# Calculus 1 & 2 / AB / BC

If it’s in your course, it’s on this site.

Whatever the level of Calculus 1 or 2 you are rocking – Calculus 1 or 2 in college, Advanced Calculus AB or BC (first 2/3 of the course), or another level of high school Calculus, you have found the perfect help site! This course will take you through differential and integral calculus offering 100’s of Calculus lesson videos and 1,000+ practice problems with video explanations and written solutions to each problem, complete notes, and a master calculus teacher full of the energy of a rock star and the knowledge of Newton.

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## Chapter 1 – Limits

This chapter takes you on a journey through the foundation of much of Calculus – Limits!  We begin by learning all of Calculus in one lesson with Distance = Rate x Time…seriously one lesson…all of Calculus!  From there you will understand what limits are using graphs and tables of numbers.  After this awesome mental party, you will master evaluating limits using direct substitution and several algebraic techniques.  Then, it is off to continuity, one-sided limits, and the Intermediate Value Theorem before studying vertical and horizontal asymptotes as limits approach infinity.  The chapter finishes off with some challenging AB and BC Exam Practice problems which are also great if you who have a difficult teacher or professor.

## Chapter 2 – Derivatives

This chapter begins your epic quest through differential calculus!  You will start with the concept and limit definition of the derivative before learning about differentiability and sketching graphs of the derivative of f(x).  From there, it is time to shine a light on differentiation rules so you can then tackle position, velocity, and acceleration – all very cool!  Then, it is off to master the Product, Quotient, and Chain Rules and then on to implicit differentiation.  The chapter rounds out with a rockin’ study of related rates and a host of Advanced Calculus AB and BC free response and multiple choice practice questions featuring all you learned about the derivative.  Time to dive in and get your blind blown by the beauty of the derivative!!!

## Chapter 3 – Uses of the Derivative

This chapter is all about the awesome applications of derivatives!  You begin with absolute extrema and finding critical numbers.  Then it is off to Rolle’s and the Mean Value Theorems.  From there your quest takes you through using f ‘ to figure out where is increasing and decreasing along with rocking the First Derivative Test!  The study of the second derivative, f “, and the concavity and points of inflection of f is the next important stop.  The 2nd derivative test is explored.  You will then learn how to sketch curves using all of the calculus rocked thus far.  You will master the fun and classic lesson on optimization and make easy work of tangent line approximations (local linearization) and differentials.  From there, you will make quick work of Newton’s method.  TONS of original AB and BC Exam practice problems all about the applications of the derivative close out the chapter!

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## Chapter 4 – Integration

This chapter opens with rocking the antiderivative and a tour through all the basic integration rules and fundamental problem types.  Riemann sums, midpoint, and trapezoidal sums master you in the art of approximating area between the curve and the x-axis.  You will see the beauty of definite integrals and their properties along with finding area of graphs forming geometric figures.  The First Fundamental Theorem of Calculus will have you finding areas between the x-axis and a graph easily!  With this knowledge comes finding average value and the Second Fundamental Theorem of Calculus as you find derivatives of integrals.  The chapter begins to wind down with a fun exploration of “U” substitution or integration by substitution.  The final stop in this epic chapter consists of oodles of original AB and BC exam practice problems involving integration concepts.  Tons of free response and multiple choices questions await you!

## Chapter 5 – Derivatives and Integrals of Exponential Functions, Logarithms, and Inverse Trigonometry

This chapter is all about derivatives and integrals of new functions, but also serves as a review of all Calculus applications you have learned!  You begin with the derivative of lnx or the natural log, before learning about integrals involving lnx.  From here, you will tackle derivatives of inverse functions.  Then, it is off to differentiate and integrate e^x.  After rocking the Calculus of e, you will learn how to take the derivatives and antiderivatives of exponential and logarithm functions of any base.  What follows is a fun journey into the derivatives and integrals of inverse trig functions (arcsin anyone?).  The chapter rounds out with a lesson on L’Hopital’s (L’Hospital) Rule and some original AB and BC exam practice problems.  A thorough review of precalculus knowledge is given in many lessons to ensure you are fresh on prior knowledge.  Let’s get on this!

