Welcome to Calculus!
What is Calculus? Calculus is a branch of mathematics that is fundamentally different from any mathematics that you have studied previously. The origins of Calculus date back at least 2500 years to the ancient Greeks. Unlike Algebra, Calculus is less static and more dynamic. In fact, Calculus was once referred to as "fluxions" because it has the power to describe things that are in flux; that is, things that are constantly changing. For example, in a typical Algebra exercise you might be asked to determine the speed of a car that has traveled a specified distance during a certain amount of time. By substituting the known quantities into the formula d = r x t , this becomes an easy task. However, during your Algebra class did you ever stop to think that whenever you travel, your rate fluctuates due to traffic signals, pedestrians, road conditions, etc.? Using Calculus, you will be able to determine the instantaneous rate at a specific point in time.
Another valuable comparison between Algebra and Calculus would be to consider various functions that you have studied in Algebra such as linear, quadratic, or cubic functions. Although transformations of these functions (such as vertical or horizontal shifts, etc.) are possible, you can predict their general shape. Calculus, on the other hand, allows us to work with functions that have no predictable shape because they are constantly changing. Due to the power of Calculus to model so many dynamic real world phenomena, Calculus is justly considered to be one of the greatest achievements of the human intellect.
How will this course be different from AP Calculus? This course is designed to be an introductory Calculus course. Students enrolled in this class will develop a strong foundation in the Calculus that will enable them to make a smooth transition to college mathematics. Depending on the college and the major chosen in college, some students may opt to enroll in a college level Calculus class or perhaps a course in Probability and Statistics. Homework expectations for this course, as stated in the student agenda, are described as follows: “Students should plan to devote from 30 to 40 minutes of homework preparation for study outside of class every day in each subject.”
AP Calculus, on the other hand, is a Calculus course designed for students who intend to take the Advanced Placement Test in Calculus. This is a rigorous exam; hence, the AP Calculus course will require intense effort to prepare for this exam. College credit for this course is dependent on the Advanced Placement Test Score, and the expectations of the college the student is applying to. Homework expectations for a typical college level class are as follows: Students are expected to spend 2-3 hours of homework for each one-hour spent in class. Students must be highly motivated and willing and able to devote many more hours of study than previous math courses.
What will our introductory Calculus class be like? Students will be expected to participate in and absorb class material, delve into the text on their own, work cooperatively in assigned groups, link all previous math knowledge to the new material, and complete all assignments. To accommodate different learning styles, a variety of methods will be used, as needed, such as linking concepts, cooperative groups, informal lecture, discussion, projects, and short essays.
Please note that cell phones and other electronic devices are not allowed and will not be tolerated.
What supplies will I need? To start, you will need the following:
- a three-ring binder with loose-leaf paper
- a pencil with an eraser
- a graphing calculator
Notes: A three-ring binder (one-inch) is ideal for this class because many printed hand-outs will be provided which cannot be easily organized in a spiral notebook. Also, spiral notebooks will not be collected to check homework assignments.
Assume that you will need to carry your book to class daily, unless told otherwise. Your book must be covered and should be labeled with your name.
What if I need help? Don’t wait! Strong math skills continue to be the ultimate gateway to college acceptance and career options. Students should not hesitate to ask for help as soon as possible. Always remember that I love to teach, and that I am here to help. Sometimes a student just needs a few extra minutes to clear up a topic. Mathematics is cumulative, and a small misunderstanding can rapidly become a major hurtle for student success. With the exception of unexpected meetings, my scheduled office hours will be Monday 2:10 - 2:45 pm and Thursday 2:10 – 2:45 pm. Please note that coaches will allow you to be late to practice, if you need help after school. Also, if you have an early release work schedule, it is important to note these office hours when arranging your work schedule.
Questions/Comments? Please indicate that you have read "Welcome to Calculus!" by signing the attached form. Questions or comments can be noted below or emailed at any time. This letter should be returned to the teacher during the first week of school. Parents/guardians may reach me by email at firstname.lastname@example.org.
I look forward to the year ahead, and I hope that you will enjoy Calculus as much as I do!
Math Department Chair, EHS