Part 1, The Derivative Concept, Spring 2017

As we finish the first part of the course and prepare for the first exam, it is time to clean up the details on the concept of the derivative.

The concepts of ``calculus" were discovered in the 1600's towards the end of the Renaissance period.  Prior to that (indeed by 300 AD) most of the mathematics of our high school curriculum had been discovered.  But the new powerful mathematics discovered in the Seventeenth Century changed the world!  It initiated the modern age of technology (beginning with the Industrial Revolution) and ushered in an age of science and prosperity unrivaled in human history.

The new mathematics was so efficient and explained so many things, that people spoke of it as "the way to calculate" or, in short, "the calculus."  Once people understood the new way to calculate, there was no reason to return to the old ways of the Greeks or Babylonians!

This first part of our calculus class focuses on the main concept of Calculus 1, the concept of slope.  I will take this in an order that is not in the standard textbooks, since I want to emphasize concepts over calculation.  The concept of slope is really a simple one, but we will use it to great effect, by generalizing the slope of a line to the slope of an arbitrary function.

As we do this, we introduce the average rate of change (ARC) and the instantaneous rate of change (IRC) and then make these concepts precise by introducing the concept of limits.

We cover this material in nine lectures across the first three weeks of this semester.

The course material in available in Ken's Google Drive folder. Here is the schedule for Spring 2017, along with links to the relevant material in that folder.

Wednesday, January 18, 2017
1.1, The Slope of a Function

Friday, January 20, 2017
1.2, The ARC and the IRC

Monday, January 23, 2017
1.3, Limits and the IRC

Wednesday, January 25, 2017
1.4, Limit Laws and  Continuity

Friday, January 27, 2017
1.5, Limits and Infinity

Monday, January 30, 2017
1.6, The Formal Definition of Limit and Derivative

Wednesday, February 1, 2017
1.7, The IRC of Powers of x

Friday, February 3, 2017
1.8, The IRC of Transcendental Functions

Monday, February 6, 2017
1.9, Euler's Marvelous Formula

Also in that folder are some subfolders with quizzes and exams from Spring 2017, their solutions, and some older exams and solutions.

Tomorrow we move on to the second part of our semester, the computation of the derivative.