Section Two: Applications to Physics

• Expressing position, velocity and acceleration in terms of slopes and rates of change

Section Three: The Mean Value Theorem

• The Geometry of secant and tangent lines and their connection to derivatives

Section Four: Concavity

• Looking at the rate of change of the rate of change and the connections to Physics

Section Five: Optimization of Functions

• Determining critical points of functions and whether they represent local maxima or minima

Section Six: Techniques of Graphing

• Interpreting, explaining and creating a graphical representation of the behavior of functions

Section Two: Trapezoidal Approximations

• Using the trapezoidal rule to approximate area under a curve

Section Three: The Average Value of a Function

• Determining, explaining and graphically representing the concept of average value

Section Four: Area Between Curves

• Using trapezoids and summation notation to approximate the area of bounded regions

Section Five: Solids of Revolution

• The Geometry of rotating a function about an axis and approximating its volume

Section Two: Arc Length

• Approximating the length of a curve using the hypotenuse of lots of right triangles

Section Three: Series

• The Geometry of arithmetic and geometric series - convergence and divergence

Section Four: Vectors

• The Algebra, Geometry and Physics of directed line segments

Section Five: Hyperbolic Functions

• The unit hyperbola and the hyperbolic functions of sinh, cosh and tanh

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