Course Description
This course will introduce the mathematical method through (One Variable) Calculus. By the mathematical method, what we primarily mean is the ability to express one's self with absolute precision, and then to use logical proofs to establish that certain precise statements are universally true. We assume that the Caltech freshman has 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 and the real number system. Sequences and Series Continuous Functions Differential Calculus Integral Calculus Polynomial Approximations L'Hopital's rule for 0/0 Improper Integrals Integral Tests, Abel summation for series Complex Numbers Course Meeting Time and Location
LectureMonday, Wednesday and Friday
10:00 - 10:55 am
Baxter Lecture Hall
RecitationAll recitations take place on Thursday
TA Contact Information and Office Hours
Wednesdays 18:00 - 19:00 in 387 Linde Thursdays 17:00 - 18:00 in 187 Linde Fridays 18:00 - 20:00 in 387 Linde Saturdays 18:00 - 20:00 in 387 Linde Sundays 14:00 -17:00 in 387 Linde
Course Administrator156 Linde Hall 626-395-4336 Instructor and Office Hours277 Linde Hall
F: 3-5 pm Course Ombudspersons
Notes: written by D.Ramakrishnan (with figures by M.Mnatsakanian)
Course PoliciesEveryone will be allowed to submit one HW solution set late, but he/she/they will need to arrange it with the relevant TA, and abide by when it is required by the TA to be turned in.
Assignments
Midterm and Final ExamThe midterm exam is available here. The password was emailed to you. If you have issues accessing the exam, please contact Meagan. The exam will be due on Monday November 5th at 9:01 am. Midterm review with Josh Lieber - Saturday November 3rd, 7 - 9 pm in B127 GCL (Building #26). The solutions for the midterm exam are now available here. The final exam is available here. The password was emailed to you. If you have issues accessing the exam, please contact Meagan. The exam is due on Wednesday December 12th at 9:00 am.
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. |