What you'll learn

An Intuitive Understanding of Limits

Understand Limit Notation in Calculus

Understand what a Limit actually is and what it means for a Limit to Exist

How to Compute Limits from a Graph

How to Compute Limits Analytically

How to Compute Limits by Rationalizing

How to Compute Limits by Factoring Quadratics

How to Compute Limits with the Difference of Cubes

How to Compute Limits with Absolute Values

How to Compute Limits with Piecewise Functions

How to Think More Deeply about Limits

How to use the Squeeze Theorem to Compute Limits

How to use the Squeeze Theorem to do a Simple Proof

How to Compute Limits using Special Trigonometric Limits

How to Compute Limits that have Trigonometric Functions in them

How to Write a Delta Epsilon Proof for a Linear Function, Quadratic Function, Cubic Function, and Trigonometric Function

Understand what Continuity Means Intuitively

Understand the Definition of Continuity in a Very Deep Way

Understand what Removable and Nonremovable Discontinuities are

How to Find Removable and Nonremovable Discontinuities in Rational Functions, Trigonometric Functions, and Absolute Value Functions

How to Find Removable and Nonremovable Discontinuities in Piecewise Functions

Understand the Intermediate Value Theorem

How to Use the Intermediate Value Theorem

Understand What Infinite Limits actually are

How to Compute Infinite Limits with Rational and Trigonometric Functions

Understand what a Vertical Asymptote is and the Precise Definition via Calculus

How to Find Vertical Asymptotes with and without Calculus

Understand what a Derivative is

Understand How to Construct the Concept of Derivative from Scratch

How to Find the Derivative of a Function using the Limit Definition

How to use all Basic Differentiation Formulas for Polynomials and Trigonometric Functions

How to use the Product Rule, Quotient Rule, and Chain Rule for Differentiation

How to Compute Higher Order Derivatives

How to Find the Slope of the Tangent Line

How to Find Horizontal Tangent Lines

How to Find the Equation of the Tangent Line

How to Various Challeg Calculus Problems involving Derivatives

How to Some of Key Derivative Formulas

Understand the Average Rate of Change

Understand the Instantaneous Rate of Change

How to Compute the Average Rate of Change

How to Compute the Instantaneous Rate of Change

Understand the Relationship Between Position, Velocity, Acceleration, Speed, and Jerk with Calculus

How to Compute Velocity and Acceleration and Speed

How to do Harder Word Problems Involving Velocity and Acceleration

Understand Implicit Differentiation

How to Differentiate Implicitly

How to Find the Equation of the Tangent Line using Implicit Differentiation

How to Find Vertical and Horizontal Tangent Lines using Implicit Differentiation

How to Find the Second Derivative with Implicit Differentiation

Understand Related Rates Word Problems

How to do Related Rates Word Problems

Understand the Difference Between Absolute and Relative Extrema

How to Find Absolute and Relative Extrema from a Graph

Understand what a Critical Number Actually is

Understand the Definition of a Critical Number

How to Find Critical NUmbers

Understand the Extreme Value Theorem

How to Find the Absolute Maximums and Minimums of a Continuous Function on a Closed Interval

Understand Rolle's Theorem Intuitively and Why it Works

How to Use Rolle's Theorem

Understand the Mean Value Theorem Intuitively and Why it Works

How to Use the Mean Value Theorem

Understand the Relationship Between the First Derivative and where the Graph of a Function is Increasing or Decreasing

How to Use the First Derivative Test to Find Relative Maximums and Relative Minimums

How to use the First Derivative to Detee the Intervals where a Function is Increasing and Decreasing

Understand the Notion of Concavity and How the Second Derivative is Involved

How to use the Second Derivative to Find Inflection Points and Intervals where a function is Concave Up and Concave Down

How to use the Second Derivative Test to Find Relative Maximums and Relative Minimums

How to Compute Limits at Infinity

How to Find Horizontal Asymptotes

How to Do Optimization Word Problems

How to use Newton's Method

How to Compute the Differential dy and use it to Approximate the Actual Change in y

Understand Indefinite Integration

Learn all of the basic integration formulas

How to Evaluate Indefinite Integrals

How to Solve Differential Equations

How to Integration by Substitution

Understand the Summation Formulas used to Compute Definite Integrals with the Definition

Understand the Detailed Construction of the Riemann Integral

How to use Limit Definition of a Definite Integral to Find the Area under a Curve

Understand the First Fundamental Theorem of Calculus

How to Use the Fundmantal Theorem of Calculus to Evaluate Definite Integrals

How to Evaluate Definite Integrals with u substitution and how to carefully change the limits of integration

How to Evaluate Definite Integrals with Absolute Values

How to Find the Area Bounded by a Region using Definite Integrals

Understand the Mean Value Theorem for Integrals and it's Relationship to the Average Value of a Function

How to use the Mean Value Theorem for Integrals

How to Find the Average Value of a Function over an Interval

How to use the Second Fundamental Theorem of Calculus

How to use the Extended Fundamental Theorem of Calculus

How to use Simpson's Rule

How to Compute Derivatives involving the Natural Logarithm

How to Integrate using formulas involving the natural logarithm

How to Compute Derivatives involving e^x

How to Compute Integrals involving e^x

How to Compute Derivatives and Integrals involving Bases other than e

Requirements

Precalculus and Trigonometry are the Standard Prerequisites

NOTE: You can still understand A LOT of this material without the above prerequisites

Description

!!

Basically just,

1) Watch the videos, and try to follow along with a pencil and paper, take notes!

2) Try to do the problems before I do them(if you can!)

3) Try to complete the assignments. Solutions are included to every single assignment and in some cases the solutions are very detailed.

4) Repeat!

If you finish even 50% of this course you will know A LOT of Calculus 1 and more importantly your level of mathematical maturity will go up tremendously!

Calculus 1 is an absolutely beautiful subject. I hope you enjoy watching these videos and working through these problems as much as I have:)

Who this course is for:

Anyone who wants to learn Calculus



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