KindiakMath

Calculus

Here are my write-ups on the theory of calculus and some non-trivial exercises therein. Enjoy!

Theory

Limits

  1. Exploring o-Calculus
  2. Formalising Continuity
  3. Completing the Derivative

Differentiation

  1. The Nuclear Weapon of Differentiation
  2. The Trifecta of Differentiation
  3. The Meanest Theorem in Calculus
  4. Differentiating Inverses

Applying Differentiation

  1. The Exponential Anti-hero
  2. Technical Optimisation
  3. Profit Maximisation for Math People
  4. The Overrated L’Hôpital’s Rule

Integration

  1. Defining Integration
  2. What’s with the +C?
  3. Why u-Substitution is So Awesome
  4. How to Reverse the Product Rule

Applying Integration

  1. What is an Angle?
  2. Constructing Real Trigonometry
  3. Proving the Area of a Circle and More
  4. The Derivative of Sine
  5. Proving that Pi is Irrational
  6. Proving Volumes
  7. Launching Calculus

Exercises

Limits

  1. Several Limit Drills
  2. Curious Continuity

Differentiation

  1. Several Differentiation Drills
  2. The Intermediate Value Derivative
  3. Harder than it Seems
  4. An Increasing-Derivative Quotient
  5. An Inequality Puzzle

Applying Differentiation

  1. A Doubly Taylor Theorem
  2. Classical Optimisation

Integration

  1. The Massive Difference of Plus One
  2. Some Integration Drills
  3. The Classic Secant Integral
  4. Several Laborious Integrals
  5. Calculus Recap (Polytechnic)

Applying Integration

  1. A Bounded Derivative Integral
  2. Some Calculus of Variations
  3. Odd and Even Functions
  4. Some Normal Distribution Trivia
  5. Exponential Fourier Series
  6. The Wallis Product
  7. When Integrals Approximate One

Weekly Practice

  1. Tricky Limits
  2. Tedious Differentiation
  3. Exploiting the Trifecta
  4. Nontrivial Rates of Change
  5. Optimised Geometry
  6. Tedious Integration
  7. Substitution Magic
  8. Reduction Formulae
  9. The Negative Integral
  10. Classic Applied Calculus