Calculus I
Sample Syllabus
Instructor: Sr. Barbara Reynolds, Ph.D., Cardinal Stritch University
[Editor's note: This detailed syllabus is a sample only, not a model for every possible course that can be taught from this text. It includes many features of Sr. Barbara's own teaching philosophy and practice that are consistent with the spirit of the text but not a requirement from teaching a successful course. Please feel free to pick and choose (and modify) elements that you think will work for you. In particular, several items marked in red must be replaced with your local information.]
(Substitute your own catalog description.) Calculus is a transition course to upper-division mathematics and computer science courses. Students will extend their experience with functions as they study the fundamental concepts of calculus: limiting behaviors, difference quotients and the derivative, Riemann sums and the definite integral, antiderivatives and indefinite integrals, and the Fundamental Theorem of Calculus. Students review and extend their knowledge of trigonometry and basic analytic geometry. Important objectives of the calculus sequence are to develop and strengthen the students’ problem-solving skills and to teach them to read, write, speak, and think in the language of mathematics. In particular, students learn how to apply the tools of calculus to a variety of problem situations.
When you turn in an assignment, please do not give me pages which have been torn out of a spiral-bound notebook (unless you first trim the edges with scissors).
Arithmetic and algebra make use of three basic computational tools and their inverses (addition and subtraction, multiplication and division, and exponentiation and taking roots). Calculus provides two fundamentally new computational strategies – differentiation and integration. The focus of this semester is on differential calculus. We will cover material in Chapters 1 through 5 of the text. In this course, we will focus on definitions and conceptual development of the important ideas of calculus.
One goal this course is to engage students in thinking deeply about some problems which can be studied using strategies of calculus. The authors of our text have very deliberately chosen to include topics that allow us to investigate important and interesting problems. For this reason, the order of topics in this course is a bit different than the order of topics in other calculus courses; in particular, if you have taken calculus at another school, you may notice that we cover some topics in this first semester that are often covered in a second or third semester of calculus.
Our goal this semester is to cover Chapters 1 through 5. Calculus II will continue from where this course ends.
Chapter 1: Relationships
The central question of this introductory chapter – which contains no calculus – is “What is a function?” The objective is to help students separate this concept from other relationships between varying quantities, and especially to separate the idea of function from such ideas as formula and equation. The concept of function is the basic building block of mathematics. A deep understanding of function will facilitate your future study of mathematics and computer science. Throughout this course, we will be working with multiple representations of functions. The authors of our text present functions verbally, numerically, and visually as well as algebraically.
Chapter 2: Models of Growth: Rates of Change
In this chapter, we will investigate some basic reasons for studying calculus. In particular we will investigate problem situations which can be modeled using differential equations. Topics introduced in this chapter include difference quotients, derivatives, slope fields, initial value problems whose solutions are functions and families of functions. The primary example of this chapter is natural population growth, the simplest ODE (ordinary differential equation) to solve. This example provides an immediate reason for moving beyond polynomials to other families of functions (e.g., to exponential and logarithmic functions). We will conclude this chapter by using tools of calculus to analyze the spread of the AIDS virus.
Chapter 3: Initial Value Problems
This short chapter builds on Chapter 2, introducing Newton’s Law of Cooling (exponential decay) to solve a murder mystery, then studying falling objects without air resistance (polynomial solutions).
Chapter 4: Differential Calculus and Its Uses
This chapter is the heart of first-semester calculus, consolidating what has been learned about derivatives to take up problems involving optimization, concavity, Newton’s Method (as an exercise in local linearity), and the basic formulas for differentiation. The product rule is introduced to study the growth rate of energy consumption, the chain rule to study reflection and refraction, and implicit differentiation to calculate derivatives of logarithmic functions and general powers. The process of zooming in on a graph is related to differentials and Leibniz notation. The chapter concludes with an interesting application of calculus to a problem in air-traffic control.
Chapter 5: Modeling with Differential Equations
This chapter builds on the problems introduced in Chapter 3, introducing air resistance to problems of falling bodies (e.g., raindrops and skydivers). The authors introduce problems of periodic motion, which are modeled using trigonometric functions and their derivatives.
This chapter also provides a summary of techniques of differentiation.
