Spring: Calculus and Analytic Geometry 2 (Math 222)

INSTRUCTOR:
Botong Wang, Van Vleck Assistant Professor, (wang@math.wisc.edu)

TEACHING ASSISTANTS:

Discussion section 321 and 324: Li, Yining (yli525@wisc.edu)
Discussion section 323 and 326: Branman, Benjamin (BRANMAN@WISC.EDU)
Discussion section 325 and 331: Julian, Ryan (mrjulian@math.wisc.edu)
Discussion section 327 and 329: Wang, Weitong (wwang374@wisc.edu)
Discussion section 328 and 330: Shi, Ziming (zimingshi@math.wisc.edu)

LECTURES:

TTh 9:30-10:45AM, Room VAN VLECK B102

DISCUSSION SESSIONS:

Section Time Location Teaching Assistant
321 MW 8:50-9:40AM B317 Van Vleck Hall Li, Yining
323 MW 9:55-10:45AM B317 Van Vleck Hall Branman, Benjamin
324 MW 9:55-10:45AM B329 Van Vleck Hall Li, Yining
325 MW 11:00-11:50AM B309 Van Vleck Hall Julian, Ryan
326 MW 11:00-11:50AM B211 Van Vleck Hall Branman, Benjamin
327 MW 1:20-2:10PM B329 Van Vleck Hall Wang, Weitong
328 MW 1:20-2:10PM B309 Van Vleck Hall Shi, Ziming
329 MW 2:25-3:15PM B231 Van Vleck Hall Wang, Weitong
330 MW 2:25-3:15PM B211 Van Vleck Hall Shi, Ziming
331 MW 3:30-4:20PM B223 Van Vleck Hall Julian, Ryan

OFFICE HOURS:

Instructor / TA Disscusion Section Time Location
Botong Wang Lecture We 10-11AM, Th 2:30-3:30PM 403 Van Vleck Hall
Li, Yining Section 321 and 324 Tu 4-6pm 618 Van Vleck Hall
Branman, Benjamin Section 323 and 326 Tu 11-12AM, Friday 10-11AM 818 Van Vleck Hall
Julian, Ryan Section 325 and 331 Mo 12-1PM, Tu 1-2PM 518 Van Vleck Hall
Wang, Weitong Section 327 and 329 MoWe 11AM-12PM 101-14 Van Vleck Hall
Shi, Ziming Section 328 and 330 Mo 3:30-4:30PM, We 12:10-1:10PM 722 Van Vleck Hall

DESCRIPTION:

This course will cover second semester calculus, including: techniques of integration; improper integrals; Taylor expansions; elementary differential equations; sequences and series; and an introduction to vectors.

TEXTBOOK:

There is no commercial textbook for Math 222. Instead we use the math department Calculus Notes, which can be bought in room B227 Van Vleck Hall during the first week of class, or at the reception desk on the 2nd floor thereafter. Our textbook is also available here.

GRADE:

Homework: 10%
Quizzes at discussion session: 10%
Midterm 1: 20%, Midterm 2: 20 %, Final exam: 40%.
The final grade will be curved.
The homework will be assigned weekly on Tuesday and will be posted online (see bellow), and due on the discussion session the following Monday.
There will be weekly quizzes on Wednesday. The lowest quiz grade will be dropped.

MIDTERM AND FINAL EXAMS:

Midterms 1 and 2 will be in class. The first Midterm will be on February 23rd, and the second Midterm will be on March 30th. The final exam will be on Sunday, May 7, from 7:25pm to 9:25pm at SOC SCI 6210. The scale for Midterm 1 is here.

All exams are closed book exams. Books, tablets, cellphones, computers, headphones, and calculators will not be permitted for exams. Bring ONLY your student ID, and pencils or pens to all exams.

If you are eligible for special consideration on exams, please let me know as soon as possible, so that I can ensure that your needs are accommodated.

Make-up exams will be considered only if there is a conflict with another university-related event, or a last-minute medical/family emergency. In the former case you need to contact me or your TA as soon as possible. In the later you need to show proof of such emergency (doctor's notes, for example).

Some old exams and practice exams can be found here.

HOMEWORK AND QUIZ POLICY:

Where there is a conflict with other university-related events, students are allowed to submit homework earlier than deadline, or to arrange a quiz before the discussion session. No late homework is accepted. There will be no make-up quizzes.

BRIEF LECTURE SCHEDULE:

We plan to follow the following schedule.

  • Week 1: Techniques of integration: trigonometric integrals/ integration by parts
  • Week 2: Techniques of integration: trigonometric and rational substitutions
  • Week 3: Techniques of integration: partial fractions and reduction formulas
  • Week 4: Improper integrals: definition and examples
  • Week 5: Improper integrals: estimating and convergence
  • Week 6: Differential equations: separable and linear
  • Week 7: Differential equations: direction fields, Euler's method, applications
  • Week 8: Taylor expansions: examples of Taylor polynomials
  • Week 9: Taylor expansions: the remainder term /Lagrange's formula
  • Week 10: Taylor expansions: little oh notation and algebraic manipulations
  • Week 11: Taylor expansions: differentiation and integration
  • Week 12: Sequences and series: definitions and examples of sequences and series
  • Week 13: Sequences and series: convergence of Taylor series
  • Week 14: Vectors: definition, dot product, equation of line
  • Week 15: Vectors: equation of plane, cross product

    HOMEWORK:

  • Homework 1, Due Jan 30: I.4, Problem 1, 2, 4, 5, 6, 7, 10, 12.
  • Homework 2, Due Feb 6: Section I.7, Problem 1, 4, 11, 15. Section I.9, Problem 2(b), 3, 7, 20, 21, Section I.13, Problem 3, 6.
  • Homework 3, Due Feb 13: Section I.15, Problem 1, 3, 8, 10, 16. Section II.4 Problem 1, 5, 10, 13, 18.
  • Homework 4, Due Feb 20: Section II.4, Problem 15, 20. Section II.6 Problem 3, 4, 5, 12, 13, 15.
  • Homework 5, Due Mar 6: Section III.4, Problem 2, 5, 7. Section III.6, Problem 1, 3, 4, 6, 9, 11, 13.
  • Homework 6, Due Mar 13: Section III.9, Problem 1, 2, 3. Section III.11, Problem 1, 2, 3, 7, 8.
  • Homework 7, Due Mar 27: Section IV.4, Problem 1, 3, 4, 7, 10, 15, 17, 19, 22, 31, 35. Section IV.7, Problem 1, 2, 3, 4. (The problems in Section IV. 7 will not be graded. )
  • Homework 8, Due April 10: Section IV.9, Problem 1, 2, 3, 8, 9, 12, 14(a)(c), 22, 29, 34
  • Homework 9, Due April 17: Section V.3, Problem 1, 2, 3, 4, 5, 6, 7, 8, 9.
  • Homework 10, Due April 24: Section V.6, Problem 1, 4, 5, 8, 9, 11, 15, 16.
  • Homework 11, Due May 1: Section VI.9, Problem 1, 2, 4, 6(a)(c), 8. Section VI.10, Problem 2, 3, 4. Section VI.11, Problem 1, 2. Section VI. 12, Problem 1, 2, 3, 5. Section VI. 13, Problem 1, 2, 6, 8.