## Calculus 12

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## Table of Contents

*Each lesson is designed to take 60 – 90 minutes to complete with the exception of major projects and assignments.

Lesson 1: Introduction to Calculus

Lesson 2: Review of Function Terminology And More

Lesson 3: Graphing Calculators

Lesson 4: Compositions and Transformations of Functions

Lesson 5: Some Common Functions

Lesson 6: Inverse Functions

Lesson 7: Exponential and Logarithmic Functions

Lesson 2: Review of Function Terminology And More

Lesson 3: Graphing Calculators

Lesson 4: Compositions and Transformations of Functions

Lesson 5: Some Common Functions

Lesson 6: Inverse Functions

Lesson 7: Exponential and Logarithmic Functions

Lesson 1: Introduction to Limits

Lesson 2: Properties of Limits

Lesson 3: Limits Involving Infinity

Lesson 4: Continuity and The Sandwich Theorem

Lesson 5: Applications of Limits

Lesson 2: Properties of Limits

Lesson 3: Limits Involving Infinity

Lesson 4: Continuity and The Sandwich Theorem

Lesson 5: Applications of Limits

Lesson 1: The Derivative

Lesson 2: Rules of Differentiation

Lesson 3: Trigonometric Derivatives and The Chain Rule

Lesson 4: Derivatives of Exponential, Logarithmic, and Inverse Trig Functions

Lesson 5: Implicit Differentiation

Lesson 2: Rules of Differentiation

Lesson 3: Trigonometric Derivatives and The Chain Rule

Lesson 4: Derivatives of Exponential, Logarithmic, and Inverse Trig Functions

Lesson 5: Implicit Differentiation

Lesson 1: Analyzing Functions Part I: Curve Sketching

Lesson 2: Analyzing Functions Part II: Maximums and Minimums

Lesson 3: Applied Maximum and Minimum Problems

Lesson 4: Distance, Velocity, Acceleration, and Rectilinear Motion

Lesson 5: Related Rates

Lesson 6: The Mean-Value Theorem and L’Hopital’s Rule

Lesson 2: Analyzing Functions Part II: Maximums and Minimums

Lesson 3: Applied Maximum and Minimum Problems

Lesson 4: Distance, Velocity, Acceleration, and Rectilinear Motion

Lesson 5: Related Rates

Lesson 6: The Mean-Value Theorem and L’Hopital’s Rule

Lesson 1: Area Approximation and Riemann Sums

Lesson 2: Introduction to the Definite Integral

Lesson 3: The Fundamental Theorem of Calculus

Lesson 4: Integrals and Antiderivatives

Lesson 5: Integration by Substitution

Lesson 6: Integration by Parts

Lesson 7: The Definite Integral

Lesson 2: Introduction to the Definite Integral

Lesson 3: The Fundamental Theorem of Calculus

Lesson 4: Integrals and Antiderivatives

Lesson 5: Integration by Substitution

Lesson 6: Integration by Parts

Lesson 7: The Definite Integral

Lesson 1: Finding The Area Under and Between Curves

Lesson 2: Volume by Discs (Slicing)

Lesson 3: Volume by Shells

Lesson 4: Work

Lesson 5: Average Value of a Function and Rectilinear Motion Revisited

Lesson 2: Volume by Discs (Slicing)

Lesson 3: Volume by Shells

Lesson 4: Work

Lesson 5: Average Value of a Function and Rectilinear Motion Revisited

Lesson 1: Differential Equations – An Introduction

Lesson 2: Initial Value Problems, Slope Fields, and Euler’s Method

Lesson 3: Linearization and Newton’s Method

Lesson 4: Numerical Approximation Methods with Integrals

Lesson 2: Initial Value Problems, Slope Fields, and Euler’s Method

Lesson 3: Linearization and Newton’s Method

Lesson 4: Numerical Approximation Methods with Integrals

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## Course Features

- Many lessons include fun, interactive applets and dynamic graphs which help foster a conceptual and even intuitive understanding of fundamental topics.
- Digital DESMOS Graphing Calculator within the course