Math 1aIntroduction to CalculusSpring 2004Course DetailsStaffMatthew Leingang, professorScience Center 323(617-49)[email protected] hours: 1:00-2:00pm Tuesdays and FridaysKeziah Cook, course [email protected]• Functions• Limits• Derivatives• Applications• Introduction to IntegrationPrerequisitesPrecalculus. This includes algebra, the basics of graphing, and acquaintance withtrigonometric and exponential functions. If you are concerned about meetingprerequisites, you may take an online placement test athttp://spade.fas.harvard.edu/placement.Section MeetingsThis course meets Mondays, Wednesdays, and Fridays at 10:00am in Science Center 309.Unlike other courses taught in the calculus sequence this semester (Xb, 1b, 21a, 21b), wemeet in a single section. No sectioning by computer is required.HomeworkHomework will be assigned each class meeting and due the next class meeting. It will bereturned, graded, at the following class meeting. Solutions will be made available on thecourse web site. Late homework will not be accepted. The lowest three homeworkscores will be dropped.Homework problems are themselves an extension of the course material. Cure yourselfof the idea that there is a limited number of “types” of problems in mathematics and thatyour instructor is responsible for showing you how to do each type. Some problems willrequire you to apply the concepts of the lecture to solve problems not explicitly coveredin class.By all means you may work in groups on the homework assignments. However, eachstudent must turn in his or her own write-up of the solutions, with an acknowledgment ofcollaborators. This is in line with good habits of scholarship in general.ExamsThere are two midterm exams, one on Friday, March 12, and one on Monday, April 26.The final exam is tentatively scheduled for Friday, May 21, 2004. No calculators will beallowed on the exams.Exams are to test your mastery of the course topics. Exam problems may be likehomework problems but may also synthesize various parts of the course.GradesYour course grade will be determined as the following weighted average:40%Final20%Midterm I25%Midterm II15%Homework100%TotalTextSingle Variable Calculus, Concepts and Contexts by James Stewart, 2nd edition, ISBN 0-534-37862-5. Available at the Harvard Coop or various online bookstores.There is a companion web site1 to the text, and you may find the Review of Algebra2linked there useful.You might also consider buying a refresher book on precalculus such as Schaum’sOutline.CalendarDateSection(s)Topics2/4 (W)1.1Four ways to represent a function2/6 (F)1.2Mathematical models2/9 (M)1.3New functions from old2/11 (W)1.4Graphing calculators and computers2/13 (F)1.5—1.6Exponential functions, inverse functions, logarithms2/16 (M)No class (Presidents’ Day)2/18 (W)2.1—2.2Tangents and velocities, Limits of functions2/20 (F)2.3Limit laws2/23 (M)2.4Continuity2/25 (W)2.5Limits involving infinity2/27 (F)2.6Tangents, velocities, and other rates of change3/1 (M)2.7Derivatives3/3 (W)2.8The derivative as a function3/5 (F)2.9Linear Approximation3/8 (M)2.10What does € f ' say about f?3/10 (W)3/12 (F)ReviewMidterm I3/15 (M)3.1Derivatives of polynomials and exponential functions3/17 (W)3.2The product and quotient rules3/19 (F)3.3Rates of change in the natural and social sciences3/22 (M)3.4Derivatives of trigonometric functions3/24 (W)3.5The chain rule3/26 (F)3.6Implicit differentiation3/27—4/4Spring Break4/5 (M)3.7Derivatives of logarithmic functions4/7 (W)4.1Related rates4/9 (F)4.2Maximum and minimum values4/12 (M)4.3Derivatives and the shape of curves4/14 (W)4.5Indeterminate forms and L’Hôpital’s Rule4/16 (F)4.6Optimization Problems4/19 (M)4.7Applications to Economics4/21 (W)4.8Newton’s Method4/23 (F)Review4/26 (M)Midterm II4/28 (W)5.1Areas and distances4/30 (F)5.2The definite integral5/3 (M)5.3Evaluating definite integrals5/5 (W)5.4The fundamental theorem of calculus5/7 (F)5.5The substitution rule1 http://www.brookscole.com/cgi-brookscole/course_products_bc.pl?fid=M20b&product_isbn_issn=0534378625&discipline_number=1 is the full URL of the text’s companion web site.2http://www.brookscole.com/math_d/templates/student_resources/shared/Review_of_Algebra.pdf is the URL of the algebra
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