Math 123 - Calculus I (4 credits)
Dakota State University … Fall Semester 2011

Professor
Dr. Jeffrey S. Palmer
Office: Science Center 146I

Phone: 256-5190

Email: jeff.palmer@dsu.edu

Office Hours: MWF 8:30 - 8:50 am, T 9:30 - 9:50 am, MTWF 11:00 - 11:50 am, MW 2:00 - 2:50 pm, or by appointment

Homepage: http://www.homepages.dsu.edu/palmerj/

 

Prerequisite

Math 102 and Math 120 (concurrent enrollment with Math 120 allowed), or appropriate math placement.

 

Catalog Description

The study of limits, continuity, derivatives, applications of the derivative, antiderivatives, the definite and indefinite integral, and the fundamental theorem of calculus (2011-2012 DSU Undergraduate Catalog)

 

Required Text

Calculus - Early Transcendental Functions, Single Variable, Third Edition by Robert T. Smith and Roland B. Minton (McGraw-Hill)

Use of Tablets in the Classroom
The Tablet PC platform has been adopted across the DSU campus for all students and faculty, and tablet usage has been integrated into all DSU classes to enhance the learning environment. Tablet usage for course-related activities, note taking, and research is allowed and encouraged by DSU instructors.  However, inappropriate and distracting use will not be tolerated in the classroom.  Instructors set policy for individual classes and are responsible for informing students of class-specific expectations relative to Tablet PC usage. Failure to follow the instructor’s guidelines will hinder academic performance and may lead to disciplinary actions. Continued abuse may lead to increased tablet restrictions for the entire class. Because tablet technology is an integral part of this course, it is the student’s responsibility to ensure that his/her Tablet PC is operational prior to the beginning of each class period.

Introduction and Methodology

This course will probably be very different from any mathematics course you have ever taken. Typically, mathematics is taught by the “plug-and-chug" method; students are given a number of examples of certain problem types and asked to practice these manipulations on a long list of related problems. The hope is that through repetitive manipulation, skill and understanding of important concepts will be attained. Too often, however, it seems that this is not the case.

 

I hope you will develop knowledge of, skill in, and understanding of those fundamental calculations that are needed in your mathematical toolbox. Mathematics is not moving symbols around on a piece of paper and obtaining the correct answer. You should always be asking yourself what you are doing and why you are doing it. We will use our mathematical toolbox to examine applied problems from a variety of disciplines. Applications from biology, chemistry, physics, business, economics, and other areas form an integral part of the course. Mathematics is not a cookbook discipline; the ultimate validation of your skills and understanding is reflected in your ability to develop solutions to problems that are new and unfamiliar to you. You will encounter, in course assignments and evaluations, activities that require problem solving and critical thinking. Finally, I hope that you will come to understand and appreciate both the power and the shortcomings of technology, particularly the computer, as a tool for understanding mathematical concepts and for solving applied problems. In conclusion, as a student in this course you are expected to

On Mondays and Wednesdays we will typically spend the first 15-20 minutes answering questions on homework problems you have been assigned. The remaining 30-35 minutes will be devoted to classroom presentation, principally lecture and computer demonstration, of the material covered in chapters 1-4 of your textbook (the core material). Certain additional topics may from time to time be introduced and some sections will be skipped. On Tuesdays we will usually have another 30-35 minute classroom presentation on the core material followed by a 15-20 minute quiz. On Fridays we will be discussing material (roughly from chapter 7 of your text) on mathematical modeling and differential equations. When appropriate, we will take advantage of the computer algebra system Maple, Excel spreadsheets, and the systems modeling software Stella to assist us with our inquiries and investigations.

 

Lecture time is at a premium, so it must be used efficiently. You cannot be "taught" everything in the classroom. It is your responsibility to learn the material. Most of this learning must take place outside the classroom. In order to succeed, you must do your homework assignments on a daily basis. I expect that, for an average student, each will take approximately two or three hours of solid time to complete. It is critical that you not only solve problems but that you understand what you did and why. Expect this course to be both extremely challenging and yet fair. I subscribe to the philosophy that if challenged, students will respond to meet that challenge.

