# Calculus

## Limits

Why Limits are Important in Calculus

Finding Real limits Graphical & Numerical Approach

Finding Limits with Properties Examples inc Quotients

Limits of Trigonometric Functions with Correction

Limits Involving Absolute Value Functions

Squeeze Theorem or Sandwich Theorem

Continuity Open & Closed Intervals & 1 Sided Limits

Infinite Limits & Vertical Asymptotes

## Introduction to Differentiation

Definition of Derivative & Tangent Line Problems (Full Length)

Slope of Tangent Line Derivative at a Point

Finding Derivative with Definition of Derivative

Definition of Derivative and Vertical Tangent Line

Graphical Comparison of Function vs Derivative Graphs

## Rules of Differentiation

Derivatives with Sine and Cosine

Instantaneous Velocity and Speed of Linear Motion

Tangent Line Through Point Not On Curve

Tangent Line of Curve Parallel to A Line

Deriving the Derivative Rules for Trigonometric Functions Tan, Cot, Sec, Csc

Derivative Rules of Trigonometric Functions

Higher Order Derivative Introduction

Chain Rule for Derivatives & General Power Rule

Chain Rule Harder Algebraic Examples

Chain Rule with Trigonometric Functions

Chain Rule with Trig Functions Harder Examples

Derivative of Absolute Value Functions

Horizontal Tangent Lines and Differentiation

## Implicit Differentiation

Introduction to Implicit Differentiation

Implicit Differentiation Examples

## Related Rates

Related Rates in Calculus Part 1

Calculus Related Rates Example Volume of Cone

Related Rates Part 2 Linear vs Angular Velocity

## Applications of Differentiation

Extrema Intro Extrema on an Interval

Application of Rolle's Theorem with Intermediate Value Theorem

Mean Value Theorem for Derivatives

## Graphing with Derivatives

Graphical Comparison Function to its 1st and 2nd Derivative

Sketching Derivatives from Graphs of Functions 5 Examples

First Derivative Test Increasing Decreasing Functions

Concavity Inflection Second Derivative Test

Limits at Infinity Rational, Irrational, and Trig Functions

Horizontal Asymptotes of Irrational Functions

Even and Odd Functions Many Examples

Summary of Curve Sketching Rational Function with Slant Asymptote

Summary of Curve Sketching Rational Exponent Odd Function

## More Applications of Differentiation

Optimization Calculus Problems Minimizing Lengths

Optimization Calculus Problems Volume

Newton's Method for Estimating Zeros of a Function

Differentials Tangent Line Approximation Propagated Error

## Introduction to Integration

Antiderivative & Indefinite Integration

Initial Condition Particular Solution for Antiderivative

Indefinite Integration Word Problems

Sigma Notation & Infinite Sums with Limits

Estimating Area with Riemann Sums Finite Rectangles

Estimating Area with Rectangles Part 1 of 2

Definition of Area Reimann Sum Limit of Sums Part 2 of 2

Estimating Area with Rectangles & Reimann Limit of Sums Definition of Area

Area Against y Axis Reimman Limit of Sums

Reimann Sum Defined w/ 2 Limit of Sums Examples

Definite Integrals Defined w. Reimann Limit of Sums Example

Definite Integrals Common Geometric Area

Properties of Definite Integrals

## Fundamental Theorems of Calculus

First Fundamental Theorem of Calculus

Mean Value & Average Value Theorem of Integration

Application of Definite Integration Volume & Rate of Flow Corrected

Definite Integration & Displacement and Total Distance of Linear Motion

Definite Integral as a Function of X

Second Fundamental Theorem of Calculus

Indefinite Integration by Substitution

Definite Integration with U Substitution

AP Calculus Project - Derive So Hard (E.M.P.)

## Logarithmic, Exponential, and More Transcendental Functions

Derivative of Natural Logarithm Functions

Integrating Natural Logarithm Function

Derivative of Inverse Functions

Derivative of Natural Exponential Function

Integration of Natural Exponential Functions

Derivative of Exponential Functions Base a

Integrating Exponential Functions Base a

Derivative of Logarithms Base a

Derivative Rules for Inverse Trigonometric Functions Derived

Derivative of Inverse Trigonometric Functions Examples

Integrating Inverse Trigonometric Functions 6 Examples

## Introduction to Differential Equations

Verifying Particular Solutions to Differential Equations

Intro to Solving Separable Differential Equation

Separable Differential Equations & Growth and Decay Model

More Solving Separable Differential Equations

## Area Between Curves & Volume of Revolution

Area Between 2 Curves using Vertical and Horizontal Representative Rectangles

Area Under a Curve & Definite Integrals with TI NSPIRE

Volume of Solid of Revolution Disk Method and Washer Method

Volumes of Solids with Known Cross Sections 3 Examples

Volume of Solid of Revolution Shell Method 3 Examples