James Jones, Professor of Mathematics

Mathematics & Sciences Division,
Richland Community College

Section 01 meets from 1:15 pm to 2:40 pm on Monday, Wednesday, and Friday in room S137.

James Jones, Professor of Mathematics.

Phone: 875-7211, ext 490

Office: C223

Email: james@richland.edu

Web: http://people.richland.edu/james/

These are the times I'm scheduled to be in my office. I often spend portions of my office hour in the classroom helping students, so if I'm not in my office, check room S137. If these times are not convenient for you, please see me to make an appointment for some other time.

- Monday: 8:45 - 9:20 am, 12:25 - 1:05 pm, 4:20 - 4:45 pm
- Wednesday: 8:45 - 9:20 am, 12:25 - 1:05 pm
- Friday: 8:45 - 9:20 am, 12:25 - 1:05 pm

*Calculus of a Single Variable, 9th edition*. Ron Larson, Bruce Edwards. Copyright 2010, Brooks/Cole Cengage Learning. ISBN 978-0-547-20998-2 (Required)

Transfer students. Students pursuing degrees in engineering, mathematics, computer science, natural sciences, and life sciences.

Successful completion (C or better grade) of Math 116, College Algebra, and Math 117, Trigonometry, or satisfactory score on the Mathematics placement exam.

** MATH 121 - Calculus & Analytic Geometry I**

Hours: 5 lecture - 0 lab - 5 credit

Mathematics 121, Calculus and Analytic Geometry I, includes instruction in Calculus topics common to the standard college first semester Calculus course. It begins with a review of algebra and trigonometry; then the idea of limits and continuity is introduced. With the knowledge of limits and continuity the student develops the concept of the derivative and its applications. At the end, the student studies the antiderivative of elementary functions and the applications of the definite integral in geometry, science, and engineering.

Applicable toward graduation where program structure permits.

- Certificate or degree: All certificates and all degrees.
- Group requirement: Mathematics
- Area of Concentration: Mathematics.

The mathematics component of general education focuses on quantitative reasoning to provide a base for developing a quantitatively literate college graduate. Every college graduate should be able to apply simple mathematical methods to the solution of real-world problems. A quantitatively literate college graduate should be able to:

- interpret mathematical models such as formulas, graphs, tables, and schematics, and draw inferences from them;
- represent mathematical information symbolically, visually, numerically, and verbally;
- use arithmetic, algebraic, geometric, and statistical methods to solve problems;
- estimate and check answers to mathematical problems in order to determine reasonableness, identify alternatives, and select optimal results; and
- recognize the limitations of mathematical and statistical models.

Courses accepted in fulfilling the general education mathematics requirement emphasize the development of the student's capability to do mathematical reasoning and problem solving in settings the college graduate may encounter in the future. General education mathematics courses should not lead simply to an appreciation of the place of mathematics in society, nor should they be merely mechanical or computational in character.

To accomplish this purpose, students should have at least one course at the lower-division level that emphasizes the foundations of quantitative literacy and, preferably, a second course that solidifies and deepens this foundation to enable the student to internalize these habits of thought.

Math 121, Calculus & Analytic Geometry I, satisfies the Illinois Articulation Initiative Definition of a General Education Mathematics Course. It corresponds to M1 900-1, College-level Calculus I.

**M1 900-1: College-level Calculus I (4-5 semester credits)**

Topics include (but are not limited to) the following: limits and continuity; definition of derivative: rate of change, slope; derivatives of polynomial and rational functions; the chain rule; implicit differentials; approximation by differentials; higher order derivatives; Rolle's Theorem: mean value theorem; applications of the derivative; anti-derivative; the definite integral; the fundamental theorem of calculus; area, volume, other applications of the integral; the calculus of the trigonometric functions; logarithmic and exponential functions; techniques of integration, including numerical methods; indeterminate forms: L'Hôpital's rule; improper integrals; sequences and series, convergence tests, Taylor series; functions of more than one variable, partial derivatives; the differential, directional derivatives, gradients; double and triple integrals: evaluation and applications. Prerequisite for Calculus I: College Algebra and Trigonometry with grades of C or better or Elementary Functions with a grade of C or better.

Math 121, Calculus & Analytic Geometry I, also satisfies the requirements for the IAI Mathematics Major course *MTH 901: Calculus I* and the Engineering Major course *EGR 901: Calculus I (part of three-course Calculus sequence)*.

For more information on the Illinois Articulation Initiative, visit their website at http://www.itransfer.org/

While learning calculus is certainly one of the goals of this course, it is not the only objective. Upon completion of this course, the student should be able to ...

- demonstrate comprehension and understanding in the topics of the course through symbolic, numeric, and graphic methods
- demonstrate the use of proper mathematical notation
- use technology when appropriate and know the limitations of technology
- work with others towards the completion of a common goal
- use deductive reasoning and critical thinking to solve problems

Upon completion of this course, the student should be able to ...