 

System General Education Goals

This course satisfies Regental General Education Goal 5: Students will understand and apply fundamental mathematical processes and reasoning.

These outcomes shall be addressed through our study of the theory and application of limits, derivatives, and integration and will be assessed through quizzes, worksheets and examinations.

 

Evaluation Procedure

It is my plan to give a minimum of ten 10-point quizzes/worksheets during the semester. Your eight highest scores will count toward your final grade. Additionally, there are four 60-point examinations scheduled for this course. Each exam will be cumulative, covering material from the beginning of the course through the preceding Friday, however, the emphasis will be on new material.

 

Exam 1 Tuesday 27 September In-Class  
Exam 2 Tuesday 25 October In-Class  
Exam 3 Tuesday 22 November In-Class  
Exam 4 Monday 12 December 10:30 am - 12:30 pm  

 

Your grade will be calculated using your accumulated point total (240 points from four examinations, and 80 points from collected quizzes/worksheets). The grading scale is

 

A B C D F
272 - 320 224 - 271 192 - 223 160 - 191 000 - 159

 

Students near a cutoff may receive the higher grade at the discretion of the instructor.

 

Attendance

While there is no policy of required attendance of lectures in this course, it is unlikely that you will be able to earn a good grade without regularly attending the lectures. When you miss class, whatever the reason, you really miss important material from three lectures not one. Obviously the lesson covered that particular day is missed but you also miss out on important connections of that day’s material with the previous day’s lesson and the following day’s lesson. Also, if you are on academic probation or are an at-risk student, you are required to attend every class meeting. You are expected to arrive at lecture on time and to remain for the entire class period. If for some reason you must arrive late or leave early please do so quietly. Talking or other behavior that disrupts lecture will not be tolerated. If for any reason I am late for the start of class and you have not received official notification that the class has been canceled, you are expected to remain for 15 minutes before “assuming" that the lecture has been canceled for the day. Above all else, show respect for your classmates. Your attendance, behavior, and participation in the class have effects on others beside yourself.

 

Academic Honesty

Cheating and other forms of academic dishonesty run contrary to the purpose of higher education and will not be tolerated in this course. Academic dishonesty includes giving, receiving, or using unauthorized aid on any academic work. All academic work done contains an implicit pledge by you that no unauthorized aid has been received. A student guilty of first-offense academic dishonesty will receive a grade of zero for the work attempted. A student guilty of the second offense will receive a grade of “F" for the course. DSU’s policy on academic integrity (DSU Policy 04-05-00) is available online at http://www.departments.dsu.edu/hr/newsite/policies/032200.htm

 

Freedom in Learning Statement
Students are responsible for learning the content of any course of study in which they are enrolled. Under Board of Regents and University policy, student academic performance shall be evaluated solely on an academic basis and students should be free to take reasoned exception to the data or views offered in any course of study.  It has always been the policy of Dakota State University to allow students to appeal the decisions of faculty, administrative, and staff members and the decisions of institutional committees.  Students who believe that an academic evaluation is unrelated to academic standards but is related instead to judgment of their personal opinion or conduct should contact the dean of the college which offers the class to initiate a review of the evaluation.

 

ADA Statement

If you have a documented disability and/or anticipate needing accommodations (e.g., non-standard note taking, test modifications) in this course, please contact the instructor. Also, please contact Dakota State University’s ADA coordinator, Keith Bundy (located in the Student Development Office in the Trojan Center Underground or via email at Keith.Bundy@dsu.edu or via phone at 605-256-5121) as soon as possible. The DSU website containing additional information, along with the form to request accommodations is available at http://www.departments.dsu.edu/disability_services/. You will need to provide documentation of your disability. The ADA coordinator must confirm the need for accommodations before officially authorizing them.