A primary objective of a course in calculus is to provide a bridge for the student from high-school or lower-division mathematics courses to upper-division mathematics. The student will be challenged to grow in mathematical maturity, and to develop and strengthen problem-solving skills. Beyond the content of individual courses, the major in mathematics is designed to prepare students for the 21st century by helping students to become problem solvers, effective communicators, users of appropriate technology, and team players. In this course, students will be engaged in a variety of activities which will help them to move toward achieving these goals. The text I have chosen for this calculus course supports these goals. By the end of this course, students should be able to
In a calculus course taught using traditional pedagogy, students learn to use calculus to formulate problems, to solve problems, and to communicate their solutions to others. In addition to these skills, students who successfully complete this course will learn to
- Understand concepts rather than merely mimic techniques
- Demonstrate understanding by explaining in written or oral form the meanings and important applications of concepts
- Construct and analyze mathematical models of real-world phenomena, including both discrete and continuous models
- Distinguish between discrete and continuous models, and make judgments about the appropriateness of the choice for a given problem
- Understand the relationship between a process and the corresponding inverse process
- Select between formal and approximate methods for solution of a problem, and make judgments about the appropriateness of the choice
- Select the proper tool or tools for the task at hand
- Use mathematics to structure their understanding of the world around them, and investigate interesting questions in this world
- Use technology as an integral part of the process of formulation and solution of problems, and communication of their solutions to others
- Work together productively, and learn cooperatively
To be successful in this course, a student should have a strong background in algebra and some familiarity with trigonometry. Ordinarily this means high school trigonometry and advanced algebra, or a course in College Algebra and Trigonometry. Quiz #1 at the end of the first week of class will help the instructor identify any student whose background in algebra and trigonometry is weak.
It is not necessary to know anything about computers at the beginning of this course. We will cover computer skills as needed as we progress through the course. Please see the instructor if you have any questions about your preparation for this course.
Much of the work of this course will require students to work in cooperative learning groups. For mathematical problem solving, group sizes of about three students seem to work best. Students will be expected to work in groups in the lab on in-class activities. Students are encouraged to work together on homework problems. While some students enjoy group work more than others, working well in a group is an important skill for life beyond the mathematics classroom. Many of our graduates tell us that skills developed while working in cooperative learning groups in our classes have been very helpful in the workplace.
Problem-solving is a social activity. One of the primary objectives of any mathematics course is to help students learn to think about problems mathematically and to solve problems independently. Working in small groups, doing the lab activities, and talking about problems with other students are all strategies to assist the student in achieving these objectives. Students will need to work regularly in the computer lab on homework assignments, and are strongly encouraged to meet with their group at least twice each week in addition to class time.
Calculators and computers are tools for doing mathematics. In this course, the computer will be used primarily as a learning tool, giving students the opportunity to investigate a concept by solving many more problems than is practical when all the calculations are done by hand. Visualization is an important problem-solving tool. Computer graphing software has made visualization more accessible to undergraduates than it has been in the past. Students will be using a computer algebra system (Maple) to explore important concepts of calculus.
Throughout the semester, students will be given opportunities to use electronic communication tools (such as email and a graphical web browser). Class assignments will be regularly posted on Educator (our campus course management system). Students will be expected to get course assignments and materials from the web, and to communicate with the instructor and each other using email. The instructor will send a message via Educator whenever a new assignment has been posted. Homework hints may also be sent by email between class sessions. Students are expected to check their Educator email regularly, or to set this email account to forward messages to their preferred e-address.
In this course students will often be asked to experiment with an idea before it has been discussed formally in class. This teaching strategy provides students with multiple opportunities to think critically about problems, and to learn problem solving by solving problems. Research into how people learn has shown that students who learn mathematics using these methods have both deeper understanding and longer retention of what they have studied, and are better able to think about new problems than those taught using traditional methods. If this is your first course in which you are being challenged to work this way, it may take several weeks to adjust to these methods. The payoff in increased understanding is well worth the investment of time and energy it takes to adapt to this style of learning. Your instructor is committed to helping you to make this adjustment.
The overall objective is to learn mathematics and to develop effective problem-solving and critical-thinking strategies. Even though students are expected to use the computer regularly in their study, there are certain calculations which they will be expected to learn to do by hand. These will be clearly identified as we go through the course.
Ordinarily, in-class tests will focus on mathematical concepts; students may use a scientific calculator during in-class tests. On benchmark tests, which focus on more routine computations, students will not be allowed to use a calculator.
