SYLLABUS MATH 219 Calculus I Framingham State University Summer 2016

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1 SYLLABUS MATH 219 Calculus I Framingham State University Summer 2016 Disclaimer: This syllabus is intended to give the student guidance in what may be covered in the course and will be followed as closely as possible. However, the professor reserves the right to modify, supplement and make changes as needs arise. Instructor: Professor Sonia Sandberg ssandberg@framingham.edu Office Hours: By appointment Credit: 4 Teaching Hours: 60 Time 2 hours/day Mon - Fri Text: Anton, Bivens, Davis, Calculus Early Transcendentals, Single Variable, 10th edition, John Wiley & Sons. Prerequisite: MATH200 Precalculus Course Objectives: In this class you will learn a variety of mathematical skills related to differentiation of functions and integration of functions. You will learn applications where these techniques can be used to solve problems and you may these topics to be useful in some of your other courses. In particular, you will learn to find the derivative of a function using the definition of a limit and rules of differentiation sketch graphs of functions using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity solve max/min problems and related rate problems using the derivative differentiation to solve applied max/min problems use Riemann sums and the Fundamental Theorem of Calculus to evaluate integrals Topics to be covered include: limits, derivatives, implicit differentiation, related rates, curve sketching using derivatives, integration (chapters 1-4). (Note that Chapter 0 is a review chapter and contains material that that you should already know.) Course Outline Topics Textbook Sections Week 1 Limits (Intuitive) section 1.1

2 Computing Limits section 1.2 More Limits section 1.3 Continuity section 1.5 Exam 1 Week 2 Trig, Exponential and Inverse Continuity section 1.6 Tangent Lines, Rates of Change section 2.1 Derivative Function section 2.2 Differentiation Techniques section 2.3 Product and Quotient Rules section 2.4 Trig Function Derivatives section 2.5 Exam 2 Week 3 Chain Rule section 2.6 Implicit Differentiation section 3.1 Log Function Derivatives section 3.2 Exponential and Inverse Trig Derivatives section 3.3 Related Rates section 3.4 Local Linear Approximation section 3.5 L Hopital s Rule, Indeterminate Forms section 3 6 Exam 3 Week 4 Increasing and Decreasing Functions section 4.1 Relative Extrema, Graphing Polynomials section 4.2 Rational Functions, Cusps, Tangents section 4.3 Absolute Max/Min Problems section 4.4 Applied Max/Min Problems section 4.5 Rectilinear Motion section 4.6 Exam 4 Week 5 Newton s Method section 4.7 Rolle s Theorem, Mean-Value Theorem section 4.8 Area Problem section 5.1 Indefinite Integral section 5.2 Integration by Substitution section 5.3 Exam 5 Week 6 Area as Limit, Sigma Notation section 5.4

3 Definite Integral section 5.5 Fundamental Theorem of calculus section 5.6 Final Exam Homework: Homework will be regularly assigned, but will not be collected. It is, however, very important to do all the homework because this is when you learn. Although you may understand everything I say in class and feel that know all the new material, you really don t know it until you practice. It is like watching someone drive a car or ride a bicycle or paint a painting. It looks easy when some when someone else is doing it, someone who is experienced, but when you try it yourself for the first time, it is not so easy. Exams: There will be an hour-long, closed-book exam each week. THERE WILL BE NO MAKE-UP EXAMS. In the event that a student misses an exam and presents an acceptable reason to the instructor, the final exam grade will be counted for the missed exam. If you are able to do the homework problems, then you should do well on the exams because the questions on the exams will look very similar to the homework. If they don t, please come and see me right away. I have frequent exams so that you and I both know how you are doing throughout the semester. If you start doing poorly on the exams, please come and see me so that we can together figure out how you can improve. Don t get behind in this class because it is very difficult to catch up when you do. Final Exam: A comprehensive final exam will be given during the last week. Blackboard: There is a blackboard site for this class. The syllabus, homework assignments, the exam schedule and your exam grades will be listed there. Grading: The exam average will count 70% of the final grade and the final exam will count 30%. The letter grade will be calculated as follows: Overall Average Grade Letter Grade A A B B B C C C D D D-

4 00-59 E Attendance: Regular attendance in class is expected and very important. While there is no direct penalty for absences, poor attendance usually results in poor performance. If you should miss a class, it is your responsibility to get the notes from a classmate and try the homework. If you have questions after this, then come and see me. Academic Honesty: I expect that all of your work will be your own. Please see the undergraduate catalog for the college s policy on academic honesty ( I plan to attend every class and come to class prepared to work. I expect that you will do the same. You should arrive in class on time prepared to work. Before class, you should have read the appropriate sections in the book and worked on the homework assignment. If you have questions or perhaps got stuck on a problem or two, make a note of this. Then at the beginning of class, you will be ready to ask your questions before I start on new topics. Preparing for math exams 1. I ll start with what you should not do! Don t prepare for a math exam by reading your book or your class notes or your homework or old exams. Reading math, even if you think you understand what you are reading, does not prepare you. Now here s what you should do. Do prepare for a math exam by doing more problems. You can find problems to practice on by using previously assigned homework, but be sure to start from scratch and only peek at your previous work if you get stuck. You can find new problems to try in the review section at the end of each chapter. 2. Be sure to get an adequate amount of sleep the night before the exam. Don t stay up late cramming for the exam. Also, eat something before the exam so that you will not be hungry while you are taking the exam. 3. When you receive the exams, quickly look over all the questions. Start with the ones that you know how to do and that you think are the easiest. This is a good time management strategy and will enable you to maximize the points that you receive. If you get stuck on a problem, set it aside and go on to another one. You don t want to use up a lot of time on a problem where you may receive little or no credit. This strategy is also successful from a psychological point of view because you will feel more confident as you complete more of the exam. Then you will be in a better frame of mind to tackle the more difficult problems.

5 How to do really well in your math class Although each person has his or her own learning style and preferred methods for studying, there are some steps that everyone can take in order to improve the chances of doing well when learning new mathematical topics. 1. It is very important to attend every class. The instructor will present the new material in a way that will prepare you for doing the homework and learning the material. If you miss a class, be sure to get a copy of the notes from a classmate. 2. Come to class prepared to work. That means, you should bring your book and your calculator to every class. You should have done the homework and the reading before class and be prepared to ask questions if you had difficulty with some of the homework. 3. Learning mathematics is an active process, so in class you should work along with the teacher. Be sure to ask questions if you don t understand something. Don t be shy about asking questions because most likely, you re not the only person with that question. 4. Sometimes you may feel that you really understand the new material when it is presented in class, but when you try the homework, you get struck. This is actually what often happens when you study math. The real learning takes place when you practice on you own by doing the homework. 5. Some students find that it is helpful to have a study partner or a study group. That way, if you get stuck, you have someone nearby to help you. Even if both of you are stuck, frequently you are able to figure it out by working together. It s the old idea that two heads are better than one. 6. When you get stuck, it helps to review a similar problem and go over this problem step by step. You will find similar problems in your class notes and your book. 7. Try the homework as soon as possible after class. That way, if you get stuck on some problems, you will have a chance to look at them again later. It is a surprising fact, but sometimes when you look at a problem a second time the next day, you can easily figure out how to do it. It s as if your brain was working on it in the background and you didn t know it. 8. Be sure to check your answers with the answers in the back of the book.