Statement on Feedback and Communications
Typically I access and read email once per day Monday through Friday when classes are in session. I generally respond to email messages within 48 hours, excluding weekends and holidays. Feedback from assignments is almost always provided within 1 week, excluding holidays, of the assignment due date unless otherwise noted.

Student Concerns

There is an established policy for resolving concerns regarding grades and other academic matters. This policy may be found in the university catalog. If you should have a complaint or concern about grades or any other aspect of this course you are responsible for following this established procedure.

 

The instructor reserves the right to make adjustments in this course!

Approximate Schedule and Course Outline

30 Aug T Introduction and Overview  
31 Aug W 1.2 The Concept of Limit  
01 Sep R    
02 Sep F 1.2 / 1.3  
       
05 Sep M No Class - Labor Day  
06 Sep T 1.3 Computation of Limits  
07 Sep W 1.4 Continuity and Its Consequences
Last Day to Add/Drop a Full Semester Class
 
08 Sep R    
09 Sep F 1.4 / 1.5  
       
12 Sep M 1.5 Limits Involving Infinity  
13 Sep T 1.6 Formal Definition of the Limit  
14 Sep W 1.6 / 2.1  
15 Sep R    
16 Sep F Modeling Application: A Simple Epidemic - Introduction  
       
19 Sep M 2.1 Tangent Lines and Velocity  
20 Sep T 2.2 The Derivative  
21 Sep W 2.2 / 2.3  
22 Sep R    
23 Sep F Modeling Application: A Simple Epidemic - Conclusion  
       
26 Sep M 2.3 Computation of Derivatives: The Power Rule  
27 Sep T EXAM 01  
28 Sep W 2.4 The Product and Quotient Rules  
29 Sep R    
30 Sep F Modeling Application: Constant Flows - Introduction  
       
03 Oct M 2.4 / 2.5  
04 Oct T 2.5 The Chain Rule  
05 Oct W 2.6 Derivatives of Trigonometric Functions  
06 Oct R    
07 Oct F Modeling Application: Constant Flows - Conclusion  
       
10 Oct M No Class - Native American Day  
11 Oct T 2.6 / 2.7  
12 Oct W 2.7 Derivatives of Exponential and Logarithmic Functions  
13 Oct R    
14 Oct F Modeling Application: Exponential Growth and Decay - Introduction  
       
17 Oct M 2.8 Implicit Differentiation and Inverse Trigonometric Functions  
18 Oct T 2.8 / 3.1  
19 Oct W 3.1 Linear Approximations and Newton's Method  
20 Oct R    
21 Oct F Modeling Application: Exponential Growth and Decay - Conclusion  
       
24 Oct M 3.2 Indeterminate Forms and L'Hopital's Rule  
25 Oct T EXAM 02
Mid-term Deficient Grades Due
 
26 Oct W 3.2 / 3.3  
27 Oct R    
28 Oct F Modeling Application: A Model Lake - Introduction  
       
31 Oct M 3.3 Maximum and Minimum Values  
01 Nov T 3.4 Increasing and Decreasing Functions  
02 Nov W 3.4 / 3.5  
03 Nov R    
04 Nov F Modeling Application: A Model Lake - Conclusion  
       
07 Nov M 3.5 Concavity and the Second Derivative Test  
08 Nov T 3.6 Overview of Curve Sketching  
09 Nov W 3.6 / 3.7  
10 Nov R Last Day to Withdraw  
11 Nov F No Class - Veterans Day  
       
14 Nov M 3.7 Optimization  
15 Nov T 4.1 Antiderivatives  
16 Nov W 4.1 / 4.2  
17 Nov R    
18 Nov F Modeling Application: Newton's Law of Heating and Cooling - Introduction  
       
