UBC Calculus Online Course Notes
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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
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