MATH 201 – CALCULUS I



MATH 201 – CALCULUS ITompkins Cortland Community CollegeCourse Outline and PoliciesFall 2013Instructor:Mr. Nick PianellaOffice:Room 301Phone:(607) 693-8105 (school)Email:NPianella@hcs.Office hours: During Collaborative Time before school on Tuesday, Wednesday, and Thursday or by appointment during or after school. Textbook: Calculus, Eighth Edition, Larson, Hostetler, and Edwards (Heath), 2002, ISBN # 0-618-50303-X, and a TI-83/86 graphing calculator.Optional: The student study guide to the above text is highly recommended; it contains solutions of many assigned problems.Calculator: A graphing calculator is required. TI-83 graphing calculator is recommended. If you are buying a calculator for this course, then a TI-84 Silver Edition is suggested. Instruction in class will be done using both. There are a limited number of calculators that can be signed out.Prerequisites: Completion three years of high school math, MATH132 – College Algebra and Trigonometry, and MATH 135 – Precalculus Mathematics. The minimum skills needed are an ability to understand and apply mathematical formulas and manipulate algebraic and trigonometric expressions easily.Attendance Policy: Students are expected to attend classes. Attendance will be taken. Note that exam questions are modeled on lecture and homework problems, so attending class is an important ingredient in course success. After the equivalent of one week of absences (4 class hours), a student's final number grade may be lowered by one point per absence.Class Structure: Material is presented in lecture, examples, and discussion format; homework is assigned and gone over in detail in subsequent classes. Feel free to ask questions in class at any time.Assistance: Any time you are having difficulty understanding material, see the instructor. It is useful to work together with other students as well. Organize a study group.Course Objectives: The student completing this course should be able to answer questions concerning the theory and concepts of the topics covered. More specifically,Analyze polynomials, rational functions and trig functions graphicallyEvaluate limits by (1) direct substitution, (2) algebraic manipulation, and (3) numerically “approaching” the value of interest.Find derivatives of algebraic power (+, -, or fractional) expressions by evaluating the limit of the difference quotient.Find vertical and horizontal asymptotes using the concept of limitsState the definition of continuity at a pointGive the requirements for differentiability at a pointWrite the equation of the tangent line to a curve at a given point.State and be able to use Rolle's and the Mean Value Theorems.Differentiate any algebraic or trigonometric function using the rules of differentiation, including implicit differentiation, and write answers in simplified form.Find higher derivatives.Use calculus to sketch algebraic and trigonometric functions using the concepts of increasing/decreasing functions, critical points, inflection points, and concavity (2nd derivative test).Solve max/min and related rates problems using calculus.Obtain approximations using differentials and Newton's Method.Anti-differentiate algebraic and trigonometric functions, including the technique of u-substitutionBe able to evaluate constants of integration for the indefinite integralExpress sums with the “sigma” notation.Evaluate Riemann sums.Understand and be able to use the Fundamental Theorem of Calculus to evaluate definite integrals.19.Differentiate natural logarithm and exponential functions, inverse trig functions, andhypebolic sine and cosine functions.Integrate log form and inverse tangent form and distinguish the two.Integrate functions involving exponentials.Integrate functions involving trig.Integrate by parts to some depth.Integrate using trig substitution in at least the tangent case.Be able to use a graphing calculator to produce graphs of functions and their derivatives and perform other calculus related operations.Course Content: TopicsText Sections Lines, Graphs, Functions and their graphs, Polynomial and Rational Functions, and Review of Trigonometry, ModelingSupplement Limits, Continuity Indefinite Limits1.1-1.5Review and Assess – Exam #1 Derivatives as Slopes andRates of Change,Rules of Differentiation2.1, 2.2 Product and Quotient Rules2.3Chain Rule, Implicit Differentiation2.4, 2.5Related Rates 2.6 Review and Assess – Exam #2Extrema & The Mean Value Theorem3.1, 3.2First Derivative Test, Second DerivativeTest, Limits at Infinity, Curve Sketching 3.3-3.6Optimization Problems, BusinessApplications3.7Differentials, Newton's Method3.8, 3.9 Review and Assess – Exam #3Antiderivatives & Indefinite Integrations,Area, Riemann Sums4.1-4.3Fundamental Theorem, Integrationby u-Substitution 4.4, 4.5Review and Assess – Exam #4Natural logs5.1 Natural Logarithmic integrals5.2Inverse Functions5.3Exponentials5.4Bases other than e and Applications5.5Inverse trig functions5.6 Integrals and inverse trig functions5.7Hyperbolics5.8Review and Assess – Exam #5Review for Final ExamFinal ExamEvaluation: Final grades will be determines by a point system. Tests, Quiz/Written Assignments, Homework/Preparedness and a final exam cover 100% of your grade.Exams40%Quizzes15%Written Assignments15%Professional Attitude/Preparedness/Homework10% Final20%Final Grade:The final grade will be determined from the following percentages of total possible points that each student accumulates: 93 – 100% = A 73 – 76.9% = C 90 – 92.9% = A- 70 – 72.9% = C- 87 – 89.9% = B+ 67 – 69.9% = D+ 83 – 86.9% = B 63 – 66.9% = D 80 – 82.9% = B- 60 – 62.9% = D- 77 – 79.9% = C+ Below 60% = FExams: Exams given during the semester will be worth 40% of your grade. These exams will assess your knowledge of the content from the unit as well as assess content from previous taught units.Quizzes: During the semester, you may expect to have a quiz every few days on the content taught. You will be made aware when a quiz is planned. Professional Attitude/Preparedness/Homework: Professional Attitude takes into account your attendance, class participation, and attitude towards fellow students and instructor. You must be prepared for each class as well. Homework assignments are an integral part of the learning process for this course and assists in ensuring you are prepared. They are given daily and are based on the content presented that day. In addition, reading the text book is an important part of your learning process. Each section covered will require you to pre-read the section and take notes. Written Assignments: You will be given problems from the book covering each section. Make sure all written assignments have your name, date, and assignment listed at the top of the page. No spiral edges on paper – please and thank you. These assignments must be handwritten, with all answers documented and all work shown. You must explain your answers or solutions in order to receive full credit. You may cooperate with others but you must submit a separate homework and explain your answers or solutions in order to receive full credit. A correct answer is worth 20% of the grade and the work/documentation counts for 80%. You may also seek assistance from me as needed. Each assignment is worth 100 points. Late assignments are penalized 10 points for each day late (weekends included).There are no written assignments for the first section (Section P). Written assignments are due two (2) days after the section is complete. The Written Assignments are: Sec 1.1 - #6, 8, 10Sec 3.4 - #10, 20, 36, 44, 66Sec 1.2 - #4, 6, 10, 26, 32Sec 3.5 - #14, 20, 24, 30, 48Sec 1.3 - #16, 22, 26, 36, 38, 52, 58, 68Sec 3.6 - #8, 14, 18Sec 1.4 - #4, 12, 18, 24, 28, 46, 92Sec 3.7 - #2, 18, 22, 26Sec 1.5 - #8, 22, 28, 44, 50Sec 3.8 - #4, 8, 18, 22Sec 2.1 - #10, 20, 24, 26, 36Sec 3.9 - #2, 10, 14, 20, 28Sec 2.2 - #18, 20, 24, 34, 44, 50, 58, 60Sec 4.1 - #18, 22, 28, 40, 44, 60Sec 2.3 - #4, 8, 12, 36, 54, 72, 96Sec 4.2 - #4, 10, 18, 44, 64Sec 2.4 - #24, 32, 64, 66, 68, 92Sec 4.3 - #14, 20, 22, 38, 44Sec 2.5 - #6, 10, 24, 36, 46Sec 4.4 - #18, 20, 22, 30, 40, 48, 54Sec 2.6 - #4, 16, 24, 30, 32Sec 4.5 - #16, 26, 30, 48, 56, 80Sec 3.1 - #12, 22, 26, 34Sec 7.1 - #18, 24, 32, 48Sec 3.2 - #14, 20, 42, 48Sec 7.2 - #4, 10, 14, 32Sec 3.3 - #12, 26, 38, 46, 62, 70Sec 7.3 - #4, 8, 24, 30Final Exam: A cumulative final exam will be given during the last week of the semester at a time and date to be determined. The final exam is worth 20% of your final grade so it is important that you are present for it.Statement of Academic Integrity: Harpursville Jr./Sr. High School Academic Honesty Parental/Student AgreementAcademic honesty and integrity lie at the heart of any educational enterprise. Students are expected to do their own work and neither to give nor to receive assistance during quizzes, examination, or other class exercises. One form of academic dishonesty is plagiarism. Plagiarism is intellectual larceny: the theft of ides or their manner of expression. When in doubt about rules concerning plagiarism, students are urged to consult individual faculty members. Because faculty and students take academic honesty seriously, penalties for violations may be severe, depending upon the offense. Staff members will gladly explain procedures for taking tests, writing papers, and completing other course requiment5s so that students may understand fully their instructor’s expectations.A complete copy of the Harpursville Jr./Sr. High School Academic Honesty Policy is available upon request.Student Responsibilities: Students have a responsibility to attend class, does their homework on time, participate in classroom discussions, and ask questions when they don’t understand, seek extra assistance when they need it, read the textbook as it is well written and easily understandable textbook that will help you immensely. Students are expected to assist in maintaining a classroom environment that is conducive to learning. Students are asked not to engage in any form of distraction to assure all students have the opportunity to gain from the time spent in class. Inappropriate behavior will not be tolerated. Appropriate action(s) will be taken immediately.Success in Calculus requires consistent attendance, class participation, completion of assigned work on time, and seeking assistance when needed. We are on a tight schedule and there is a lot of content to be covered and work to be done. I am very willing to assist in any way I can. This course outline is subject to change as the instructor deems necessary. Any changes will be communicated during class time.Good Luck and Best Wishes for a successful school year,Mr. Pianella ................
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