Course Title: (4 credits) Prerequisites: MA 1010 Applied Finite Mathematics or MA 1002 Precalculus or equivalent Semester: Fall 2013 Class schedule: Tuesday period 2 (10:35) G-21 Friday period 2 (10:35) G-21 and period 3 (12:10) G-4 Office hours: Tuesday period 3, Friday period 4 - make an appointment to confirm, or just drop by Contact: Email: Ruth.Corran@aup.fr Office: Grenelle G26 Mailbox: Grenelle 3 rd floor COURSE DESCRIPTION: STUDENT LEARNING OUTCOMES: This course introduces differential and integral calculus and develops the concepts of calculus as applied to polynomial, rational, logarithmic and exponential functions. Topics include limits, derivatives, techniques of differentiation, applications to extrema and graphing, the definite integral, the fundamental theorem of calculus and its applications, logarithmic and exponential functions, growth and decay, partial derivatives. Appropriate for students in the biological, management, computer and social sciences. On completion of this course, students should: Understand the notions of function, domain, range, inverse function and composition of functions, and be able to work practically with these concepts. In particular, for polynomial, rational, exponential and logarithmic functions, be able to work comfortably with their graphs, derivatives, and integrals. Know what the graph of a function is, be able to read and interpret graphs, and be able to sketch graphs using different techniques including tables, transformations of graphs and first and second derivatives. Understand the concepts of limit and continuity of a function, and be able to make calculations of limits and determine when a function is continuous or not. Understand and be able to work with the notion of derivative in various forms: as the instantaneous change in a function, the slope of the tangent of the graph of a function, as a limit, and algebraically via rules for differentiation. Understand and be able to work with the notion of integral: as the area under a curve, as a limit, as the inverse of differentiation, using rules for integration. Know what the Fundamental Theorem of Calculus is. Be able to put the ideas of limit, continuity, derivative and
integral to work concretely in real world applications as well as in other areas of mathematics. Have a familiarity with partial derivatives, double integrals and Lagrange multipliers. A proposed class schedule is attached to this sylus. TEXTBOOKS: CLASS NOTES: ATTENDANCE: HOMEWORK: Hughes-Hallett et al, Single variable Calculus, 6 th edition. Please come to class prepared, having read all assigned material. Good notes from class are essential. If you miss a class, it is recommended that you get copies of the notes from that class from a colleague in the class. Attendance is compulsory. You will need a homework book for this course, which will be collected periodically and graded for completeness. Your homework book should be a 64-page softcover exercise book with grid paper pages (eg 5mm x 5mm). Bring it with you to every class, along with a different coloured pen for corrections. Homework will be set most classes, and marked during the following class. You will need to bring a different coloured pen to class to mark your work. Refer to the separate Guidelines for Homework handout for more information. Homework is not group work. While you may work with other students to understand the material, your answers must be written up individually. Homework may be set from the 6 th edition of Single Variable Calculus, so if you have a different edition, it is up to you to make the correspondence with the correct homework questions. CLASS TESTS: There will be a class test approximately every week, of about 20 minutes duration each. GRADING: Homework: 30% Class tests: 40% Final: 30%
ATTENDANCE POLICY: Students studying at The American University of Paris are expected to attend all scheduled classes, and in case of absence, should contact their professors to explain the situation. It is the student s responsibility to be aware of any specific attendance policy that a faculty member might have set in the course sylus. The French Department, for example, has its own attendance policy, and students are responsible for compliance. Academic Affairs will excuse an absence for students participation in study trips related to their courses. Attendance at all exams is mandatory. In all cases of missed course meetings, the responsibility for communication with the professor, and for arranging to make up missed work, rests solely with the student. Whether an absence is excused or not is always up to the discretion of the professor or the department. Unexcused absences can result in a low or failing participation grade. In the case of excessive absences, it is up to the professor or the department to decide if the student will receive an F for the course. An instructor may recommend that a student withdraw, if absences have made it impossible to continue in the course at a satisfactory level. Students must be mindful of this policy when making their travel arrangements, and especially during the Drop/Add and Exam Periods. ENGLISH LANGUAGE PROFICIENCY STATEMENT: As an Anglophone university, The American University of Paris is strongly committed to effective English language mastery at the undergraduate level. Most courses require scholarly research and formal written and oral presentations in English, and AUP students are expected to strive to achieve excellence in these domains as part of their course work. To that end, professors include English proficiency among the criteria in student evaluation, often referring students to the university Writing Lab where they may obtain help on specific academic assignments. Proficiency in English is monitored at various points throughout the student's academic career, most notably during the admissions and advising processes, while the student is completing general education requirements, and during the accomplishment of degree program courses and senior theses.
Preliminary Class Schedule Class number Day Date Event Topic Content Read 1 Tuesday 10/09/2013 Functions 2 3 4 Tuesday 17/09/2013 5 6 7 Tuesday 24/09/2013 8 9 10 Tuesday 01/10/2013 11 12 13 Tuesday 08/10/2013 14 15 16 Tuesday 15/10/2013 17 18 19 Tuesday 22/10/2013 20 21 midsemester grades due Functions and change Functions (sets, domain, range) - linear and exponential functions Inverse functions; graphs of functions; logarithmic, polynomial and rational functions; transforming functions 1.1, 1.2 1.3, 1.4, 1.6 Trigonometric functions 1.5 Quiz 0! Introduction to continuity and limits 1.7 Quiz 1. Ch1 Quiz 2. Ch 2 Quiz 3. Ch 3 Workshop workshop Quiz 4. Ch 4 Meet the derivative Ways of finding derivatives Ways of using derivatives More applications Meet the DEFINITE integral Zooming in, slope and average rate of change The derivative at a point and the derivative function Interpreting the derivative, second derivatives and differentiability Power rule; derivatives of polynomial, exponential, trig fns The product, quotient and chain rules, derivatives of log fns Linear approximation and the derivative Relating the shape of graphs with 1st and 2nd derivatives Families of functions, optimization, geometry and modeling Marginality, rates and related rates Motivation and definition of the definite integral; Fundamental Theorem of Calculus Interpreting the definite integral, theorems 1.8, 2.1 2.2, 2.3 2.4, 2.5, 2.6 3.1, 3.2, 3.5 3.3, 3.4, 3.6 3.9 4.1 4.2, 4.3, 4.4 4.5, 4.6 5.1, 5.2 5.3, 5.4
22 Tuesday 29/10/2013 Fall break - no class 01/11/2013 23 Tuesday 05/11/2013 24 25 26 Tuesday 12/11/2013 27 28 29 Tuesday 19/11/2013 30 31 32 Tuesday 26/11/2013 33 34 Quiz 5 ch 5 - workshop quiz 6 ch 6 quiz 7 - ch 7 quiz 8 - ch 8 Ways of finding antiderivatives Methods of integration Using the definite integral Modeling with DEs 35 Tuesday 03/12/2013 Revision week Differentiation 36 37 38 39 Tuesday - Tuesday - 13:45 10/12/2013 (make up class) quiz 9 -ch 11! Graphical and numerical approaches, analytic approaches 6.1, 6.2 Differential equations 6.3 Fundamental theorem revisited 6.4 integration by substitution, by parts, by tables Approximation methods - Riemann sums, errors, Simpsons rule Areas, volumes and other geometric applications Applications to physics/economics/probability/stats Differential equations, slope fields and Euler's method Separation of variables, growth and decay Peak oil case and the logistic model Integration Practice exam 7.1, 7.2, 7.3 7.4, 7.5 8.1, 8.2 8.5-8.8 11.1, 11.2, 11.3 11.4, 11.5 11.6, 11.7