# 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:)**

## 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.