MATH231 Spring 2025: Calculus II

Course Information

Instructor: Xinran Yu

Office: Altgeld Hall 108

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

Course Webpage: https://xinrany.github.io/home/teaching/math231-spring2025.html

Campuswire: This course utilizes Campuswire for posting and answering questions. I will monitor the page during my office hours.

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

Syllabus: Access the syllabus. The course will cover Chapters 7, 8, 10, and 11. You can also refer to the department syllabus.

Class & Office Hours

Class Schedule: MWF 10:00 - 10:50 AM, 1ALLEN-40, Allen Residence Hall

Office Hours: Wednesdays 3:00 - 4:00 PM, 147 Altgeld Hall (floor plan)

Key Dates

• Class Start: January 21
• Spring Break: March 15–23 (No classes)
• Last Day of Instruction: May 7
• Reading Day: May 8

Homework & Extra Practice

Homework

Homework assignments will be posted on Canvas.

Extra Practice

If additional practice is needed, you can refer to the following online resources:

• Paul's Online Notes
• Calculus Problems with Step-by-Step Solutions (Prof. Kouba)
  Includes practice from the "Beginning Integral Calculus" section.
• Prof. Frinkle's Math Page

Lecture Notes

Lecture Notes (Current Version: Apr 2, updates ongoing throughout the semester)

Spring 2022 Notes (Covers nearly the same material)

• Calculus I Review
• Chapter 7
• Chapter 8
• Chapter 10
• Chapter 11

Supplementary Resources

Optional resources for additional insights, proofs, and strategies (not required for exams or homework):

• Simpson's (1/3) Rule:
  • Proof of Simpson's Rule
  • Proof of the Error Bound
• Proofs of Limit Laws (using the definition of a limit of a sequence)
• Ratio and Root Tests:
  • Proof of Ratio Test and Intuition
  • Proof of Root Test and Intuition
• Flowchart for Testing Series Convergence
• Arc Length and Surface Area Summary (in rectangular, parametric, and polar coordinates)

Exam Information

No calculators are allowed for midterms or the final exam.

Midterms

Midterms will take place during regular class time and will cover the specified chapters. Details will be provided closer to the exam dates.

Final Exam

The department will assign the time and location. You can check this on the Course Explorer.
Past Exams

Materials to Memorize

• Chapter 7: Substitution Rule, Integration by Parts, Trigonometric Identities, Improper Integrals
• Chapter 8: Arc Length and Surfaces of Revolution
• Chapter 10: Parametrization, Arc Length, Surfaces of Revolution
• Chapter 11:
  • Geometric Series, Harmonic Series
  • Comparison Tests for Series (Divergence Test, Integral Test, etc.)
  • Absolute and Conditional Convergence

Grading

Grades will be posted via Canvas. Canvas will automatically calculate your raw score once all grading is complete. Homework and exams will not be curved individually, but final grades will be adjusted based on the overall distribution.

Homework (30%)

There will be weekly homework assignments, except during exam weeks. The lowest homework score will be dropped.

Quizzes (15%)

There will be weekly in-class quizzes, each lasting 10 minutes. The lowest two scores will be dropped.

Midterms (30%)

There will be four midterms, all held during regular class time (45 min). No conflict exams or make-up exams will be given. Instead, the lowest midterm score will be dropped.

Final Exam (25%)

Extra Credit (up to 3 points)

Extra credit is available for participation and solving challenging problems. You can earn up to 3 extra credit points through the following:

• