| Section | Problems to do | Submit | Due date | Comments |
|---|---|---|---|---|
| 1.1 | 1,3,7,9,11,13,15,21,23,33,39,49,51,55,57 | 26,62 | Friday, January 23 | See note below on Problem 62. |
| 1.2 | 1,3,5,9,15,17,19,27,31,33,35,41,63 | 8,18 | Monday, January 26 | |
| 1.3 | 1,5,9,13,15,17,31,41,51,61,63 | 42,52 | Tuesday, January 27 | |
| 1.4 | 1,3,5,9,11,13,15,21,25,29,33 | 24,36 | Thursday, January 29 | |
| 1.5 | 1,3,5,7,9,15,25,27,29,31,37,39,43,51,53 | 10,40 | Friday, January 30 | |
| Exploring limits | 1-16 | None | ||
| 2.2 | 1,5,9,11,17,57 | None | ||
| 2.2 | 25,27,29,33,35,45 | 34,44 | Thursday, February 5 | I initially had #64 rather than #44. Note that #64 is part of the next submitted set. |
| 2.1 | 1,7,19 | None | ||
| 2.2 | 61,62,65 | 64,66 | Friday, February 6 | |
| 2.2 | 81,82,87 | None | ||
| 2.4 | 23,25,29,33 | None | ||
| 2.4 | 1,3,5,7,9,17,37,41,45,47,51,53,55,57,83 | None | ||
| 2.5 | 5,17,21,23,41,61 | None | ||
| 2.6 | 5,7,9,11,13,19,23,27,35,39,41 | 16,36 | Tuesday, February 17 | |
| 2.7 | 9,15,21,27,29,33 | 8,30 | Thursday, February 19 | |
| 3.1 | 1,3,5,13,27-30,31,39,41 | None | ||
| 3.1 | 7,19,35 | 18,22 | Monday, February 23 | |
| 3.2 | 1-11 odd, 17-35 odd, 47,51,63 | 12,24 | Thursday, February 26 | |
| 3.4 | 1,3,7,9,11,13,15,17,21,25,31,33,37 | 24,34 | Friday, February 27 | |
| 3.3 | 3,9,13,15,21,25,27 | 12,26 | Monday, March 2 | |
| 3.5 | 1,3,5,7,9,13,17,19,23,25,29,31,33,35,37,39,41,47,61,65 | None | ||
| 3.6 | 1,3,9,11,17,27,41,43,53 | 14,44 | Tuesday, March 10 | |
| 3.7 | 11,13,15,21,25,27,29,57,59,63 | 30 | Thursday, March 12 | |
| 3.8 | 21,23,33,41 | 34 | Thursday, March 12 | |
| 3.7 | 1,5,9,67,71,75,81 | None | ||
| 3.9 | 3,13,15,17,23,25,31 | 18,20 | Thursday, March 26 | |
| 3.10 | 5,6,11,15,17 | 8 | Friday, March 27 | |
| Euler's method | 1,2,3 | 4 | Friday, March 27 | |
| 3.10 | 25,33,47,49,54,61 | None | ||
| 4.1 | 1-6,7,9,11-14,23,31,33,41,47,51,53 | None | Also do Problem 3 from the class handout. | |
| 4.3 | 3,7,11,17,21,23,25,47 | None | ||
| 4.4 | 1,3,5,65,69,77 | None | ||
| 4.4 | 17,22,25,41 | None | Also finish off the example from the class handout. | |
| 4.5 | 7,9,11,15,19,25,29,32 | None | For #25, don't spend too much time on part (a). You can do parts (b) and (c) using the result given in (a). | |
| 4.2 | 1,5,7,15,19,45,48 | None | Also do #3 from the MVT handout. | |
| 4.6 | 1,15,19,21,23,25,43 | None | ||
| 4.6 | 38,40,45,47,49,51,61,63 | None | ||
| 4.8 | 1-19 odd,23,29,31,35,43,51,61,81,119,121 | None | ||
| 5.1 | 1,3,5,7,9,13,19 | None | ||
| 5.2 | 1-13 odd,31,37 | None | ||
| 5.3 | 9,11,13,17,19,27,33 | None | ||
| 5.4 | 1,3,5,7,15,17,19,21,27,29,33,53,55,57,69 | None | Last homework assignment! |
For Tuesday May 12, I will be around my office from 9:00 to 10:30 in the morning and from 1:30 to 4:00 in the afternoon.
