estimating the area under a curve, this time using midpoints.

We consider one final method for approximating the area under a curve: the Trapezoidal Sum.

Here we cover an example involving Riemann sums, using the four methods covered in the previous videos.

In this video, we take a break from considering the area under a curve. We consider antiderivatives. Later, these antiderivatives will be used to find the area under a curve but for now, we interchange the terms integral and antiderivative.

In this video, we cover three more rules for integration that are somewhat intuitive.

In this video, we cover the six common integrals in AP Calculus AB. They should look familiar...

We cover several special integrals that will be of importance in the next few videos.

In this video, we consider u-substitution in integration.

Here we consider a few tips for success in u-substitution.

Here we consider a situation where double u-substitution is required. It is somewhat analogous to the triple chain rule introduced in the differentiation module.

Here we consider an example involving u-substitution.

In this video, we consider one final example incorporating several integration rules covered in this module.

Here I have attached a test on integration, where you can practice the integration techniques covered in this chapter; some of the practice with Riemann sums will come in the Applications of Integration Test.

In this video, we answer the question of how to find the area under a curve. We also consider a major theorem in calculus.

In this video, we cover a few examples of definite integration.

Here we cover the first part of the fundamental theorem of calculus.

Here we consider a few complex applications of the first part of the fundamental theorem of calculus.

In this video, we cover the average value theorem, a theorem that occurs quite frequently on AP exams.

Here we consider areas between two curves and how to obtain an expression for these areas.

In this video, I introduce a topic that will be central to the next few videos: Volumes of Solids of Revolution.

Here we consider rotating a region about the y-axis.

In this video, we cover an example of volumes of solids of revolution involving rings.

In this video, we cover another scenario of volumes of solids of revolution.

In this video, we cover an example of a question involving volumes of solids of revolution.

Here we cover a concept tied into volumes of solids: cross sections. The picture used is from epsilon-delta.org.

In this video, we cover an FRQ from the 2009 AP Calculus AB exam. The question focuses on cross sections and area.

In this video, we cover a method to solve differential equations relevant to the AP Calculus AB exam.

Here I have attached a test on applications of integration that has four free response questions. You will practice the major concepts from this section that often appear on AP exams.

In this video, we introduce one final application of integration and differentiation: motion. We also cover 5 important rules in motion.

Here we cover an example of a simple question in motion.

In this video, we cover an application of differentiation with motion: changing directions.

Here we introduce the integration involved in motion.

In this video, we cover two concepts closely related to position and velocity.

In this video, we cover two multiple choice questions involving motion with graphs.

In this video, I cover an FRQ that covers all of the concepts learned in this module.

Here I have attached a motion quiz with solutions. The quiz only has one free response question and three multiple choice but it covers a bunch of the topics in this section.