L’Hospital’s rule and proof first in a particular case, then in the general case. Your course grade will be determined by your cumulative average at the end of the quarter. Here are self-contained notes on the Weierstrass Function , which is continuous but nowhere differentiable. Relationship between integration and differentiation. Continuous functions are integrable. It will be expected that you read the assigned material in advance of each lecture.
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All posted reading and homeowork assignments will refer to matj chapter and section numbers of this textbook. Least square properties of Fourier partial sums. Proof of Parseval’s theorem first for continuous functions, then in general.
It will allow you to post messages openly or anonymously and answer posts made by your fellow students, about course content, homework, exams, etc. It will be expected that you read the assigned material in advance of each lecture.
Midterm II Friday, May Monotonic functions are integrable.
You are expected to write as you would in any professional correspondence. Lower and upper integrals.
Homework 2due Friday, April 8. Uniform limit of continuous functions is continuous.
Homework 3due Friday, April The due date of some of the problem sets may change during the quarter depending on the pace at which we cover the relevant 140bb. Example of a function which is continuous but nowhere differentiable. Riemann’s criterion for integrability. APM Office hour: L’Hospital’s rule and proof first in a particular case, then in the general case.
Regrading maath not possible after the exam leaves the room.
Syllabus Welcome to Math B: Students may not receive credit for both Math B and Math B. Intermediate value property and derivatives.
However, the work you turn in must be your own. Uniform convergence implies equicontinuity. Your cumulative average will be the best of the following two weighted averages: We will use TritonEd formerly known as Ted to disseminate grades.
We will use Piazzaan online discussion board. No calculators or other electronic devices will be allowed. Properties of the integral: Posts about homework or exams on Piazza should be content based.
Uniform convergence and differentiability. There will be two midterm exams given on April 26 and May In addition, here are a few of our expectations for etiquette in and out of class. Refinements of partitions and effects on upper and lower sums. We will be communicating with you and making announcements through an online question and answer platform called Piazza sign up link: Homework assignments are posted belowand will be due at 5: Homework 8due Friday, May Memorial Day, no class Friday, June 9:
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