You are welcome to come find me whenever I'm in my office. If you don't want to risk climbing the stairs to find I'm gone, e-mail or call (3567) to set up a specific time.
For Monday May 11, I will be busy with exams and other commitments until 2:30. I will be available from 2:30 to 3:30.
For Tuesday May 12, my tentative plan is to be available most of the day between 9:00 am and 4:00 pm. I currently have commitments from 10:30 to 11:00 and noon to 1:30. I will post an update on Tuesday morning.
You are welcome to come find me whenever I'm in my office. If you don't want to risk climbing the stairs to find I'm gone, e-mail or call (3567) to set up a specific time.
For Friday May 8, I will be around from 9:00 to 11:30 in the morning and from 2:30 to 3:30 in the afternoon.
For Monday May 11, I will be giving exams at 8 and noon. My tentative plan is to be available from 2:30 to 3:30 in the afternoon.
You are welcome to come find me whenever I'm in my office. If you don't want to risk climbing the stairs to find I'm gone, e-mail or call (3567) to set up a specific time.
I've put together a master list of objectives for the course. The objectives that are most relevant to Part A of the final exam are highlighted.
For Thursday May 7, I plan to be around my office from 10:30 to noon in the morning and from 1:00 to at least 3:30 in the afternoon.
For Friday May 8, my tentative plan is to be around from 10:00 to 11:30 in the morning and from 2:30 to 4:00 in the afternoon. I'll post an update on Friday morning.
You are welcome to come find me whenever I'm in my office. If you don't want to risk climbing the stairs to find I'm gone, e-mail or call (3567) to set up a specific time.
I've put together a master list of objectives for the course. The objectives that are most relevant to Part A of the final exam are highlighted.
For Wednesday May 6, I plan to be around my office from 10:00 to 11:30 in the morning and from 2:30 to 4:00 in the afternoon. After 4:30, I'll be at the department's end-of-year picnic in the Harned courtyard (or inside Harned if it's raining). All are welcome.
For Thursday May 7, my tentative plan is to be around from 10:00 to noon in the morning and from 1:00 to at least 3:30 in the afternoon. I'll post an update on Thursday morning.
You are welcome to come find me whenever I'm in my office. If you don't want to risk climbing the stairs to find I'm gone, e-mail or call (3567) to set up a specific time.
Exam #5 will be tomorrow (Tuesday May 5) from 9:30 to 10:50 am. It will cover material from Section 4.8 and 5.1-5.4. (You can use the "equal-size subintervals" definition of definite integral from class rather than the more general definition from the text. The First Fundamental Theorem of Calculus will not be included.) For this exam, a well-prepared student should be able to
I have office hour from 2:30 to 3:30 this afternoon. I will also have an evening office hour from 7:30 to 8:30 pm in TH 374.
After much hard work to understand how definite integral is defined and how one can be evaluated directly from the definition, we arrived today at the Second Fundamental Theorem of Calculus (FTC2). FTC2 is a powerful tool for evaluating definite integrals.
You may be wondering "What happened to the First Fundamental Theorem of Calculus (FTC1)?" There is such a thing but we have gone directly for FTC2 because FTC2 is of greater utility. FTC1 is also useful and informative but of lower priority for our purposes. I'll give you a quick look at FTC1 on Monday but not hold you accountable for it on Tuesday's exam.
In the text's logical development, FTC1 comes first because it is easier to prove. A proof of FTC2 is then based on using FTC1. So FTC1 comes first in this logical progression. We were able to skip over FTC1 because we have not give a proof of FTC2. We have made FTC2 seem reasonable by looking at relations between flow rate and accumulation. FTC2 is both reasonable (as we've seen) and true (which we have not established in this course).
In class, we went over some logistical details on the last week of classes and the final as listed on this handout.
Exam #5 will be on Tuesday May 5 from 9:30 to 10:50 am. It will cover material from Section 4.8 and 5.1-5.4. (You can use the "equal-size subintervals" definition of definite integral from class rather than the more general definition from the text. The First Fundamental Theorem of Calculus will not be included.) For this exam, a well-prepared student should be able to
Our main goals for class today were to reinforce the definition of definite integral and to look at some properties of definite integrals. The handout on defining definite integral gives a version you will be held accountable for. This is less general than the definition stated in the text.
I've assigned problems from Section 5.3 that involve using various properties of definite integrals.
Exam #5 will be Tuesday, May 5.
A lot happened in class today. The basic plan was to
I have assigned two additional problems from Section 5.2. The last of these (Problem 37) asks you to do a calculation similar to what we did in class today.
In class, we looked at some plots from Friday's examples. We then began working toward more a more efficient way of representing the sums that we are building to estimate accumulation given flow rate. Our goal is to build an expression for the sum in which the number of terms is a variable. We will then be in position to think about the limit as the number of terms increases without bound.
I've assigned problems from Section 5.1. These involve estimating accumulation or area using sums of rectangle areas. I've also assigned problems from Section 5.2 to give you practice in using the summation notation we introduced in class today. The sums in these problems are not necessarily sums of rectangle areas.
In class, we used this handout to begin exploring the last major topic for the course. The motivation for this topic is this general problem: Given the rate of change (with respect to time) in some quantity, compute how much of the quantity accumulates over a given interval interval of time. In class, we looked at how to estimate an accumulation given limited information about the rate of change. Next week, we'll explore how to compute the exact accumulation given complete information about the rate of change.
I have not assigned additional problems so you should continue working on the assigned problems from Section 4.8. Your goal should be to become proficient in finding basic antiderivatives.
In class, we discusses antiderivatives and antidifferentiation by working through the examples on this handout. I've assigned problems from Section 4.8. I've assigned a lot of problems to give you practice in the skill of finding antiderivatives.
Note that we will not be covering the material in Section 4.7 of the text.
Exam #5 will be Tuesday, May 5.
Exam #4 will be tomorrow from 9:30 to 10:50 am. The exam will cover material from Sections 4.1 through 4.6. For this exam, a well-prepared student should be able to
I will be available in my office this afternoon from 2:30 to 4:30. I'll also have an evening office hour from 7:30-8:30 pm in TH 374.
In class, we looked at some extensions of and variations on L'Hopital's Rule. L'Hopital's Rule itself applies to indeterminate forms 0/0 and ∞/∞. We can use algebra or the "exp-ln" idea to manipulate other interminate forms into one of these and then apply L'Hopital's rule.
Exam #4 will be on Tuesday April 21 from 9:30 to 10:50 am. The exam will cover material from Sections 4.1 through 4.6. For this exam, a well-prepared student should be able to
Today we looked at using L'Hopital's Rule to evaluate limits that have the indeterminate form 0/0. Tomorrow, we'll look at some variations on this basic use of L'Hopital's Rule.
Exam #4 will be on Tuesday April 21 from 9:30 to 10:50 am.
In class, we discussed the Mean Value Theorem which means we've gone back to Section 4.2 in the text. There you will see reference to Rolle's Theorem. Rolle's Theorem is a special case of the MVT in which the function f is zero at both endpoints. In this case, the secant line through the endpoints has slope zero so the theorem's conclusion guarantees that there is at least one input for which the corresponding tangent line has slope zero.
Exam #4 will be on Tuesday April 21 from 9:30 to 10:50 am.
In class today, we looked at problems from Section 4.5. For most of these, we started the problem but did not finish. You should work on finishing these and any other problems from the Section 4.5 assignment.
We also took a quick look at the Greek alphabet for reference when you encounter Greek letters used as variable or parameter names.
Words of the day: fisticuffs, kerfuffle, brouhaha, hootenanny
I've assigned problems from Section 4.5. Some of these are more challenging. For problems that involve some geometry, start with a relevant sketch. Identity relevant variables and name them. You'll then be in better position to build the relevant relation(s) among the variables. Also identify the relevant domain for any independent variable.
