Course Description and GradingThis course will introduce the mathematical method through (One Variable) Calculus. By the mathematical method, what we primarily mean is the ability to express oneself with absolute precision, employ critical thinking to approach the problem with the available tools, show clearly the relevant calculations, and then to use logical proofs to establish that certain precise statements are true - in a given context or universally, as the case may be. We assume that Caltech freshmen have a reasonable familiarity with single variable calculus as a computational endeavor, and in this course we emphasize explanations of WHY things work and HOW to justify one's propositions. The underlying concepts will be stressed, as well as the need for checking the hypotheses precisely as to where the results apply. A main focus will be on the writing of complete proofs so the case one is making is ironclad and unassailable. It will emerge that when we do this, we actually know more than the standard computational aspects of single variable calculus and that we can answer questions which are new to us and come up naturally once all the terms in Calculus are carefully defined and the definitions used. Some of these questions are also quite natural from the point of view of the scientist and engineer.
The topics listed below will be treated during the Fall quarter: Mathematical induction The Real numbers, and the preponderance of rational numbers Sequences and Series Continuous Functions Differential Calculus Integral Calculus Polynomial Approximations L'Hopital's rule for 0/0 Improper Integrals Complex Numbers and functions Integral Tests, Abel summation for series The course will be graded on a pass/fail system, based on the
with the following breakdown: 60% HW sets, 20% each for Midterm and Final
60% HW (first four sets), 40% Midterm Exam score Grading Scheme for Shadow midterm grade (this is NOT the final grade, just for the term so far): A+ 97-100 A 90-96 A- 86-89 B 83-86 B 69-82 B- 65-68 C+ 61-64 C 54-60 D 50-53 F 1-49 Course Meeting Time and LocationLectureMonday, Tuesday, Wednesday and Friday 10:00 - 10:55 am Baxter Lecture Hall Course TextCALCULUS, volume 1 (second edition), by Tom Apostol Course Instructor Contact Information and Office HoursTA Contact Information and Office HoursHead TA: Victor
Lecture Notes
Course PoliciesLate work: Each student can turn in at most one homework late without penalty. You must contact the TA of your assigned section number and notify them beforehand in order to use this policy. Otherwise, there will be a heavy penalty for late work but we will still grade it. Late work can only be accepted up to 1 week after the original due date, when solutions will be posted. Exceptions are given only with note from the Health Service or the Dean. This policy will be strictly enforced.Final deadline for all late work: All outstanding work must be turned in before or with the final exam, because the graders leave for the winter break and be unable to grade.Section Recitations: Any student can attend any section or office hour, regardless of the assigned section number. But the earliest opportunity to collect graded work is during the recitation for your assigned section number, when the TA hands it out. Afterwards it will be put in the drop box.Questions about graded work: If you have a confusion about the grading if your homework, please first look at the posted solution and the grading rubric. After that, if you still need to please refer to grading schedule below and contact the TA who graded the problem.Homework 1, 3, 6, 8: Problem 1 - Victor, Problem 2 - Lingfei, Problem 3 - Kushal, Problem 4 - Frid Homework 2, 4, 7, 9: Problem 1 - Konrad, Problem 2 - Luciena, Problem 3 - Jiaxin, Problem 4 - Allen Some homeworks have a problem 5, whenever this is the case, Konrad is grading it. EXCEPTIONS: HW7 and HW8: Lueicena and Lingfei are switching grading duties HW9: Jiaxin is grading for Allen Final Exam: 1. Konrad 2. Victor, Kushal, Luciena, Frid 3. Lingfei 4a: Luciena 4b: Jiaxin 5. Kushal, Frid AssignmentsMidterm and Final ExamThe midterm is due on Tuesday, November 5 at 10:01 AM, and is available here. Please check your email for accessing the file linked to this course page. The midterm review session is 3pm Sunday Nov 3 in Linde 387. It is aimed to last 90 minutes.The final exam is due Wednesday, Dec 11 at 10:01 am, and is available here. Grading will begin soon after the due time. The final review session is 3pm Sunday Dec 8, in Bridge 201. It is aimed to last 90 minutes.Collaboration Table
* You may use a computer or calculator while doing the homework, but may not refer to this as justification for your work. For example, "by Mathematica" is not an acceptable justification for deriving one equation from another. Also, since computers and calculators will not be allowed on the exams, it's best not to get too dependent on them. |