21 Nov M 4.2 Sums and Sigma Notation  
22 Nov T EXAM 03  
23 Nov W No Class - Thanksgiving Holiday  
24 Nov R No Class - Thanksgiving Holiday  
25 Nov F No Class - Thanksgiving Holiday  
       
28 Nov M 4.3 Area  
29 Nov T 4.3 / 4.4  
30 Nov W 4.4 The Definite Integral  
01 Dec R    
02 Dec F Modeling Application: Newton's Law of heating and Cooling - Conclusion  
       
05 Dec M 4.5 The Fundamental Theorem of Calculus  
06 Dec T 4.5 / 4.6  
07 Dec W 4.6 Integration by Substitution  
08 Dec R    
09 Dec F Wrap Up and Conclusion  
       
12 Dec M EXAM 04  

 

 

Modeling Application Topics

 

A Simple Epidemic
Some students entering Calculus have been exposed to empirical modeling (curve fitting); however, very few (if any) have any experience with dynamic systems modeling. To introduce systems modeling, we formulate a simple SIR epidemic model for the spread of an infectious disease in a population. Assuming constant population size and recovery with permanent immunity we describe mathematically the process of disease transmission (movement from the susceptible class S to the infected class I) and recovery (moving from the infected class to the recovered class R). A computer simulation of the model is built using Stella. Computer simulations of the model are used to discover the Threshold Theorem, the epidemic cannot spread unless the size of the susceptible population exceeds a critical size. Students are encouraged to investigate extensions of this basic model such as allowing immigration into the population or allowing recovery with temporary immunity. Students also complete a tutorial on Stella.

Constant Flows
Having in our previous modeling lesson introduced the idea of a systems model, in this lesson we take a giant step backward and consider the simplest possible dynamical system. Namely, what happens to a system experiencing a constant flow, in or out of the system? We begin with a simple data collection experiment, measuring the volume of water in a coffee can placed under a faucet dripping at a slow, but approximately constant, rate. A linear regression model of the data (done in Excel) is used to estimate the flow rate of the faucet. We then formulate, solve, and simulate (using Stella) the corresponding dynamical systems model and illustrate the assumptions underlying linear growth and decay.

Exponential Growth and Decay
Having studied the behavior of systems experiencing a constant flow in or out, we now consider flows proportional to the present size of the system. Beginning again with a simple data collection experiment, this time we measure the volume of water in our coffee can over time as it drains from a small nail hole punched into the bottom. An exponential decay curve fit to the data (using Excel) is used to estimate the half-life of the volume of water in the can. We then formulate, solve, and simulate (using Stella) the dynamical systems model for a flow in/out of a system that is directly proportional to the size of the system. This illustrates the underlying physical assumptions behind exponential growth and decay processes (simple population growth, continuously compounded interest, radioactive decay).

A Model Lake
This combines the components examined in our previous two lessons. What will happen to the volume of water in the can if water is flowing in at a constant rate and flowing out at a rate directly proportional to the current volume? We begin by formulating the dynamical systems model (using the estimated parameters from our previous experiments), however, direct solution of the equation is not possible for us at this point in the course. Hence, we develop a qualitative analysis of the model behavior involving using algebraic techniques and the basic concepts of differential Calculus. We are able to completely predict the behavior of the system without actually solving the model equation directly. A Stella simulation of the model is constructed and used to verify the results of our analysis. This is actually more useful than are computational techniques for directly solving the equation. Except in relatively simple cases, most models do not have exact, analytical solutions. This model also introduces the very important concept of equilibrium behavior.

Newton's Law of Heating & Cooling
Newton’s Law of Heating/Cooling states that the time rate of change of the temperature of an object is directly proportional to the difference between the current temperature of the object and the temperature of the surrounding environment. The model equation is essentially identical to that covered in our Model Lake exercise and the problem is used to review and illustrate the use of qualitative analysis to determine the behavior of a model without actually solving the model equation (which we still cannot quite do).