In class, we worked on this example of curve sketching using calculus techniques. In this type of problem, our goal is to produce a sketch of the given function's graph that shows all essential features (including values or limits at endpoints, zeros, local extremes, and inflection points). You can use a graphing calculator or other technology to plot a function graph but to do so, you must pick a specific window. Calculus techniques are useful in helping ensure you use a window that shows all essential features. In practice, most functions you encounter in applications have parameters in addition to the dependent and independent variables. Calculus techniques are a necessity for determining the essential features of a function that includes parameters.
I've assigned a few more problems from Section 4.4. You should also finish off the problem from class today.
Project #3 is due tomorrow.
I've assigned a few problems from Section 4.4 dealing with concavity and the second derivative. I'll assign more on Thursday after we've talked about putting everything together to understand all essential features on the graph of a function.
Project #3 is due on Friday.
We're skipping over the main idea of Section 4.2 for now, namely the Mean Value Theorem. You'll see a brief reference to the Mean Value Theorem in Section 4.3; you can ignore this reference for now.
Project #3 is due on Friday.
In class, we worked on the problems from this handout. The first of these is an example of applied optimization. We'll do more of this type of problem later when we hit Section 4.5. Another theme in these problems is working with functions that include parameters. Many applications of mathematics (in biology, chemistry, economics, physics, business,...) are phrased with parameters rather than specific numerical values so it is good to become comfortable in working around parameters.
Project #3 is due Friday, April 10.
In class, we began looking at the problem of locating extreme values (or extrema) for a function. The text uses language that differs from what I'll use in class. What the text calls an absolute minimum or maximum, I will call a global minumum or maximum.
Exam #3 will be on Tuesday, March 31 from 9:30-10:50 am. It will cover material from Sections 3.6-3.10 (including Euler's method). For this exam, a well-prepared student should be able to
Today, I'll be available for office hour from 2:30-3:30. You should also be able to find me from 3:30-4:00 and 4:30-5:00 but not from 4:00-4:30.
This evening, I'll have an office hour from 7:30-8:30 in TH 374. Depending on how many of you show up, I'll either answer questions individually or we'll get small groups working together on problems at the boards. Note: If the exterior doors to Thompson are locked, your card should work in the card reader. If you have problems with this, call Security.
In class, we looked at examples of how to use differentials in a variety of ways, including getting a derivative from an implicit relation and for organizing the calculations in Euler's method. We can also use differentials in related rates problems. The idea there is
You can choose how much you want to use the differentials approach in working with implicit differentiation, related rates, and Euler's method. You might want to redo some problems from Sections 3.6-3.10 in order to compare the derivative approach with the differentials approach. One significant advantage of the differentials approach is that the chain rule is done for you automatically whenever it is relevant.
Exam #3 will be on Tuesday, March 31 from 9:30-10:50 am. It will cover material from Sections 3.6-3.10 (including Euler's method). For this exam, a well-prepared student should be able to
In class, we looked at differentials. Here's one way to think about differentials: If two quantities, say p and q, are related to each other, then small changes in one quantity are related to small changes in the other quantity. For small enough changes, the relationship is essentially linear. We use differentials to express this linear relationship. So the relationship between the differentials dp and dq is linear. We might express this relationship as dp=a dq or as dq=b dp or as A dp + B dq=0. For example, from the relation y=x3 we get the linear relation dy=3x2 dy between dx and dy. As another example, for the relation x2+y2=1, we get the linear relation 2x dx+ 2y dy=0 between dx and dy. For x≠0, we can rewrite this as dx=-(y/x) dy. For y≠0, we can rewrite this as dy=-(x/y) dx.
I've assigned a few problems from Section 3.10 to give you some experience in working with and thinking about differentials. Since we are too close to an exam for me to evaluate any more problems, there are none to submit.
Exam #3 will be next week on Tuesday, March 31. It will cover material from the last half of Chapter 3 and possibly a bit of Chapter 4.
In class, we discussed one use of linearization that is not discussed in the text, namely Euler's method for approximating a solution for a differential equation. Euler's method involves repeatedly approximating using linearization. We looked at one example in class from this handout.