Regular attendance, participation, homework, lab activities, quizzes: 10%
You are expected to come to class regularly, and to be on time. The material in this course has a well-deserved reputation for being difficult. If you miss a class, you are expected to find out what happened. The computer lab activities are designed to help you learn the mathematical concepts. You are expected to work with the members in your group, and to seriously attempt the lab activities. You will need to meet with your group outside of class, probably once or twice each week. Sometimes you will be asked to turn in individual work; other times you will be asked to turn in your group's response to some questions.
Some homework exercises will be assigned using WeBWorK, an on-line homework management system. WeBWorK assignments will be announced almost every week and ordinarily will be open for about two weeks. You may work together on these WeBWorK assignments, but each student will have their own problems. To get credit for doing the WeBWorK problems, you will have to submit your solutions into your own WeBWorK space. When you submit your solutions online, you will receive immediate feedback about whether your solutions are correct. During the two-week window, you may submit your solutions an unlimited number of times. Your score on these WeBWorK assignments will be included in your participation/homework grade.
At the end of each class period, I will ask you to fill out a Class Participation Form. I use these forms to check attendance, respond to your self evaluation, and give you a score for class participation. There may be occasional (unannounced) quizzes which you will be able to do in your small groups; it is not possible to make-up a quiz.
If you must miss a class for any reason (excused or unexcused absence), your participation score for that day will be recorded as 0. Missing more than two class periods without submitting written work to make up the absence will bring down your grade for this course. If you wish to make up an absence, you may turn in written evidence that you have done some work to make up missed lab/class activities. This make-up work must be turned in within two class periods of the missed class. In general, such make-up work will earn 7 points to replace the 0 for missing class.
Participation Score |
Meaning |
10 (A) |
Student arrived on time, stayed to the end of class, and presented work at the board and/or gave a helpful explanation to the class about a problem. |
9 (A-) |
Student arrived on time, stayed to the end of class, worked well with her/his small group on class activities, and made appropriate contributions throughout the class session. Student asked and/or answered questions in small group and whole class discussion. |
8 (B-) |
Student arrived a few minutes late or left a few minutes early, yet still made a good contribution to the class discussion and group work. |
7 (C) |
Student was quiet and polite, but made minimal contribution to class discussion. Student was inattentive or distracted throughout the class session. Student turned in carefully written work which was mostly correct to make up a missed class; this make up work must be submitted within two class periods of the missed class. Student arrived more than five minutes late and/or left class more than five minutes early. |
Less than 7 (D or F) |
Student’s contribution to the class was disruptive or in some ways less than expected from college students; an indication of why participation was less than acceptable will be indicated in written comments. Student turned in written work to make up a missed class, but this work was carelessly done and/or had many errors. |
Subtract 5 points |
Student’s cell phone rang during class: 5 points will be subtracted from class participation score. |
Tests: 40%
There will be three tests; the first will be weighted 10%, while the second and third will each be weighted 15%. A detailed study guide for each test will be posted about a week before the scheduled test date. Tests are tentatively scheduled for the following dates:
Quiz 1: Week 1, Day 3 (This quiz will cover prerequisite skills. If you do very well on this quiz, you can earn up to 4 extra-credit points on Test 1. The Study Guide for this Quiz is now available. If you do very poorly on this quiz, you will be advised to take a lower-level course before continuing your study of Calculus.)
Test 1: Week 4, Day 11
Test 2: Week 8, Day 22
Test 3: Week 13, Day 38
Mathematics is a discipline in which new material naturally builds on previous material. Tests in this class are cumulative. You are expected to know and use skills that you learned in the prerequisite courses (high school algebra, trigonometry, and high school geometry). You must understand and continue to use concepts from the early part of the course as we progress through later topics. Ordinarily, I do not give make-up tests; exceptions to this policy will be considered on a case-by-case basis.
Projects: 20%
There are many interesting problems which can be studied using the tools of calculus. You will have an opportunity to investigate some of these problems which you may find more challenging than typical textbook exercises. This semester you will be asked to work on one or two such projects in your groups, which will typically be extended assignments, requiring one or two weeks of work. You will be asked to write a three- to five-page paper reporting on your investigations of these problems. This semester, I anticipate that these projects will come toward the ends of Chapters 2 and 4. The tentative schedule for these projects is as follows:
Project 1: Available about Week 5, Day 12, due Week 6, Day 17
Project 2: Available about Week 9, Day 24, due Week 11, Day 29
Benchmark testing is the department's way of assuring that students have achieved minimum levels of computational competency. It is generally expected that students who have successfully taken a semester of calculus can do certain calculations by hand. Although we will be using computers and calculators throughout this course, you will be expected to become proficient with these hand calculations. Throughout the semester, these calculations will be indicated, and you will be expected to do whatever practice you need to do to master these calculations.
