# Calculus 1 with the Math Sorcerer

## 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 Challenging 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 Determine 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

**This is literally the ULTIMATE Calculus 1 Course!!!**

**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:)**

Note this course has lots of very short videos with assignments. If you are trying to learn calculus then this format can be good because you don't have to spend tons of time on the course every day. Even if you can only spend time doing 1 video a day, that is honestly better than not doing any mathematics. You can learn a lot and because there are so many videos you could do 1 video a day. Good luck and I hope you learn a lot of math.

## Who this course is for:

- Anyone who wants to learn Calculus

## Instructor

I was born on a small unnamed Island in the Pacific Ocean inhabited mostly by natives who practiced mathematics on a daily basis.

My mother was a witch who specialized in Calculus and my father was a warlock who was well versed in the dark arts of Algebra.

As I grew older so did my thirst for knowledge, and so I set out on a long voyage to improve my mathematical skills. I traveled the world for years and learned a great deal of mathematics, but it wasn't until I met that raging Hobbit that my true powers started to show.

I am here today to share my magical powers with you.

Come join on me on this journey as we explore the world of mathematics together.