I've assigned problems from Section 3.10 and some additional problems on Euler's method on a handout.
Exam #3 will be next week on Tuesday, March 31. It will cover material from the last half of Chapter 3 and possibly a bit of Chapter 4.
Note that two problems from Section 3.9 are due Thursday.
Exam #3 will be next week on either Tuesday or Thursday. I'll make a decision before class tomorrow.
In class, we worked on the second example from this handout. I've now assigned two problems to be submitted from Section 3.9. These will be due Thursday, March 26.
In class, we looked at two examples of related rates problems including the one on this handout. I've assigned problems from Section 3.9 but haven't yet picked ones to submit. I'll do this soon and post an update. These will be due sometime after spring break.
I've assigned a few additional problems from Section 3.7 that relate to what we discussed in class today.
In class today, we looked at derivatives of inverse functions. Two things to take away from our examples are
In class, we looked at implicit differentiation using the example on this handout. I've assigned problems from Section 3.6 on this idea.
Project #2 will be due on Friday, February 13. The project involves understanding part of the article "Reduction of HIV Concentration during Acute Infection: Independence from a Specific Immune Response", Andrew N. Phillips, Science, New Series, Vol. 271, No. 5248 (Jan. 26, 1996), pp. 497-499. (Note: This link is to the JSTOR database to which our library subscribes. If you are on the campus network, you should be able to access the article online.)
Exam #2 will be Thursday from 9:30 to 10:50 am. It will cover material from Sections 2.6, 2.7, and 3.1-3.5 from the text except for the material on parametric equations in the last two subsections of Section 3.5. For Exam #2, a well-prepared student should be able to
If you are looking for more practice, you can turn to the Practice Exercises at the end of Chapter 3. Not all of these are relevant to what we have done so far. Here's a list of odd-numbered problems that should be relevant among the Chapter 3 Practice Exercises: #1-43 odd, 85,87,89,93,95,97,99,101,107,121,123,125,126,135
Today (Tuesday, I have office hour from 1:30 to 2:30. I have an appointment from 2:30 to 3:30. I am currently available from 3:00 until about 5:00.
For Wednesday, I am currently available from 10:00 until about noon, from 2:15 to 3:30, and from 4:30 until at least 5:00.
Exam #2 will be Thursday from 9:30 to 10:50 am. It will cover material from Sections 2.6, 2.7, and 3.1-3.5 from the text. I'll post a list of specific objectives tomorrow.
In class, we motivated the chain rule using an example in context with careful attention to units.
You'll need to get lots of practice with the chain rule in order to become accurate and efficient. I've assigned problems from Section 3.5 to help you in this.
Exam #2 will be Thursday, March 5 from 9:30 to 10:50 am. It will cover material from Sections 2.6, 2.7, and 3.1-3.5 from the text.
Exam #2 will be Thursday, March 5 from 9:30 to 10:50 am.
Problems to submit from Section 3.2 are due Thursday. Problems to submit from Section 3.4 are due Friday. We can address more questions on Section 3.4 problems in class on Thursday.
Exam #2 will be Thursday, March 5 from 9:30 to 10:50 am.
I've assigned problems from Section 3.4. These add trignometric functions to our mix. You should be working to become accurate and efficient in computing derivatives.
We're skipping over Section 3.3 for now. We'll come back to this soon.
Project #1 is due tomorrow.
Today in class, we began developing the results and rules that will allow us to compute derivatives efficiently. All of these results and rules come from the definition of derivative as the limit of a difference quotient. Today, we used graphs to motivate most of the rules and results. Next week, we'll return to give arguments based on limits of difference quotients. For now, focus on learning to use the results and rules correctly and efficiently. This takes practice so I have assigned a lot of problems from Sections 3.2.
A few of the problems I've assigned ask you to compute a second derivative. The idea is easy. Start with a function f. Compute the derivative to get a new function f′. Now compute the derivative of f′ to get yet another function which we denote f″ (that is, f with a double prime). We call f&Prime the second derivative of f. For example, if we start with f(x)=x3, we differentiate to get the first derivative f′(x)=3x2 and then differentiate again to get the second derivative f″(x)=3(2x)=6x.
