MATH231 Spring 2022: Calculus II

Course Information

Instructor: Xinran Yu

Office: Altgeld Hall 108

Email: xinran4@illinois.edu (Please include MATH231 in your email subject.)

Course Webpage: https://xinrany.github.io/home/teaching/math231-spring2022.html

Campuswire: This course will have a campuswire page where you can post and answer questions. I'll monitor campuswire during my office hour.

Textbook: James Stewart, Calculus: Early Transcendentals, 8th edition

Syllabus: Here is the Syllabus. We will cover Chapters 7, 8, 10 and 11 of the textbook, see also department syllabus.

Class & Office Hour

Class: MWF 10-11am, 9 FAR

Office Hour: Thursday 3-4pm.
Office hours are at Altgeld 108 (floor plan) unless the university moves instructions online. In that case, you may use the Zoom link on Moodle.

Spring Break: March 12-20, no class

Reading Day: May 4th, instruction ends

Homework & Extra Practice

• Homework

  Assignments and solutions will be updated in the same document. You can save the link for future use.

  Homework assignments
  Homework solutions

• Extra practice

  If you need extra practice, the following online sources contain problems with solutions.

  • A commonly recommended source is Paul's online notes

  • Prof. Kouba provided a list of Calculus problems with step-by-step solutions. We covered some topics in the "Begining Integral Calculus" section.

    There is also a Calculus II directory where you can find problems only for Calculus II (inside each topic folder, there is an .html file, scroll down to find practice problems.)

  • Prof. Frinkle's Math page search "Calculus II".

Lecture Notes

Supplementary Resources

The following are some supplementary resources such as proofs which you might be interested in though we wouldn't have time to go through. These are not required material for the course, hence will not be tested.

• Simpson's (1/3) rule
  • proof of Simpson's rule
  • proof of the error bound
• Proofs of limit laws
  Here you will see how the definition for the limit of a sequence is used.
• Ratio tests and root test
  • Proof and intuition of ratio test
  • Proof and intuition of root test
• Strategy for testing series
  • Summary of convergence and divergence tests for series
  • How do we know which test to use?
  • Link to a flow chart made by Steven Gubkin
• List of commonly used Taylor series
• Wolfram MathWorld page on Limaçon and Rose curve
  Here are some pictures from those websites.
  
  
• Arc Length And Surface Area Revisited
  The above contains a summary of the arc length and surface area formulae in rectangel coordinates, parametrization and polar coordinates respectively.

Exams

No calculators are allowed for midterms or the final exam.

Midterms will be held during our usual class time. Each midterm will be timed for 45 minutes and there will be 6 questions.

• Midterm 1 will be held during the 5th week on Friday. It will cover Ch7.
• Midterm 2 will be held during the 8th week on Friday. It will cover Ch8-Ch11.4.
• Midterm 3 will be held during the 12th week on Friday. It will cover Ch11.4-11.9.

Final exam will be held on May 9th, 1:30pm - 4:30pm at 9 FAR.

List of materials to memorize

• Chapter 7: substitution rule, integration by parts, trigonometric identity, double angle formulae, improper integrals: definition and the comparison test.
• Chapter 8: arc length and surface of revolution
• Chapter 11:
  • Geometric series, harmonic series.
  • All the comparision tests for series: the divergence test, the integral test, the comparison test, limit comparison test, alternating series test, the ratio and root tests.
  • Absolutely convergence, conditionally convergence, radius and interval of convergence.
  • The power series expansion of 1/1-x for |x| < 1. Also be familar with Taylor's formula and some commonly used Maclaurin series.
• Chapter 10: parametrization of curves, arc length and surface of revolution

Grading

Grades will be posted via Moodle.

Moodle will automatically calculate your raw score when all grading work is done. Homework and exams themselves are not curved but the grade distribution is based on everyone’s final grade.

• Homework (30%)
  • I'll assign handwritten homework rather than online homework. It helps you get used to the format of paper-based exams.
  • There will be eight handwritten homework. All of them are due on Friday, by the end of the class.
  • Generally, missed homework is taken care of with the policy of dropping the lowest two scores. Late homework counts 50% of the grade you get.
• Midterms (40%)
  • There will be three midterms.
  • No conflict exams or make-up exams will be given. Rather, one lowest midterm score will be dropped.
• Final Exam (30%)
• Extra Credit (up to 3 points)
  • Extra credit will be offered in order to encourage your participation in class. You may earn a maximum of 3 points towards your final grade.
  • You may earn extra credit by solving problems (e.g. homework problems, exercises in lectures) on the board. Each problem is worth 1 point.
  The default letter-grade cut-offs are as follows.

  Percentage	Letter Grade
  [97-100]	A+
  [93-97)	A
  [90-93)	A-
  [87-90)	B+
  [83-87)	B
  [80-83)	B-
  [77-80)	C+
  [73-77)	C
  [70-73)	C-
  [67-70)	D+
  [63-67)	D
  [59-63)	D-
  [0-59)	F