- find the limits of expressions involving algebraic and trigonometric functions
- determine where functions are continuous and classify discontinuities as removable or non-removable
- find the derivative of a function using the limit definition
- apply the basic rules of differentiation to find the derivatives of algebraic and trigonometric functions
- find higher order derivatives
- use implicit differentiation
- analyze the graph of a function using the first and second derivative
- use the derivative to solve applied problems involving maximums and minimums
- find the antiderivative of algebraic and trigonometric functions
- understand the relationship between Riemann sums and definite integrals
- apply the fundamental theorem of calculus to evaluate definite integrals
- find the area under a curve and between two curves
- find volumes of rotation, lengths of planar curves, and surface areas of revolution
- work application problems from physics including work, force, and pressure

Discussion, problem solving, student questions, student participation, oral presentations, and lecture. Students are expected to read the material before coming to class and are strongly encouraged to come to class with a list of questions and to ask these questions.

Could include any of the following: problem solving exams, objective exams, essays, research papers, oral presentations, group projects, quizzes, homework.

Letter grades will be assigned to final adjusted scores as follows:

- A: 90 - 100%
- B: 80 - 89%
- C: 70 - 79%
- D: 60 - 69%
- F: below 60%

Missed quizzes may not be made up.

Consideration may be given to such qualities as attendance, class participation, attentiveness, attitude in class, and cooperation to produce the maximum learning situation for everyone.

The instructor will give you a grade sheet so that you can record your scores and keep track of your progress in the course. There is also a web page that you can use to check your grades throughout the semester. If you are concerned about your grades, see the instructor.

Assignments are due at the beginning of the class period on the date they are due. The instructor may be gracious and allow you to turn them in later that day without counting them late, but do not count on his graciousness. Late assignments lose 20% of their value per class period. The instructor reserves the right to apply this rule to missed exams as well as regular assignments. No late work will be accepted after the final.

Regular attendance is essential for satisfactory completion of this course. Mathematics is a cumulative subject and each day builds on the previous day's material. If you have excessive absences, you cannot develop to your fullest potential in the course.

Students who, because of excessive absences, cannot complete the course successfully, are required to be administratively dropped from the class at midterm. If a student stops attending after midterm, it is the student's responsibility to withdraw to avoid an "F". Do not stop attending and assume that you will be withdrawn from the class by the instructor.

Although dropping students for non-attendance at midterm is required, students whose attendance is occasional or sporadic may be dropped from the class at any point during the semester at the instructor's discretion. If you miss any two consecutive days without communicating with the instructor, you may be dropped. The safest way to make sure you're not dropped for non-attendance is to continue to attend classes.

The student is responsible for all assignments, changes in assignments, or other verbal information given in the class, whether in attendance or not.

If a student must miss class, a call to the instructor (RCC's phone system has an answering system) should be made or an email message sent. When a test is going to be missed, the student should contact the instructor ahead of time if at all possible. Under certain circumstances, arrangements can be made to take the test before the scheduled time. If circumstances arise where arrangements cannot be made ahead of time, the instructor should be notified and a brief explanation of why given by either voice or email. This notification must occur before the next class period begins.

Attempting and completing homework is vital to your success in this course. Homework is the practice that strengthens your skills and prepares you to learn the material. The worked out solutions to the odd numbered exercises are available online at www.calcchat.com. This is like having the student solutions manual for free. When you get stumped with a problem, you can go online and see how to work out the problem.

Having the solutions available fosters the temptation to use them to work the problems. This approach does not benefit the student. Instead, attempt the problem on your own first. If you get stuck with a minor algebra or trigonometry problem, then look at the online solution. If you find that your problems are more conceptual or that you keep getting stuck you need to seek additional help: read the book, look for similar examples, ask another student, go to the Academic Success Center, or ask the instructor.

As calculus students, you are some of the best and brightest mathematics students we have and you have some algebraic and trigonometric skills that most students are lacking. You should voluntarily do as much homework as you need to master the material. In this class, you will be given a list of suggested problems. If you find that you are understanding the concepts, this may be enough for you, but if you find that you still don't understand the material after working those problems, it may be necessary for you to work additional problems.

The use of technology in this course is consistent with the Technology Statement in the Illinois Mathematics & Computer Science Articulation Guide (IMACC, 2008, p. 4). Technology is used to enhance the learning of Calculus, but it is not the focus of the instruction. There will be instances when we will use the calculator or computer to aid in our understanding or remove some of the tediousness of the calculations (especially in the area of numerical approximations). There may be some projects, homework, or portions of a test that require you to use technology to complete.

Here are some of the technology tools that we may use.

This class is a mathematics class and a graphing calculator is required. A scientific calculator is not sufficient. The calculator should be capable of graphing functions, finding roots, maximums, and minimums from a graph, displaying tables of values, and finding the definite integral numerically. A Texas Instruments TI-84 or TI 83 is the recommended calculator.

That said, a TI-92, TI-89, or TI Nspire CAS calculator is recommended for this course if you plan on taking additional calculus or engineering courses.

Calculators may be used to do homework and may be used on exams and/or quizzes in class unless otherwise announced.