In class, we deduced the derivatives of the sine and cosine functions. In the text, these are covered in Section 3.4. I'll assign problems on this next week. Next week, we'll also add one more rule to our collection. This rule will allow us to differentiate a composition of two functions. The rule will allows us to differentiate a function such as f(x)=cos(x2).
Project #1 is due on Tuesday.
In class, we looked at two commonly used notations for derivative. You are free to choose which to use in your own work. You'll need to be comfortable enough with both to read either in the work of others.
I've assigned a few more problems from Section 3.1 including two problems to submit.
In class, I mentioned that I might not be available for office hours today. As it turns, I will be available for office hour (1:30 to 2:30) and a bit beyond. I will not be available after 3:30 today.
In class, I distributed an overview of projects and the specific assignment for Project #1. This project is due next Tuesday.
I've assigned problems from Section 3.1. After class on Thursday, I'll assign a few more, including some to be submitted.
In class, we looked at how to compute the slope of a tangent line using the limit of a difference quotient. Some of the problems I've assigned will ask you to find the equation of a tangent line. You'll need to first compute the slope, as we did in class, and then use it together with the coordinates of a point on the tangent line in the point-slope form.
Depending on the context, the limit of a difference quotient might be interpreted as a rate of change.
In class today, we explored the idea of continuity by working through this handout. Your first look at continuity in high school might have been based on a graphical viewpoint so that continuity is phrased as the graph of a function "having no holes" or being able to "draw the graph without lifting your pencil". With the idea of limits in hand, we can now phrase a definition of limit that does not require knowing what the graph looks like. This definition of limit is much more useful in the big picture.
I've assigned problems from Section 2.6. You'll need to read Section 2.6 to understand a few ideas that we did not discuss explicitly in class.
The last problem on the handout concerned finding a function that is defined for all x so that the limit of the function at a does not exist for each a. In other words, this function is defined for all x and is discontinuous for all x. The example we arrived at is the function that has output 1 if x is rational and output -1 if x is irrational. Drawing a graph of this function is difficult (or impossible). It's true that each point of the graph is either on the line y=1 or the line y=-1. But, the fact that there is an irrational value of x between any two rational values of x (and vice versa) makes the graph jump between y=1 and y=-1 in a pretty wild way.
Exam #1 will be on Thursday from 9:30 to 10:50 am. It will cover material from Sections 1.1 to 1.6, 2.1, 2.2, 2.4, and 2.5. In Sections 2.4 and 2.5, you can ignore references to the precise definition of limit that is introduced in Section 2.3. (We'll discuss this later in the semester.) For Exam #1, a well-prepared student should be able to
* As an example of "build a function that models a given real-world situation", think about the cost function you came up with for Problem 62 in Section 1.1.
Here's my standard advice on how to prepare for an exam:
I will be available this afternoon (Tuesday) for office hour from 1:30 to 3:00 and for appointments from 4:00 to 5:00. On Wednesday, I'm available for appointments from 10:00 to 11:30 and after 2:00 in the afternoon. E-mail or call (3567) if you want to set up a time to meet.
Exam #1 will be on Thursday from 9:30 to 10:50 am. It will cover material from Sections 1.1 to 1.6, 2.1, 2.2, 2.4, and 2.5. In Sections 2.4 and 2.5, you can ignore references to the precise definition of limit that is introduced in Section 2.3. (We'll discuss this later in the semester.) By tomorrow afternoon, I'll post a list of specific objectives for the exam.
In class, we looked at one-sided limits and limits at infinity. Each of these is a variation of the basic idea of limit. Limits at infinity can tell us about horizontal asymptotes in the graph of a function.
In class, we worked through a proof of the fact that the limit of (sinx)/x at x=0 is 1. This proof uses the Sandwich Theorem. In the text, the Sandwich Theorem appears at the end of Section 2.2. The text's version of the proof we looked at is in Section 2.4 in the subsection "Limits Involving sin(θ)/θ" on pages 88-89. So, you should include that subsection in your reading about the Sandwich Theorem. I've assigned a few problems from Section 2.2 that deal with the Sandwich Theorem. I've also assigned a few problems from Section 2.4 that are related to the limit of (sinx)/x at x=0.
