# Math 221 (Calculus I) Fall 2018

## Course Description

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.

Calculus can be thought of as describing and calculating continuous change. Calculus has two main branches - Differential Calculus adn Integral Calculus. Differential Calulus involves the study of rates of change (including slopes of tangent lines) and Integral Calculus concerns the accumulation of quantities (such as areas under a curve of volumes of a solid). 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. Limits are the theoretical foundation of both derivatives and integrals. Investigating properties of derivatives and integrals (via their description by a limit) leads to amazingly beautiful and simple formulas that are used for calculations, such as the the derivative rules and the Fundamental Theorem of Calculus.

This course will begin with a study of limits from an intuitive point of view, continue with a thorough study of differential calculus, and end with some work on definite integrals. Calculus II (Math 231) includes more work on integrals and their applications, as well as the study of infinite sequences and series. Students in this course (1) will study calculus concepts from a theoretical point of view, (2) will learn techniques of calculation, and (3) will apply calculus to model scientific problems.

We will cover Chapters 2 - 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 Moodle 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 evening exams held from 7 - 8pm on September 26th, October 24th, and November 14th. You MUST bring your I-card to the exam.
• All material covered during Lecture, Discussion, or Homework may be on the exam.
• The online form to request a conflict exam is due at 5pm the FRIDAY BEFORE the exam date. Fill out the form here .

## Handouts

• Derivative Rules Handout
• Trig Formulas Handout
• Inverse Trig Examples Worksheet Solutions
• Theorems on Continuous Functions Handout
• Exam 1 Definitions and Theorems Handout
• Related Rates Formulas Handout
• Hyperbolic Trig Formulas Handout
• Integral Rules Handout
• Substitution Examples Part 1 Handout
• Substitution Examples Part 2 Handout
• L'Hopitals Limit Examples Handout
• Volume Examples Blank Worksheet Solutions
• ## Quizzes

You should expect regular weekly quizzes on Friday (mostly)s. In addition, several take-home quizzes will be assigned during the semester. The schedule of quizzes can be found in the course diary.

• 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 8 Solutions
• Quiz 8 Solutions

• ## Worksheets

Solutions to groupwork assignments will be posted the next class day following discussion.

• Worksheet 1 Solutions
• Worksheet 2 Solutions
• Worksheet 3 Solutions
• Worksheet 4 Solutions
• Worksheet 5 Solutions
• Worksheet 6 Solutions
• Worksheet 7 Solutions
• Worksheet 8 Solutions
• Worksheet 9 Solutions
• Worksheet 10 Solutions
• Worksheet 11 Solutions
• Worksheet 12 Solutions
• Worksheet 13 Solutions
• Worksheet 14 Solutions
• Worksheet 15 Solutions
• Worksheet 16 Solutions
• Worksheet 17 Solutions
• Worksheet 18 Solutions
• Worksheet 19 Solutions
• Worksheet 20 Solutions
• Worksheet 21 Solutions
• Worksheet 22 Solutions
• Worksheet 23 Solutions
• Worksheet 24 Solutions
• Worksheet 25 Solutions
• ## Suggested Textbook Problems

These problems are not for turning in, and should be completed by students after the section is covered during lecture. Solutions can be found on our moodle page.

• (§1.1) - #4, 7, 8, 25, 34, 41, 47, 51, 54, 71, 73, 77
• (§1.2) -7, 12, 18, 20
• (§1.3) - #3, 8, 10, 12, 14, 15, 18, 19, 33, 35, 37, 40, 43, 45
• Appendix D: #29, 30, 35-38, 65, 67 (you will need a calculator for 35 - 38)
• (§1.4): #2, 4, 11-17, 19-22, 25, 30, 32, 37
• (§1.5):# 5, 7, 9, 10, 15, 17, 19, 21-26, 35-41, 51-54, 57, 58
• (§2.1): #5 (§2.2): #4, 7, 8, 11, 15, 17, 23, 24, 25, 31, 33, 34, 35, 42, 45, 47
• (§2.3): #11, 13, 15, 17, 18, 20, 25, 26, 37, 39
• (§2.5): #20, 45, 51, 53, 55
• (§2.6): #8, 15, 16, 21, 24, 27, 31, 32, 35, 47, 49
• (§2.7): #5-10, 13, 14, 31-36
• (§2.8): #4, 5, 6, 12, 16, 17, 18, 21, 23, 25, 27, 29
• (§3.3): #1-19 odd, 23, 24
• (§3.4): #7-47 (odd), 50, 51, 53, 55
• (§3.5): #5, 7, 9, 11, 13, 15, 17, 19, 29-32, 49, 50, 51, 57
• (§3.6): #3, 5, 6, 9, 13, 19, 31, 34, 39, 43, 45
• (§3.7): #7-10 (§3.8): #3, 4, 8-11, 14
• (§3.9): #6, 12, 15, 17, 22, 24, 26, 29, 30, 32, 33, 42, 45
• (§3.10): #6, 23-27
• (§4.1): #2, 3 - 10, 11 - 14, 18, 20, 22, 23, 24, 25, 26, 27, 28, 30, 33, 35, 37, 38, 39, 41, 76, 77
• (§4.2): #6, 8, 9, 11, 13, 17, 19, 22
• (§4.3): #10, 13, 17, 18, 33, 39, 43, 46, 48, 53, 86
• (§4.4): #7, 11, 17, 18, 19, 21, 25, 33, 41, 45, 49, 50, 55, 57, 61, 62, 67
• (§4.5): #9, 10, 27, 35
• (§4.7): #5, 6, 13, 14, 19, 21, 32, 34, 35, 38, 49, 54
• (§4.8): #11,12,13,15,18,20,29,31
• (§4.9): #7,8,10,11,1215,17,18.22,23,28,29,37,38,39,45,49,50,51,53,60,61,64,65,68,69,74,75,76,78,79
• (§5.1): #2,3,7,13,15,16,20,21,22,23,24,32
• (§5.2): #3, 11, 18, 21, 22, 29, 33, 36, 37, 42, 48, 49, 52, 53, 55, 57, 60
• (§5.3): #23, 24, 28, 31, 32, 33, 35, 39, 51, 55, 58
• (§5.4): #3, 6, 9, 12, 14, 15, 16, 18, 27, 31, 37, 43, 53, 54, 64
• (§5.5): #8, 15, 17, 18, 20, 21, 23, 25, 28, 31, 39-42, 44, 46, 48, 54, 58-61, 65, 66, 67, 69, 81, 83
• (§6.1): #2, 8, 11, 12, 13, 14, 15, 17, 18, 20, 27, 33, 56, 57
• (§6.2): #4, 7, 9, 10, 12, 14, 16, 17, 33, 55, 56, 58
• (§6.3): #3, 5, 9, 12, 14, 15, 17, 19, 20
• (§6.4) - Physics and Engineering Students are encouraged to read section and try #1,2,7,8,9,13,15,19,20,21,23,26. No problems from this section will appear on any quizzes
• (§6.5): #1, 2, 4, 5, 7, 9, 10, 13, 14, 17
• (§7.2): #1-8, 12-18, 21-31, 34
• # Math 221 Tutoring Hours

Staring September 4th, teaching Assistants will be available in 145 Altgeld at the following dates/times for walk-in tutoring

• Mon/Tues/Wed/Thurs 5 - 8pm