Here is an interactive text to accompany the course. We invite you to take advantage of the many demonstrations to explore Calculus more deeply. Functions Functions: Stars of the Show Two Faces of Functions Relating these representations of functions Important information contained in functions The Function Zoo Straight Lines, a geometrical review Equations of Straight Lines Powers of x: positive integer exponents Polynomials Powers of x: fractional exponents How big should a cell be? Composites What is the derivative? Introduction The linear nature of graphs Rates of change and the slope of a curve Position and Average Velocities(s) of the Falling Ball So what is the derivative, after all? Summary and suggestions for further Study Tools for Calculating Derivatives Introduction to Derivatives Linear Approximations Differentiating Constant Functions Differentiating Linear Functions Differentiating Sums of Functions Differentiating Products of Functions Differentiating Constant Multipliers Differentiating Powers Differentiating Polynomials Differentiating Quotients The Chain Rule Implicit Differentiation Applications of the Chain Rule Applications of the Derivative What does a derivative tell us about a function? Maxima and minima The second derivative Sketching graphs Practice with graphs of functions Return to the function zoo Exponential functions and exponential growth Exponential growth: The Andromeda Strain Doublings: The exponential function with base 2 Exponents and logarithms: inverse functions Derivatives of Exponential Functions The Natural Logarithm Rates of Growth Trigonometric and Inverse Trigonometric functions Trigonometry: A Day at the Track Derivatives of trigonometric functions Inverse Trigonometric Functions The Zebra Danio and its escape response Some Untamed Beasts Continuity and Differentiability Simple differential equations Introducing a differential equation Initial value problems Other differential equations for growth and decay Differential equations for periodic behaviour A system of linked differential equations A love-hate relationship A second order equation and its solutions Phase, amplitude, and all that Approximations Newton's Method More Differential Equations Qualitative ideas and direction fields Limited and unlimited growth Euler's Method The HIV epidemic in Vancouver's Lower East Side