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Intro
Calculus made easy. Silvanus P. Thompson comes alive
Part 1: Car calculus
Part 2: Differential calculus, elementary functions
Part 3: Integral calculus
Part 4: Leibniz magic notation
Animations: product rule
quotient rule
powers of x
sum rule
chain rule
exponential functions
natural logarithm
sine
Leibniz notation in action
Creepy animations of Thompson and Leibniz
Thank you!
A Preview of Calculus
The Limit of a Function.
The Limit Laws
Continuity
The Precise Definition of a Limit
Defining the Derivative
The Derivative as a Function
Differentiation Rules
Derivatives as Rates of Change
Derivatives of Trigonometric Functions
The Chain Rule
Derivatives of Inverse Functions
Implicit Differentiation
Derivatives of Exponential and Logarithmic Functions
Partial Derivatives
Related Rates
Linear Approximations and Differentials
Maxima and Minima
The Mean Value Theorem
Derivatives and the Shape of a Graph
Limits at Infinity and Asymptotes
Applied Optimization Problems
L'Hopital's Rule
Newton's Method
Antiderivatives
Evaluating Limits By Factoring
Derivatives of Rational Functions & Radical Functions
Continuity and Piecewise Functions
Using The Product Rule - Derivatives of Exponential Functions & Logarithmic Functions
Antiderivatives
Tangent Line Equation With Implicit Differentiation
Limits of Trigonometric Functions
Integration Using U-Substitution
Related Rates Problem With Water Flowing Into Cylinder
Increasing and Decreasing Functions
Local Maximum and Minimum Values
Average Value of Functions
Derivatives Using The Chain Rule
Limits of Rational Functions
Concavity and Inflection Points