Course Description and Grading Breakdown40% Homework, 30% Midterm, 30% Final The two main aims for the course are: - Becoming familiar with mathematical reasoning, and writing rigorous proofs. - Learning to do explicit calculations. Both aims will be pursued in the context of Calculus: analysis of integration and differentiation of functions, along with closely related topics. The following topics will be covered, roughly in order: - Mathematical Induction
- Completeness
- Functions
- Integral for Step Functions
- Integral for More General Functions
- Applications of Integration
- Limits
- Continuity
- Intermediate Value Theorem
- Inversion
- Extreme Value Theorem
- Integrability Theorem
- Mean - Value Theorem for Integrals
- Derivatives
- Implicit Differentiation
- Extreme Values
- Mean - Value Theorem for Derivatives
- Curve Sketching
- Fundamental Theorem of Calculus
- Integration by Substitution
- Integration by Parts
- Logarithm
- Exponential Function
- Integration by Partial Fractions
- Taylor Series (
*This topic will be mainly covered in Math 1d*)
Course Meeting Time and LocationLectureMonday, Tuesday, Wednesday and Friday 10:00 - 10:55 am 387 Linde RecitationThursday 7:30 - 8:55 pm 387 Linde Course Instructor Contact Information and Office Hours256 Linde Hall e-mail (instructor's first name)@caltech.edu Office Hours: Mondays 1-2pm, or by appointment TA Contact Information and Office Hours:Luciena Xiao:e-mail: xxiao at caltech.edu Office Hours: Sundays 3-4pm, or by appointment Office Hours Location: 302 Linde Hall Course Schedule and TextbookA day-by-day list of topics covered will be posted here during the course:
Lecture Notes:Class notes are in brief summary form. Course PoliciesLate work will not be accepted except for: 1) Medical reasons (requiring a note from the Health Center) 2) Serious personal difficulties (requiring a note from the Dean's Office) AssignmentsWeekly assignments will be posted online on Mondays, and will be due the following Monday. You may discuss the problems with classmates, and are indeed encouraged to do so. However, you must write up your own solutions separately. You may use theorems from the textbook, but you must refer to them clearly. The schedule according to which the homework, midterm, and final will be posted/due is as follows.
Midterm and Final ExamThe midterm will take place during the fifth week, according to the schedule above. The midterm is available here. The password has been emailed to you. For issues accessing the file, please contact Meagan. The exam is due at 4 pm on Monday November 5th. The final will be available to the students on the last day of the course, and due a week later. There will be a practice final posted one week earlier. Here are also the Solutions to the practice final. The final is available here. The password has been emailed to you. For issues accessing the file, please contact Meagan. The exam is due at 4 pm on Friday December 14th. 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. |