MATH 158: Honors Calculus II

Spring 2017

Left: Augustin-Louis Cauchy (1789 – 1857) Right: Bernhard Riemann (1826 – 1866)

Description and goals: A rigorous account of the Riemann integral and the relation between differentiation and integration. We discuss applications of integration in geometry and physics and take a glimpse into the theory of infinite sequences and series. The course provides an opportunity to see how mathematical rigor can actually help better understand intuitive concepts. The official prerequisite of this course is Math 157. However, the true prerequisite is the intellectual curiosity to learn about a nice piece of human knowledge and the willingness to think.

References

Syllabus

Assignments

Announcements:

• 5/24: Check out your COURSE GRADE. Enjoy your summer!

• 5/23: Check out the final exam I & II solutions.

• 5/20: Check out Part I of the Final Exam.

• 5/19: Here are the solutions to a few homework problems in chapters 20-25.

• 5/13: Here are the workshop 3 problems to be discussed on Thursday 5/18. Make sure you think about them ahead of time.

• 4/28: We put Newton's law of cooling to test during lecture yesterday. Here is our experiment's data and discussions.

• 4/27: A short note on the proof of Taylor's theorem.

• 4/7: Check out your grades as of today. Enjoy your (long) spring break!

• 4/6: Check out the second midterm solutions.

• 4/4: Here are the solutions to the remaining homework problems in chapter 19.

• 4/1: Here are the workshop 2 problems to be discussed on Tuesday 4/4. Make sure you think about them ahead of time.

• 3/30: Here are the solutions to most of the homework problems in chapter 19.

• 3/23: Here are the solutions to some of the homework problems in chapter 18.

• 3/22: Enjoy looking at these Cavalieri sculptures.

• 3/21: Check out this note on the proof of the arc-length formula for smooth graphs that we discussed today rather informally.

• 3/8: Check out your grades as of today.

• 3/7: Check out the first midterm solutions.

• 3/3: Here are the solutions to some of the homework problems in chapters 13 and 14 as well as chapter 15 that we did not discuss in class.

• 2/26: Here are the workshop 1 problems to be discussed on Thursday 3/2. Make sure you think about them ahead of time.

• 2/23: The make-up lecture is scheduled for Wednesday March 1, 4:00-5:30 pm in Kiely 244.

• 1/31: Welcome!

General Information and Ground Rules:

• Class lecture meetings are Tuesdays and Thursdays, 11:00 AM - 12:50 PM in Kiely 277.

• Homework is an absolutely essential part of this course. You cannot master the course material without solving many problems consistently throughout the semester. Homework will be assigned on a weekly basis and will be discussed in class, as much as time allows. You are encouraged to work in groups and discuss the problems with one another, but the work that you hand in must be your own write up.

• The course grade is based on the following scheme:
  
  

  Home/Class Work	Two Midterms	Final Exam
  20%	20% each	40%

• The exams schedules are as follows:
  
  

  Midterm I	Midterm II	Final exam
  Tuesday March 7 (in class)	Thursday April 6 (in class)	Tuesday May 23 (in class)

• If a midterm exam is missed because of a documented illness or valid emergency, the course grade will be determined on the basis of the other work done during the semester. Exams missed for other reasons will count as failures.

• At the end of the semester, everyone who has not withdrawn from the class will receive a grade. Incompletes will not be given to avoid F's.

Saeed Zakeri