# 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