## Chapter 6 – Differential Equations and Exponential & Logistic Growth

This chapter begins with a deep dive into what differential equations are and how to check your solutions to differential equations.  From there you will tackle slope fields and Euler’s Method.  A study of how to solve separable differential equations using separation of variables is next.  You will then become well practiced in the art of exponential growth and decay functions before rocking Newton’s Law of Cooling (which is super cool…pun intended!).  Next is a fun yet comprehensive learning of logistic growth functions (logistic differential equations).  The chapter rounds out with excellent original AB and BC Exam Practice Problems.

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## Chapter 7 – Area, Volume, and Arc Length

This chapter starts with a master class in how to find the area of a bounded region and the area between two curves.  Next, you will make simple work of how to set up and solve integrals to find the volume of solids of revolution using the Disk and Washer methods.  From there you will see the beauty of simple geometry come alive when you master finding volumes of solids with cross-sections.  You will then rock how to find volumes of solids of revolution using the Shell Method.  After this, you will explore the concepts of arc length and surface area.  The chapter wraps up with original AB and BC free response questions that incorporate many of the above topics.  Time to see how basic geometry with a little Calculus can make for some awesome concepts!

## Chapter 8 – Advanced Integration Techniques and Improper Integrals

This chapter begins with tricky yet neat manipulations of integrands to make integrating those very difficult functions much easier.  From there, it is off to learn all about a staple in Calculus 2 / BC, integration by parts.  Next, you will learn how to integrate by partial fraction decomposition – sounds fancy…it’s just fun!  Then you will master the art of using trigonometric identities and some nifty manipulations to solve trigonometric integrals.  The second to last lesson is all about trigonometric substitution taught in a way you can understand!  This chapter on integration wraps up with a thorough study of improper integrals.  What are you waiting for?  Get integrating!

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## Chapter 9 – Series and Tests for Convergence and Divergence

This chapter starts with an overview of what sequences and series are.  From there it is time to master the nth-term divergence test and telescoping series.  Then it is off to learning how beautiful and simple Geometric series are.  Next you will gain confidence with the Integral and P-series tests before tackling the Direct and Limit Comparison Tests.  You then will be treated to the Alternating Series Test for Convergence and its Error Bound!  The third to last lesson of this chapter will have you feeling good about the Ratio and Root tests.  Before the final lesson, you will understand how to choose which convergence or divergence test is best.  The chapter rounds out with original BC Exam Practice problems.  Let’s get rocking and rolling with sigma notation and series!!!

## Chapter 10 – Taylor Polynomials and Power Series

This chapter starts rocking with a comprehensive study of Taylor polynomials that will make you see the beauty and simplicity of Taylor!  From there you will learn about Taylor’s Theorem, the Lagrange Error Bound, and Alternating Series Error.  Next, it is off to master power series, interval of convergence, and radius of convergence.  Then you will learn how to differentiate and integrate power series by understanding you are simply working with polynomials!  The second to last stop on this adventure will have you building power series using the sum formula for a geometric series.  The chapter finishes off smoothly with every free-response question type on series you could ever want and oodles of excellent original multiple choice question practice!  Time to feel great about Taylor polynomials and power series!!

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## Chapter 11 – The Calculus of Parametric and Polar Equations

This chapter starts with the fundamentals of parametric equations – graphing and eliminating the parameter.  Then you will see how simple and awesome derivatives, integrals, and related concepts are with parametric equations.  From there it is straight off to vector-valued functions with a focus on position, velocity, and acceleration vectors, speed, and distance.  You are then ready to tackle the basics of graphing points in polar form.  Next it is a logical hop to graphing all the basic polar equations – lines, circles, limacons, and petal (rose) curves.  Then you will see how polar differentiation is related to parametric equations.  The second to last lesson is all-time!!!  It is a journey through area of polar curves!  The chapter rounds out nicely with original BC Exam practice on parametric and polar equations and vectors.  What are you waiting for?!?  Get learning!

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