# Calculus 2 with the Math Sorcerer

## What you'll learn

- More Calculus 2 Than You Will Learn in Any Class, Guaranteed:)
- How to Find the Derivatives of the Inverse Trigonometric Functions
- How to Write a Trigonometric Expression in Algebraic Form
- How to Find the Equation of the Tangent Line
- How to Evaluate Integrals leading to Inverse Trigonometric Functions
- How to Solve Simple Differential Equations Involving Inverse Trig Functions
- How to Derive Some of the Inverse Trig Functions from Scratch
- How to Find the Tangent Line using Implicit Differentiation
- How to Find Relative Extrema using the First Derivative Test
- The Definitions of the Hyperbolic Functions
- How to Evaluate the Hyperbolic Functions
- How to do Basic Proofs for Identities Involving the Hyperbolic Functions
- How to Compute the Derivatives and Integrals of Hyperbolic Functions
- How to Compute Definite Integrals with Hyperbolic Functions
- How to Compute Limits, Tangent Lines, and Extrema in problems involving Hyperbolic Functions
- How to Graph Some of the Hyperbolic Functions
- How to Derive Some of the Hyperbolic Functions
- How to Find the Area Between Two Curves using Calculus
- How to use the Disk and Washer Methods to Find the Volume of a Solid of Revolution
- How to use the Shell Method to Find the Volume of a Solid of Revolution
- How to Derive the Formula for the Arc Length of a Curve
- How to Find the Arc Length
- How to Find the Surface Area for a Surface of Revolution
- How to Derive the Formula for Work From Scratch Using Calculus
- How to Find Work in Applications Involving Hooke's Law
- How to Find the Center of Mass and the Center of Gravity
- How to Compute Basic Integrals
- How to Compute Basic Integrals using Formulas that Lead to the Natural Log
- How to Compute Integrals with Bases other than e
- How to Use the Integration by Parts Formula
- How to Use Tabular Integration
- How to Compute Integrals Involving Powers of Sine and Cosine
- How to Compute Integrals Involving Powers of Secant and Tangent
- How to Use Trigonometric Substitution
- How to Integrate by first using Partial Fraction Decomposition
- How to Evaluate Limits at Infinity
- How to Use L'hopital's Rule
- How to Determine if an Integral is Improper
- How to Evaluate Improper Integrals with Infinite Limits
- How to Evaluate Improper Integrals with Infinite Discontinuities
- How to use the P-Test and the Comparison Test for Improper Integrals to Determine Convergence or Divergence
- How to Write Parametric Equations in Rectangular Form
- How to Graph Parametric Equations and Indicate the Orientation
- How to Determine where a Curve is Not Smooth
- How to Find the First Derivative and the Slope at a point given Parametric Equations
- How to Find the Second Derivative and the Concavity at a point given Parametric Equations
- How to Find the Open t-intervals where Parametric Equations are Concave Up and Concave Down
- How to Find the Equation of the Tangent Line Given Parametric Equations and a Point (or a value of the parameter)
- How to Determine the Vertical and Horizontal Tangent Lines Given Parametric Equations
- How to Find the Arc Length Given Parametric Equations
- How to Plot Polar Coordinates
- How to Convert Polar Coordinates to Rectangular and Rectangular to Polar
- How to Convert Polar Equations to Rectangular Equations and Rectangular Equations to Polar Equatoins
- How to Find Area using Polar Coordinates
- Understand the Definition of a Sequence
- Understand what it means for a Sequence to Converge or Diverge
- How to Find the Limit of Almost Any Sequence using Intuition and Growth Rates
- Understand what a Series Actually is
- Understand what it means for a Series to Converge and what it means to Diverge
- How to Evaluate the Sum of a Series when the Series is Telescoping
- Understand when a Geometric Series Converges and when it Diverges
- How to Compute the Sum of a Convergent Geometric Series using a Formula(not found in books)
- Understand How to Prove the nth Term Test
- How to use the nth term test for Divergence
- How to Use the Integral Test to Determine Convergence or Divergence of Series
- How to use the p-test for Infinite Series
- How to find the domain of the Riemann Zeta Function
- How to use the Direct Comparison Test
- How to use the Limit Comparison Test
- How to use the Alternating Series Test
- How to Determine if a Series Converges Absolutely or Conditionally or Diverges
- How to use the Ratio Test
- How to use the Root Test
- How to Compute Maclaurin Polynomials
- How to Compute Taylor Polynomials
- How to use a Maclaurin Polynomial to Approximate a Function
- Understand what a Power Series actually is
- Understand The Convergence Theorem both rigorously and intuitively in both the Real Case and the Complex Case
- How to Find the Center of a Power Series
- How to Find the Radius of Convergence of a Power Series
- How to Find the Interval of Convergence of Power Series
- Understand Geometric Power Series
- How to Write a Function as a Power Series and Find it's Interval of Convergence
- How to Find a Power Series Representation of a Function by Differentiating First
- Understand both Taylor and Maclaurin Series
- How to Find both Taylor and Maclaurin Series

## Requirements

- Calculus 1 is the usual prerequisite since this is Calculus 2:)
- Knowledge of basic differentiation rules and integration rules

## Description

**This is literally the ULTIMATE Calculus 2 Course as it contains over 500 videos!!**

**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) Repeat!**

**If you finish even 50% of this course you will know A LOT of Calculus 2 and more importantly your level of mathematical maturity will go up tremendously!**

**Calculus 2 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:

- Students who know basic calculus
- Students who have had calculus 1 course

## 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.