 Differential Calculus in a Single Variable
 Definition of Derivatives using big O notation
 Line Tangent to a Curve
 Exponential Function
 Tangent Lines as Linear Approximations
 Some Useful Trigonometric Limits
 Differentiating Trigonometric Functions
 Inverse Function Theorem
 The Natural Logarithm, the inverse function to the exponential mapping.
 Optimization: its motivation, the First Derivative Test, an example optimizing a rectangle’s area
 Implicit Differentiation
 Curve Sketching
 Applications
 Techniques
 Integral Calculus in a Single Variable
 The Antiderivative part 1, part 2
 Finite Series
 Riemann Summation a first step towards definite integration
 Example Riemann Sum working with
 Fundamental Theorem of Calculus
 Properties of the Integral
 Not all functions are (Riemann) integrable!
 The Natural Logarithm Revisited!
 Integration Techniques:
 Integration Technique #1: Substitution
 Integration Technique #2: Integration By Parts
 Differentiation Under the Integral Sign
 Applications of Integrals
 Calculating ArcLength of Curves
 Calculating the Area for a Surface of Revolution (Part 1) when we revolve about the axis
 Optimization
 Calculus isn’t useless: When Velociraptors Attack, calculus solving matters of life and death!
 Thinking “Infinitesimally”

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