Mark Haskins
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Honors One Variable Calculus 110.111, MTW 3-4pm, 12 Gilman Dr Mark Haskins Department: Mathematics E-mail: mhaskin@math.jhu.edu Office: Krieger 312, Tel: 410-516-4047 Office Hours: Tues 9.30-10.30, 4-5, Weds 9.30-10.30 TA/grader: He Office: TBA Office hours: TBA |
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HW1: due Sept 16 (basic properties of numbers of various kinds) HW2: due Sept 23 (basic properties of functions) HW3: due Sept 30 (limits) HW4: due Oct 7 (continuity) HW6: due Oct 21 (thms on continuity on a closed interval) HW7: due Oct 28 (least upper bounds, proofs of thms on continuity on a closed interval, uniform continuity) HW8: due Nov 4 (differentiable functions) HW9: due Nov 11 (more on differentiation) HW10: due Nov 18 (Mean Value Theorem) HW11: due Nov 25 (L'Hopital's Rule) HW12: due Dec 2 (Inverse functions) HW13: due Dec 9 (convexity and more inverse functions) |
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This is a new course for Fall 2002. Here is the official course description from the catalog. "This sequence is an honors version of 110.108-109, and meets the general education requirement for Calculus I and II. It is a more theoretical treatment of one variable Calculus than in 110.108-109, and is based on our modern understanding of the real number system as explained by Cantor, Dedekind and Weierstrass. It's by invitation only to students who have excelled on the advanced placement test. Such students who want to know the 'why's' of Calculus as well as the 'how to's' will find this course very rewarding. " More about the course and how to get to take it: Supplement to Math Placement, p18 of the Freshman Academic Handbook NOTE: The placement test for the class will take place on Tuesday, September 3, from 2-4pm in Krieger 205. Any student eligible for and needing academic adjustments or accommodations due to a disability is requested to speak with the professor no later than September 25. |
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The main text for the course is "Calculus" by Michael Spivak. In the course of the two semesters we will aim to cover most of the book. |
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The course grade will be determined as follows: Homework: 25% Homework will be assigned Monday and due the following Monday. Homework will be collected at the beginning of class on Monday. Late homework will not be accepted. Missing homework counts as as 0. The purpose of the homework is to gain better understanding of the material. You are encouraged to discuss the homework problems with each other. You must, however, write up your own homework solutions. Copying another student's homework is a violation of academic integrity and will be dealt with accordingly. Midterms: 20% There will be two in class exams, one on Tuesday October 8, and one on Monday November 11. The first exam is scheduled so that the grades will be available before the final add/drop date. Final Exam: 35% The final exam will take place during the regularly scheduled time for a class meeting MTW 3-4. That is Saturday, December 14 from 9-12am. There will be no make-up exams. For excused absences, the grade for a missed exam will be a weighted average of subsequent exam grades. Unexcused absences count as a 0. Documentation of illness etc. must be obtained from the Office of Academic Advising. Any request for a grade change on a midterm or homework must be submitted within one week from the time the papers are first handed back to students. |
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In the Fall Semester we will aim to cover Chapters 1 to 12 of Spivak, plus possibly the Epilogue. We may also cover some material from other sources. The main themes of the fall semester are continuity and differentiability of real valued functions. In the Spring Semester we will cover the remainder of Spivak i.e. Chapters 13-27. The main themes of this semester are integration, its relation with differentiation, and infinite sequences and series. An outline for the first four weeks of class: Week 1: (Chapters 1 and 2 of Spivak) Basic properties of numbers (axiomatic) - natural numbers and mathematical induction, rational, irrational, real numbers. Proofs of irrationality of some simple irrational numbers. Week 2: (Chapters 4 and 5) Basic properties of real valued functions - domain, range, sums, products, quotients, function composition, one-to-one functions, onto functions, inverse functions, odd/even functions.. Week 3: (Chapters 5 and 6) Basic properties of limits - heuristic and rigorous definitions of the limit of a function near a point, limits of sums, products, etc. Basic properties of continuous functions - heuristic and rigorous definitions of continuity of a function at a point. Sums, products, quotients, compositions of continuous functions are continuous. Week 4: (Chapters 6 and 7) More on continuous functions. Statements of 3 fundamental theorems on continuous functions and some of their consequences. (Proofs of these theorems will be given in Week 5) |
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The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition. Report any violations you witness to the instructor. You may consult the associate dean of students and/or the chairman of the Ethics Board beforehand. See the guide on "Academic Ethics for Undergraduates" and the Ethics Board web site ( http://ethics.jhu.edu ) for more information. |
| Mark Haskins |