# Math 220 (Calculus I) Spring 2018

## Course Description

Math 220, Calculus I, reviews properties of functions and
introduces the basic ideas of Calculus. Calculus can be thought
of as a sophisticated machine which describes and calculates
continuous change. The two main branches are differential
calculus (concerning rates of change of functions and slopes of
curves) and integral calculus (concerning accumulation of
quantities and areas between curves). All of these are first
introduced and defined with the notion of a "limit" - the idea of
approaching a number/quanity, rather than "plugging in" or "being
at" a certain number/quanitity.
Investigating properties of these definitions (via their
description by a limit) leads to amazingly beautiful and simple
formulas that are used for calculations.

Calculus has been historically called "calculus of
infinitesimals" or "infinitesimal calculus". Though it was
known to be done by Issac Newton and Gottfired Leibniz as
early as 1666, the first book of solid definitions and
proofs was published by Augustin Cauchy in 1840.

We will cover Chapters 1 - 6 in

- James Stewart,
*Calculus:
Early Transcendentals*, **8th edition**, with Enhanced
WebAssign.

This includes concepts
like taking derivatives and integrals of functions, and
using this in
applications such as Newton's Method, finding min/max values
of functions, exponential growth and decay, related rates
word problems, linear approximation and differentials,
calculating areas between curves and volumes of cylindrical
shells..

For most people, calculus is the most challenging math
class they have encountered so far. There are a larger number of interrelated
concepts than before, and solving a single problem can require
thinking about one concept or object in several different ways.
Because of this, conceptual understanding is more important than ever,
and it is not possible to learn a short list of “problem
templates” in lecture that will allow you to do all the HW and
exam problems. Thus, while lecture and section will include many
worked examples, you will still often be asked to solve a HW problem
that doesn’t match up with one that you’ve already seen.
The goal here is to get a solid understanding of vector calculus so
you can solve *any* such problem you encounter in mathematics,
the sciences, or engineering. That requires trying to solve new
problems from first principles, if only because the real world is sadly complicated.

## Documents

A copy of our syllabus is here.
Grades will be posted via Compass here.
The homework will be completed online via WebAssign
## Daily Schedule and Group Worksheets

These are all posted online in the course diary.

## Exams

There will be 3 in-class exams held on February
14th, March 14th, and April 25th. You MUST
bring your I-card to the exam.
All material covered during Lecture, Discussion,
or Homework may be on the exam. The practice exams
below are actual exams from previous years.
## Handouts

Trig Formulas
Handout
Inverse Trig Examples
Worksheet
Solutions
Theorems on Continuous Functions
Handout
Derivative Rules
Handout
L'Hopitals Limit Examples
Handout
Common Shape Formulas
Handout
Integral Rules
Handout
Substitution Examples Part 1
Handout
Substitution Examples Part 2
Handout
Volume Examples
Blank Worksheet
Solutions
# Extra Math 220 Tutoring Hours

**
** Teaching Assistants will be available in 445
Altgeld at the following dates/times to help review
for Exam 2

Sunday March 11th 12 - 6pm
Monday March 12th 4 - 10pm
Tuesday March 13th 4 - 10pm
**
**
## Old Exams and Quizzes

To see old exams and quizzes for Math 220 dating
back to Fall 2012 go here.
## Quizzes

Quiz 1 Solutions
Quiz 2 Solutions
Quiz 3 Solutions
Quiz 4 Solutions
Quiz 5
Solutions
Quiz 6 Solutions
Quiz 7 Solutions
Quiz 8 Solutions
Quiz 9 Solutions
Quiz 10 Solutions
Quiz 11 Solutions
Quiz 12 Solutions
## Exams

Exam 1 Solutions
Exam 2 Solutions
Exam 3 Solutions