This spreadsheet application is useful for numerical approximations. It is loaded on all of the student computers at Richland.

Maxima is an open-source computer algebra system that is free for you to download and use at home. It is not as user-friendly as Derive, but it is free. It is available at http://maxima.sourceforge.net/

WinPlot is a free graphing software package for Windows written by Rick Parris at Phillips Exeter Academy in NH. The software is useful for creating graphs and it is easy to copy/paste the graphs into other applications. You may download the software by right-clicking your mouse on the word "WinPlot" at the top of the page http://math.exeter.edu/rparris/winplot.html and choosing save.

The student should have a pencil, red pen, ruler, graph paper, stapler, and paper punch. The student is expected to bring calculators and supplies as needed to class. The calculator should be brought daily. There will be a paper punch and stapler in the classroom.

The student is encouraged to seek additional help when the material is not comprehended. Mathematics is a cumulative subject; therefore, getting behind is a very difficult situation for the student. There are several places where you can seek additional help in your classes.

You may use a recording device to record the lectures. Feel free to use a camera or cell phone to take pictures of the boards if you have trouble getting all of the information into your notes.

The textbook has an affiliated website called www.calcchat.com that provides free solutions to all of the odd numbered problems in the textbook.

I try to make myself as available to the students as I can. My office hours are listed at the beginning of this syllabus, but those are just the times I'm scheduled to be in my office. Grab me and ask me questions if you see me in the hallway. Ask questions before or after class. If I'm in my office and it's not my scheduled office hours, go ahead and stop in.

The instructor should be considered the authoritative source for material related to this class. If a tutor or other student says something that disagrees with the instructor, believe the instructor.

Probably the best thing you can do for outside help is to form a study group with other students in your class. Work with those students and hold them accountable. You will understand things much better if you explain it to someone else and study groups will also keep you focused, involved, and current in the course.

The Academic Success Center consolidates several student services into one area. It is located in the south wing of the first floor next to the Kitty Lindsay Learning Resources Center (library).

The testing center is located in room S116. You must provide a photo identification and know the name of your instructor to use this service.

Quality tutors for the upper level mathematics are difficult to find. Please consider forming a study group among your classmates.

The tutoring center provides tutoring on a walk-in or appointment basis in room S118. They also have computers with the mathematical software loaded on it.

There are accommodations available for students who need extended time on tests, note takers, readers, adaptive computer equipment, braille, enlarged print, accessible seating, sign language interpreters, books on tape, taped classroom lectures, writers, or tutoring. If you need one of these services, then you should see Learning Accommodation Services in room C148. If you request an accommodation, you will be required to provide documentation that you need that accommodation.

Each student is expected to be honest in his/her class work or in the submission of information to the College. Richland regards dishonesty in classroom and laboratories, on assignments and examinations, and the submission of false and misleading information to the College as a serious offense.

A student who cheats, plagiarizes, or furnishes false, misleading information to the College is subject to disciplinary action up to and including failure of a class or suspension/expulsion from the College.

Richland Community College policy prohibits discrimination on the basis of race, color, religion, sex, marital or parental status, national origin or ancestry, age, mental or physical disability (except where it is a bonafide occupational qualification), sexual orientation, military status, status as a disabled or Vietnam-era veteran.

The Mathematics and Sciences Division prohibits the use of cell phones, pagers, and other non-learning electronic communication equipment within the classroom. All equipment must be turned off to avoid disturbances to the learning environment. If a student uses these devices during an examination, quiz, or any graded activity, the instructor reserves the right to issue no credit for these assignments. The instructor needs to approve any exceptions to this policy.

- Graphing functions on calculators and computers
- Transformations of functions
- Symmetry
- Factoring and simplifying with rational exponents
- Extensive review of trigonometry

- An intuitive approach to limits
- Two sided limits and one sided limits
- Numerical approach to finding limits
- Techniques of computing limits
- Infinite limits
- Rigorous definition of limit
- Continuity
- Limits and continuity of trigonometric functions

- Slopes and rate of change
- The limit definition of derivative
- Techniques of differentiation
- Derivatives of trigonometric functions
- The chain rule
- Implicit differentiation
- Related rates

- Intervals where increasing, decreasing, constant, concave up, concave down
- Relative extrema and points of inflection
- Sketching functions, using technology
- First and second derivative test
- Absolute extrema
- Applied maximization and minimization problems
- Newton's Method
- Rolle's Theorem and the Mean Value Theorem
- Differentials

- Overview of the area problem
- Indefinite integrals, slope fields, integral curves
- Integration by substitution
- Sigma notation
- The definite integral as a Riemann sum
- Fundamental theorem of Calculus
- Rectilinear motion
- Definite integrals by substitution

- Logarithmic functions, differentiation
- Inverse functions
- Exponential functions, differentiation and integration

- The area between two curves
- Volumes of rotation by slicing, disks, washers, and cylindrical shells
- Length of a plane curve
- Surface area of revolution
- Work
- Moments, centers of mass, and centroids
- Fluid pressure and force