This is the FlexBook 2.0 version of CK-12's PreCalculus Concepts course. In …

This is the FlexBook 2.0 version of CK-12's PreCalculus Concepts course. In addition to new formatting and access to teacher insights, there are many curated 'Related Modalities' for each lesson. The text surveys traditional and additional content for a course in sequence after Algebra II and before Calculus or Statistics. The content in this text covers most state standards for Analysis, Trigonometry and Linear Algebra as well as the Common Core Standards suggested for a "Fourth Course" in high school.

The Calculus BC AP exam is a super set of the AB …

The Calculus BC AP exam is a super set of the AB exam. It covers everything in AB as well as some of the more advanced topics in integration, sequences and function approximation. This tutorial is great practice for anyone looking to test their calculus mettle!

This series of videos focusing on calculus covers minima, maxima, and critical …

This series of videos focusing on calculus covers minima, maxima, and critical points, rates of change, optimization, rates of change, L'Hopital's Rule, mean value theorem.

This is about as many integrals we can use before our brains …

This is about as many integrals we can use before our brains explode. Now we can sum variable quantities in three-dimensions (what is the mass of a 3-D wacky object that has variable mass)!

This series of videos focusing on calculus covers indefinite integral as anti-derivative, …

This series of videos focusing on calculus covers indefinite integral as anti-derivative, definite integral as area under a curve, integration by parts, u-substitution, trig substitution.

Limits are the core tool that we build upon for calculus. Many …

Limits are the core tool that we build upon for calculus. Many times, a function can be undefined at a point, but we can think about what the function "approaches" as it gets closer and closer to that point (this is the "limit"). Other times, the function may be defined at a point, but it may approach a different limit. There are many, many times where the function value is the same as the limit at a point. Either way, this is a powerful tool as we start thinking about slope of a tangent line to a curve.

This tutorial covers much of the same material as the "Limits" tutorial, …

This tutorial covers much of the same material as the "Limits" tutorial, but does it with Sal's original "old school" videos. The sound, resolution or handwriting isn't as good, but some people find them more charming.

It is sometimes easier to take a double integral (a particular double …

It is sometimes easier to take a double integral (a particular double integral as we'll see) over a region and sometimes easier to take a line integral around the boundary. Green's theorem draws the connection between the two so we can go back and forth. This tutorial proves Green's theorem and then gives a few examples of using it. If you can take line integrals through vector fields, you're ready for Mr. Green.

With traditional integrals, our "path" was straight and linear (most of the …

With traditional integrals, our "path" was straight and linear (most of the time, we traversed the x-axis). Now we can explore taking integrals over any line or curve (called line integrals).

You've done some work with line integral with scalar functions and you …

You've done some work with line integral with scalar functions and you know something about parameterizing position-vector valued functions. In that case, welcome! You are now ready to explore a core tool math and physics: the line integral for vector fields. Need to know the work done as a mass is moved through a gravitational field. No sweat with line integrals.

Let's jump out of that boring (okay, it wasn't THAT boring) 2-D …

Let's jump out of that boring (okay, it wasn't THAT boring) 2-D world into the exciting 3-D world that we all live and breath in. Instead of functions of x that can be visualized as lines, we can have functions of x and y that can be visualized as surfaces. But does the idea of a derivative still make sense? Of course it does! As long as you specify what direction you're going in. Welcome to the world of partial derivatives!

This 8-minute video lecture demonstrates how to use a position vector valued …

This 8-minute video lecture demonstrates how to use a position vector valued function to describe a curve or path. [Calculus playlist: Lesson 133 of 156]

In this tutorial, we will learn to approximate differentiable functions with polynomials. …

In this tutorial, we will learn to approximate differentiable functions with polynomials. Beyond just being super cool, this can be useful for approximating functions so that they are easier to calculate, differentiate or integrate. So whether you will have to write simulations or become a bond trader (bond traders use polynomial approximation to estimate changes in bond prices given interest rate changes and vice versa), this tutorial could be fun. If that isn't motivation enough, we also come up with one of the most epic and powerful conclusions in all of mathematics in this tutorial: Euler's identity.

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