Calculus Math 1a, Spring 2011 Harvard College/GSAS: 8434Course organizationMy name is Oliver Knill. Office hours are Tuesdays and Thursdays and by appointm e nt.LecturesLectures take place Monday Wednesday and Friday from 10 AM to 11 AM in SC 309.Course assistantJulian Bouma ([email protected]) Jeanine Sinanan-Singh (jsinanan-singh@colle ge. h ar vard.edu)Problem SessionsWeekly problem section will be arranged by the course assistant. Tuesday 6-7 PM, Monday 7-8PM. Check with t h e cou r se assi st ant.Exam GroupThis course is in the exam group 1.General EducationThis course, when taken for a letter grade, meets the General Education requirement for Empiri-cal and Mathematical Reasoning or the Core area requirement for Quantitative Reasoning.PrerequisitesA solid precalculus ba ckground is r equ i r ed. This course is recommended for stud ents who score18 or higher on the first p ar t of the Harvard Math Placement Test. You are not expected to havetaken calculus in high school. However, even if you have seen some calcul u s we expect that Math1a will provide you wit h a deeper, more concept ual understa n d i n g of the subject.SynopsisThe development of calculus by Newton and Leibniz is a major achievement of the p as t millennium.The co re of the course introduces differential and integral calculus. Differential calculus studies”rate of change”, integral calculus treats ”accumulation”. The fundamental theorem of calcul u slinks the two. The subject will be applied to problems from other scientific disciplines in home workand lectures.12Course PoliciesClass attendance is expected. In case of reli gi ous holidays, conflicts like a sports competitions orconcert, please send a brief email to the course head.ComputersThe use of computers and computer algebra systems or online tools to experiment with the math-ematical structures is encouraged. We do not have a lab component however in this course. Alsothe use of laptops or tablets in class to take notes is fine. No kind of computers are permittedhowever during exa m s. If you get computer assistance for h om e work it needs to be acknowledgedin the paper.Pass FailThe course may be taken pass/fail after talking to the course head. Note that there is no GenEdcredit for Pa ss/Fail.Textbook”Single Variable Calculus: Concepts and Contexts, 4th Editi on ” by Jam es Stewart (ISBN-10:0495559725 ISBN-13: 9780495559726). The Cabot library has a desk copy available. It isrecommended to read in a book but course material and homework is posted on the websitehttp://www.math.harva rd.edu/˜knill/teaching/math1a 2011 /Grades• 20 percent midterm 1• 20 percent midterm 2• 20 percent homework• 40 percent final examAs in every course, the numerical score needs to be converted to a letter grade. The cutoffs aredetermined when the final distribution is known.Math Question CenterThe mathematics question center MQC is open Sunday through Thursday in SC 309a, 8:30-10:30PM. The rooms are reserved from 7:30 PM on. This drop-in help service is staffed by calculuscourse assistant s who will be available to work with you on your homewor k . You may also stop bythe MQC to find other students in the course. Whi le staffed from 8:30 on, the room is availablefrom 7:30 on in the spring.Bureau of Study Counsel BSC3The bureau of Study councel at 5 Lin den Street is a reso u r ce outside t h e math de p ar t m ent. TheBSC offers one-on-one peer tutoring for a mi n i m al fee st u d y skills and test-taking workshops,counseling, and many other services. The website is http://bsc.harvard. ed uExamsThere are 2 midterm exams and one final exam. Here a r e th e exam d a te s:• 1. M i d t er m : Tuesday, March 1: 7-8:30, Hall D• 2. M i d t er m : Tuesday, April 4: 7-8:30, Hall DExams wil l focus on the mathematics done in the course. Calculus is a huge area. We will followan efficient and int er est i n g pa t h wh ich focuses on stuff we really need.HomeworkHomework i s due at th e beginn i n g of every cl ass. This course has a ”no late homework policy”.But we discar d t h e least 3 h om ework scores.Academic IntegrityThe poli ci es on colla bora t io n ar e the ones establ is h ed by FAS. Collaboration is permitted or evenencouraged for homework but not in exams.Accessible education:Students needing academic adjustments or accommodations because of a documented disabilityneed to submit a letter from the Access ible Education Office (AEO) and speak with the professorby the end of the second week of the term. All discussions remain confidential.Hour by hour syllabusThe following plan is subjec t to sm al l er changes. Please keep updated on the website1. What is calculus? Date Day References---------------------1. What is Calculus? Jan 24 Mon Oliver2. Functions Jan 26 Wed Johnny 1.23. Limits Jan 28 Fri Johnny 2.24 Continuity Jan 31 Mon Johnny 2.45 Intermediate value theorem Feb 2 Wed Johnny 2.46. A fundamental theorem Feb 4 Fri Oliver7. Rate of Change, tangent Feb 7 Mon Johnny 2.68. Critical points Feb 9 Fri Johnny 4.29. Derivative as a function Feb 11 Wed Johnny 2.72. The derivative4-----------------1. Differentiation rules Feb 14 Mon Johnny 3.12. Differentiation rules Feb 16 Wed Johnny 3.23. Extrema and optimization Feb 18 Fri Johnny 4.24. L’Hopital rule Feb 23 Wed Johnny 4.55. Newton method Feb 25 Fri Johnny 4.76 Review for first midterm 3/1/11 Feb 28 Mon Oliver7. Mean value and Rolle theorem Mar 2 Wed Johnny 4.38. Catastrophe theory Mar 4 Fri Oliver3. The integral---------------1. The definite integral Mar 8 Mon Johnny 5.1-22. The fundamental theorem Mar 10 Wed Johnny 5.43. Antiderivative Mar 12 Fri Johnny 5.44. Computing areas Mar 23 Wed Johnny 6.15. Volume of solids Mar 25 Fri Johnny 6.26. Improper integrals Mar 21 Mon Johnny 5.107. Applications of integration Mar 28 Mon Johnny 6.54. Calculus Techniques------------------------1. Chain rule, related rates Mar 30 Wed Johnny 3.42. Implicit differentiation Apr 1 Fri Johnny 3.53 Review for second midterm 4/5/11 Apr 4 Mon Oliver3. Substitution Apr 6 Wed Johnny 5.55. Numerical integration Apr 8 Fri Johnny 5.96. Integration by parts Apr 11 Mon Johnny 5.67. Partial fractions Apr 13 Wed Johnny 5.78. Trig substitutions Apr 15 Fri Johnny 5.75. Calculus and the world-------------------------1. Calculus and Music Apr 18 Mon Oliver2. Calculus and statistics Apr 20 Wed Bryan3. Calculus and economics Apr 22 Fri Oliver4. Calculus and computer science Apr 25 Mon Oliver5. The lighter side Apr 27 Wed