Calculus One

Calculus One is a first introduction to differential and integral calculus, emphasizing engaging examples from everyday life.

Week 3: Basics of Derivatives (21 Feb 2014)

• How to use the Textbook
• Welcome to Week 3!
• Week 3 Office Hours
• 3.01 Slope and derivatives
• 3.02 What is the definition of derivative?
• 3.03 What is a tangent line?
• 3.04 What can you say now?
• 3.05 Why is the absolute value function not differentiable?
• 3.06 What is the derivative of the greatest integer function?
• 3:07 Using the Definition of the Derivative
• 3.08 How does wiggling $x$ affect $f(x)$?
• 3.09 Why is $\sqrt{9999}$ so close to $9999$?
• 3.10 What information is recorded in the sign of the derivative?
• 3.11 Why is a differentiable function necessarily continuous?
• 3.12 Why is the derivative of $x^2$ equal to $2x$?
• 3.13 What is the derivative of $x^n$?
• 3.14 What is the derivative of $x^3+x^2$?
• 3:15 Derivative Laws Using Limit Laws
• 3.16 What about exponential functions?
• 3:17 Examples Using the Power Rule, Part 1
• 3:18 Examples Using the Power Rule, Part 2
• 3:19 Revisiting an Old Example

Week 4: Curve Sketching, The Product Rule and The Quotient Rule (1 Mar 2014)

• Week 4 Intro
• Week 4 Office Hours
• 4.01 What is the meaning of the derivative of the derivative?
• 4.02 What does the sign of the second derivative encode?
• 4.03 What does $\frac{d}{dx}$ mean by itself?
• 4.04 What are extreme values?
• 4.05 How can I find extreme values?
• 4.06 Do all local minimums look basically the same when you zoom in?
• 4.07 How can I sketch a graph by hand?
• 4.08 A plot of an unknown function
• 4.09 An example of sketching a curve
• 4.10 ZOMBIE ATTACK
• 4.11 What is the derivative of $f(x)\cdot <!--\; \cdot \; -->g(x)$?
• 4.12 Four examples of the product rule
• 4.13 Morally, why is the product rule true?
• 4.14 How does one justify the product rule?
• 4.15 What is the quotient rule?
• 4.16 Four examples of the quotient rule
• 4.17 How can I remember the quotient rule?
• 4.18 Linearization

Week 5: Chain Rule (8 Mar 2014)

• Week 5 Office Hours
• Week 5 Intro
• 5.01 What is the chain rule?
• 5.02 What is the derivative of $(1+2x{)}^5$ and $\sqrt{x^2+0.0001}$?
• 5.03 Four examples of the chain rule
• 5.04 Chaining the Chain Rule
• 5.05 Forget the Quotient Rule!
• 5.06 What is implicit differentiation?
• 5.07 What is the folium of Descartes?
• 5.08 Differentiating the astroid
• 5.09 How does ${\left(f^{-<!--\; -\; -->1}\right)}^{\prime }(x)$ relate to $f^{\prime }(x)$?
• 5.10 What is the derivative of log?
• 5.11 What is logarithmic differentiation?
• 5.12 Four examples of logarithmic differentiation
• 5.13 Discover-$e$
• 5.14 How can we multiply quickly?
• 5.15 Why does the Power Rule work?
• 5.16 How can logarithms help to prove the product rule?
• 5.17 How do we prove the quotient rule?
• 5.18 How does one prove the chain rule?

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