Lessons

Welcome to the lessons page! Here are the lessons, videos, proofs, and examples to help you learn calculus. At the very bottom of the page is a description of each category linked to on this page.

Important Subjects Prior to Calculus

Calculus I

Chapter1: Limits and Continuity

  • 1.1 Introduction to Limits
  • 1.2 Basic Rules for Limits
  • 1.3 Advanced Limits
  • 1.4 Continuity

Chapter 2: Derivatives

  • 2.1 The Derivative
  • 2.2 Basic Rules For The Derivative 
  • 2.3 The Product Rule and The Quotient Rule 
  • 2.4 The Chain Rule
  • 2.5 Higher Order Derivatives
  • 2.6 Implicit Differentiation

Chapter 3: Applications of Derivatives

  • 3.1 Related Rates
  • 3.2 Monotonicity and Concavity
  • 3.3 Extrema
  • 3.4 Optimization Problems
  • 3.5 Graphing
  • 3.6 Mean Value Theorem

Chapter 4: Integrals

  • 4.1 The Anti-Derivative
  • 4.2 Introduction to Area
  • 4.3 Definite Integrals
  • 4.4 Fundamental Theorem of Calculus

Chapter 5: Applications of Integrals

  • 5.1 Area of a Plane Region
  • 5.2 Volume using Disks and Washers
  • 5.3 Volume using Shells

 Calculus II

Coming very soon.

Calculus III

Sorry, but this, too, will be coming soon.

 

Lessons will be written explanations, just like a text book. However, they will be written from the perspective of a student and will be much easier to understand than a traditional textbook.

Videos will be just another form of lesson. However, some students prefer to learn through video, and I wish to help all types of learners.

Proofs are the reason why I have a very deep understanding of calculus. I know where it all comes from, and how things were derived. For some, learning the reasons something works is much more helpful than memorizing a formula. In the lessons, I will generally skip proofs, and provide you with formulas. However, all proofs will be shown in this page.

Examples will be done in a video format. I will eventually have several examples for each section, but please give me time to get all the content of my lessons onto the site.

Furthermore, the best way for you to learn is to PRACTICE! Don’t just read my explanations or watch me solve the problems. You need to do examples for yourself. If you get stuck, you can always ask your teacher, or email me! In order to learn, you have to get stuck a few times!