MATH 221: Calculus I

We will be using a free online textbook for this course, Calculus Volume 1, by Gilbert Strang and Edwin Herman. The book is available in pdf format or an interactive online format. Click a link below to get the book:

• PDF Version of Calculus Volume 1
• Interactive online version of Calculus Volume 1

Other resources, such as a Students Solution Manual can be found at the following link:

• Student Resources for Calculus Volume 1

We will cover chapters 1-5 and part of chapter 6.

Please note that it is a good idea to work on developing your independent reading skills. I may not be able to cover in class all the material you will be required to learn. As a result, it would be a good idea to read the textbook as a supplement to our in-class work. You should read the sections of the textbook which correspond to the material covered during the lectures. The reading will enable you to answer my questions and ask your own focused questions during lectures and help you to better understand the material.

A calculator is NOT required for this course, and you will not be able to use one during exams. If you want to get one, the Math Department recommends the TI-89 or the TI-Nspire. A free version of the TI-89 for your computer is available here: Download the TI-89. (Save the file to your computer, unzip it, and run vti.exe to run the TI-89 program on your computer.)

It may be helpful to make use of mathematical programs such as MATLAB, Maple, or Mathematica periodically. These are available in most student computer labs throughout campus.

Topics covered: Topics include limits, continuous functions, derivatives, velocity, integrals, area, and various other applications.

Math 221, Calculus I, is the first semester course of the calculus series and is intended as a development of single-variable calculus. We will cover mostly differential calculus and give an introduction to integral calculus. Differential calculus is a mathematical method for analyzing how things change. Change is measured by slopes, velocities, acceleration, and, in general, derivatives. The precise definition of an instantaneous rate of change requires an understanding of limits, a notion that also leads to the understanding of what is meant by a continuously changing quantity. Techniques like the product, quotient, and chain rules enable efficient computation of derivatives that can then be applied to, among other things, the analysis of motion, rates of change, optimization problems, and understanding the shape of a graph. Throughout the course, we will discuss applications of these techniques to problems coming from other disciplines.

We will also cover the beginnings of integral calculus, which is an important tool for applications to all parts of the natural sciences, engineering and economics. The basic concept of an integral will be introduced and used to find areas. We will cover the definition of the integral and the substitution method of integration.

Upon successful completion of this course, a student will be able to:

• Compute limits and derivatives of algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and piece-wise defined functions;
• Compute definite and indefinite integrals of algebraic, trigonometric, inverse trigonometric, exponential, logarithmic, and piece-wise defined functions;
• Determine the continuity and differentiability of a function at a point and on a set;
• Use the derivative of a function to determine the properties of the graph of the function and use the graph of a function to estimate its derivative;
• Solve problems in a range of mathematical applications using the derivative or the integral;
• Apply the Fundamental Theorem of Calculus; and
• Use appropriate modern technology to explore calculus concepts.

Your overall grade will be determined as follows:

• 12% - WeBWorK, Quizzes, and Class Participation
• 22% - Exam 1
• 22% - Exam 2
• 22% - Exam 3
• 22% - Final Exam

Your overall grade for the course will reflect how well your are doing and will be high if you are working hard on the homework and doing well on the exams. Almost all the questions on the exams will be in the same spirit with the homework questions. Therefore understanding how to do all the homework questions will enable you to do well on the exams.

Homework: Most homework will be done through the internet-based homework system called WeBWorK. However, there may occasionally be problems you must write out and hand in to me. All assignments must be completed by the given due date.

Moreover, while it is not required that you complete a handwritten version of WeBWorK assignments, it is strongly encouraged. Writing a problem out by hand, showing all calculation steps, and keeping them collected in a notebook will greatly assist you as you prepare for exams.

Exams: There will be three Midterm Exams and one Final Exam. Exams are closed book, closed notes, closed friends, and open brain. Calculators, cell phones, and other electronic devices will NOT be permitted in exams.

Quizzes and Class Participation: There will be occasional, unannounced quizzes in class to make sure students are understanding and keeping up with the course material. Quizzes will be based on material from homework and previous lectures. It is also imperative that you keep up with reading the textbook. NO MAKE-UP QUIZZES WILL BE GIVEN. Class participation will be based on your willingness to ASK and ANSWER questions in class.

It is essential not to fall behind because each lecture is based on previous work. If you have trouble with some material, SEEK HELP IMMEDIATELY in the following ways:

Accommodations: SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility will coordinate reasonable accommodations for persons with physical, emotional, or cognitive disabilities to ensure equal access to academic programs, activities, and services at Geneseo. Students with letters of accommodation should submit a letter to each faculty member and discuss their needs at the beginning of each semester. Please contact the Office of Accessibility Services for questions related to access and accommodations.

Office of Accessibility Services - Erwin Hall 22, (585)245-5112, access@geneseo.edu, www.geneseo.edu/accessibility-office