We are going to skip over the material in Section 2.3 for now. We'll come back to this later in the semester. The idea in Section 2.3 is to give a precise definition of the limit of f(x) at x=0 is L. The precise definition takes some time to understand so we'll continue to work with a somewhat vague definition for now. As you read Sections 2.4 and beyond, you will occasionally see references to this precise definition of limit. You can ignore these for now.
Exam #1 will be Thursday, February 12. I would like to see if we can use the 80-minute period from 9:30-10:50 for the exam. Note that class normally ends at 10:20 on Thursdays. I've sent out an email asking you to reply on whether or not your schedule allows you to stay for the extra 30 minutes. If you haven't already replied, please do so as soon as possible.
Exam #1 will be Thursday, February 12. I would like to see if we can use the 80-minute period from 9:30-10:50 for the exam. Note that class normally ends at 10:20 on Thursdays. Please check you schedule to see if you are available for the extra 30 minutes on this date.
I've assigned additional problems from Section 2.2 including two to be submitted on Thursday.
Exam #1 will be Thursday, February 12. I would like to see if we can use the 80-minute period from 9:30-10:50 for the exam. Note that class normally ends at 10:20 on Thursdays. Please check you schedule to see if you are available for the extra 30 minutes on this date.
In class today, we began moving from the somewhat tedious idea of using input/output tables to make a conjecture about a limit toward more efficient methods of evaluating limits. So far, we have a pretty limited (no pun intended) set of results and rules that allow us to evaluate "boring" limits. Next week, we'll develop some strategies that allow us to evaluate more interesting limits (typically those that involve division by 0 for x=a itself).
I've assigned a few problems from Section 2.2. I'll assign more next week, including a few to submit.
Today we made the transition from review to thinking about our first calculus topic, namely limits. Before class tomorrow, you should look at as many of the problems on the "exploring limits" handout as you can. Our initial way of exploring limits by looking at lists of inputs and outputs is a bit tedious. In the next week, we'll develop more efficient ways of analyzing limits.
Feel free to come ask me whenever you have questions on class, reading, or homework. You can also take advantage of free tutoring available from two sources:
This animation nicely illustrates the connection between the unit circle definition of sinx and the graph of sinx.
By the end of the week, we will be done with our review of background material and ready to begin looking at calculus ideas.
We'll continue our review of background material with a look at exponential functions. I've assigned problems from Section 1.4 on exponential functions. Some of this involve applications in which some quantity changes exponentially (growth or decay) in time. Come talk with me if you are not familiar with this type of application.
In class, we used this worksheet to get a first look at the idea of limits. Limits are a fundamental idea in calculus. After we finish our review, we'll turn our full attention to limits.
Our next topic for review is trigonometric functions. You should read Section 1.3 and work on the assigned problems from that section. If you want more fundamentals on trigonometry, you might try working through the exercises on this handout.
We'll continue reviewing prerequisite ideas in class primarily by addressing questions you bring on reading and homework problems. As you read the text and work on problems, make note of any unfamiliar language and terminology. Ask questions about these by e-mail, during class, or in person outside of class.
As I mentioned in class, the material in Chapter 1 is mostly review of topics from high school mathematics. Everyone has a different background so there may be some topics with which you are not familiar or comfortable. We'll spend most of our class sessions this week addressing the questions you have on assigned homework. If you are feeling unsure about your mathematical background, come talk with me in the next day or two. You might also consider buying the book Just-In-Time Algebra and Trigonometry. This should be available in the bookstore.
In class on Thursday, we'll look at questions you have on assigned problems from Section 1.1. For Problem 62 (to be submitted Friday), replace part (b) with "Use a table of values or a graph to estimate the distance x that gives the lowest cost C."
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You can look at exams from last time I taught Math 180. You can use these to get some idea of how I write exams. Don't assume I am going to write our exams by just making small changes to the old exams. You can use this old exam to prepare for our exam in whatever way you want. I will not provide solutions for the old exam problems.