There will be two benchmark tests in this course. Each benchmark will be offered in class on the first day of the window-of-opportunity (Week 7, Day 18 and Week 14, Day 39). A study guide for each benchmark outlining the material to be covered by will be posted well in advance of the scheduled benchmark window-of-opportunity. The windows of opportunity for each benchmark test are as follows:
Benchmark 1: Week 7
Benchmark 2: Week 14
To pass the benchmark test, you must get nine or ten of ten problems completely correct; there will be no partial credits. If you pass on the first attempt, your score will be recorded as 100%. (So there is incentive for passing on the first attempt!) If you do not pass the benchmark test on your first attempt, you may retake the benchmark once or twice within the window-of-opportunity. You must demonstrate that you have done some additional practice, and are encouraged to meet with your instructor to go over problems that are giving you difficulty. You may attempt each benchmark up to three times.
If you pass a benchmark test on a re-test, your score will be recorded as the average of the scores made on each attempt. If you have not passed a benchmark after three attempts or by the end of the window-of-opportunity date, your score will be recorded as the lower of 40% or your average on all three attempts. In calculating your average in this case, if you have not attempted to retake the benchmark, your score for these non-attempts will be considered as 0. This weighting of the Benchmark scores is designed to lower your overall course grade by at least a half letter grade if you are not able to pass a benchmark.
Note: Midterm is fill in date, and the last day to withdraw from this course is fill in date. Each student's midterm grade will be based on two tests, one benchmark, one project, and half the semester of participation. This represents approximately 45% of the graded work for the semester. If you have concerns about your progress or ability to keep up with course assignments, you should discuss these concerns with the instructor.
Final Exam: 20%
The cumulative final exam is scheduled as follows:
Scheduled date and time of the Final Exam
All tests in this course are cumulative, including the final exam.
Academic Integrity Policy
Inherent in the mission of this University is the strong belief in the principle of academic integrity. Students who cheat violate their own integrity and the integrity of the University by claiming credit for work they have not done and knowledge they do not possess. All students are expected to recognize and to abide by the policy on academic integrity found in the Student Handbook which can be found at URL for online Student Handbook, with link to information on Academic Integrity. (Look for the Academic Integrity Policy in the Table of Contents.)
Since much of the work of this course is to be done in cooperative learning groups and I encourage you to work together on the class activities and on most homework assignments, I will clearly indicate those assignments on which I expect you to work on your own. Basically, I assume that you are collaborating on homework assignments and class activities unless I tell you not to do so.
Collaborating and/or sharing your work with another student during a test or other individual graded assignment is unacceptable, and will earn a grade of 0 for that test or assignment. If you consult other sources – whether library materials or internet resources – while working on a project or paper, keep track of all the sources you consult and include these in your bibliography for the project. Failure to cite your sources on a paper is a serious offense, which will affect your grade for that paper or assignment. I am required to report each violation of academic integrity to the Department Chair. Repeated violations of academic integrity will be reported to the Dean of the College and the Academic Vice President, and may result in dismissal from the university.
Letter Grade Equivalences:
Letter Grade |
Percent range |
Letter Grade |
Percent range |
|
A |
93 or above |
C+ |
78 – 79 |
|
A- |
90 – 92 |
C |
70 – 77 |
|
B+ |
88 – 89 |
C- |
65 – 69 |
|
B |
83 – 87 |
D |
60 – 64 |
|
B- |
80 – 82 |
F |
Less than 60 |
Compliance with the Rehabilitation Act of 1973
If you have any special needs for alternative instruction and/or evaluation procedures, please feel free to discuss these needs with the instructor so that appropriate arrangements can be made.
Cell Phones and Pagers
As a matter of courtesy, students are expected to turn off cell phones and pagers during class. If extraordinary circumstances require an exception to this policy, the student is expected to discuss this with the instructor before class begins. If your cell phone rings audibly during class, five points will be deducted from your class participation score for that class period.
Office Hours
My office is located at XXX. I am on campus regularly Monday through Friday, and welcome students who drop in with a question. I also make it a point to check and respond to email regularly throughout the day. Although various responsibilities may require me to change my schedule from week to week, I try to reserve the following times as official office hours:
Mondays, Wednesdays, and Fridays |
times |
Tuesdays and Thursdays |
times |
If you need to reach me between classes:
- Email address
- Campus phone number