Calculus B, as one would expect, takes up where Calculus A left off, at the juncture between differentiation and integration. In your previous calculus class you should have learned the definition of the derivative as the limit of the difference quotient, computational rules for derivatives, and various applications of derivatives. You should have had at least a brief introduction to integration, including its connection to differentiation (the Fundamental Theorem of Calculus) and some computational experience with antiderivatives. Your mastery of the material from the previous calculus course will provide the foundation you need to learn what we will study during this course. You should be careful to review previous material for which your memories are stale.
Differentiation and integration are the fundamental operations of calculus: this course will provide a thorough introduction to integration, focusing on theoretical foundations, basic computations and some applications. We will not cover all possible applications of the definite integral, but you should come out of the course knowing that the integral has to do with accumulation of some quantity when we know its rate of change. Armed with that understanding, you'll be able to recognize novel (to you) situations in which the integral might prove useful.
In learning the basics of calculus, you will need to acquire a fairly extensive vocabulary of terms and symbols in order to absorb and apply the ideas and procedures we will study. I have furnished a list of essential terms that I expect you to know and understand as we move through the material. I have a similar list for Calculus A in case you are interested.
You will continue developing expertise with SAGE software, a computer algebra system (CAS) with powerful computational and graphing capabilities. Thoughtful use of any CAS will allow you to pay more attention to the important ideas and applications of the integral.
Calculus Concepts and Contexts, Single Variable, 4e, James Stewart, ISBN-13: 978-0-495-55972-6
A few sources that might be helpful include:
Other Resources
Class will begin promptly at 8:00 (or 1:00) with a moment of silence.
At the beginning of each class, you will have time to ask questions about current and previous assignments. I expect you to read any assigned material prior to coming to class each day; my lectures and our class work will relate to the reading, but will not be a rehash of the material. I strongly encourage you to interrupt the process at any time with a cogent comment or a request for clarification. If you ask no questions, I will have to assume that you understand the material (which often is a very poor assumption). Most days, I will take the majority of class time to lecture on new material, discussing important notions and working example problems. Thursdays normally will be set aside for you to practice skills or to examine new ideas, either with technology or pencil and paper.
You should plan to study 2 to 4 hours between each class meeting. (Including class time, that adds up to 15 to 25 hours per week for this 5 credit course.) I encourage you to adapt the good study practice of spending at least 30 minutes studying calculus shortly after each class, and getting in at least two 30 to 60 minute sessions prior to the next class meeting. This pattern will allow you to take advantage of your short-term memory soon after class. For those who need extra help (and most of you will at various times), drop-in tutoring will be available a number of nights each week. Take advantage of my office hours. In addition, the Mathematics Lounge (Dennis 210) is a nice place to have regular group or individual study sessions. While each of you is responsible for her/his own learning and performance on evaluations, almost all people learn and do mathematics better when they are involved in both independent and group work. Find a 2 or 3 classmates who will be reliable study partners, and help one another.
Remember that things get particularly tight around midterm and finals. Plan to work ahead and avoid the rush!
I will collect assigned homework each Monday. Your cumulative homework grade will count as 1 test. There will be 3 two-hour tests.
Homework - 1/4 || 3 Tests, 1/4 each
I did my undergraduate work at the United States Air Force Academy, far away from Earlham in many ways, surprisingly close in others. There are some experiences from my Academy days that still hold me strongly: one of these is the Cadet Honor Code: "We will not lie, cheat or steal, nor tolerate among us anyone who does." Earlham has an honor code comparable in spirit and in application to the one I learned to value during my undergraduate experience. I have observed over the years that most students experience similar difficulties learning to live under an honor code. Please see my comments on integrity. You also should consider Earlham's statement on academic integrity.
| Monday | Wednesday | Thursday | Friday |
| 11 January Read § 5.1, Areas and Distances Do 5.1: 2, 14, 18, 20 |
12 January Read § 5.2, The Definite Integral Do 5.2: 3, 6, 10, 18, 26, 34, 52 |
13 January Read § 5.3, Evaluating Definite Integrals Do 5.3: 31, 44, 46, 48, 55, 64, 72 |
|
| 16 January - HW 1 Read § 5.4, The Fundamental Theorem of Calculus Do 5.4: 8, 13, 16, 24 |
18 January Read § 5.5, Substitution Do 5.5: 7-35(odd), 41-57(odd), 58, 62, 68 |
19 January Workshop 1 |
20 January Read § 5.6, Integration by Parts Do 5.6: 3-25 (odd), 39,45 |
| 23 January - HW 2 Read § 5.7, Integration Techniques Do |
25 January Read § 5.9, Approximate Integration Do |
26 January Workshop 2 |
27 January Read § 5.10, Improper Integrals Do |
| 30 January - HW 3 Read § 6.1, Areas Do |
1 February Read § 6.1, 6.2, Areas and Volumes Do |
2 February Workshop 3 |
3 February Read § 6.2, Volumes Do |
| 6 February - HW 4 Read § 6.3, Volumes by Cylindrical Shells Do |
8 February Read § 6.4, Arc Length Do |
9 February Workshop 4 |
10 February Read § 6.8, Probability Do |
| 13 February HW 5 Test 1 |
15 February Test 1 |
16 February BREAK |
17 February BREAK |
| 20 February - HW 6 Read § 7.1, Modeling with DE's Do |
22 February Read § 7.2, Direction Fields Do |
23 February Workshop 5 |
24 February Read § 7.2, Euler's Method Do |
| 27 February - HW 7 Read § 7.3, Separable Equations Do |
29 February Read § 7.4, Exponential Growth and Decay Do |
1 March Workshop 6 |
2 March Read § 7.5, The Logistic Equation Do |
| 5 March - HW 8 Read § 7.6, Predator-Prey Do |
7 March Do |
8 March Test 2 |
9 March Test 2 |
| 12 March - BREAK | 14 March - BREAK | 15 March - BREAK | 16 March - BREAK |
| 19 March - HW 9 Read § 8.1, Sequences Do |
21 March Read § 8.2, Series Do |
22 March Workshop 7 |
23 March Read § 8.2, Series Do |
| 26 March - HW 10 Read § 8.3, Integral and Comparison Tests Do |
28 March Read § 8.3, Integral and Comparison Tests Do |
29 March Workshop 8 |
30 March Read § 8.4, Other Convergence Tests Do |
| 2 April - HW 11 Read § 8.4, Other Convergence Tests Do |
4 April Read § 8.4, Other Convergence Tests Do |
5 April Workshop 9 |
6 April Read § 8.5, Power Series Do last drop |
| 9 April - HW 12 Read § 8.5, Power Series Do |
11 April Read § 8.6, Functions as Power Series Do |
12 April Workshop 10 |
13 April Read § 8.6, Functions as Power Series Do |
| 16 April - HW 13 Read § 8.7, Taylor and Maclaurin Series Do |
18 April Read § 8.7, Taylor and Maclaurin Series Do |
19 April Workshop 11 |
20 April Read § 8.7, Taylor and Maclaurin Series Do |
| 23 April - HW 14 Read § 8.8, Applications of Taylor Polynomials Do |
25 April Read § 8.8, Applications of Taylor Polynomials Do |
26 April Workshop 12 |
27 April Test 3 last class |
| 30 April | 2 May - 4:30 Test 3 |
3 May | 4 May |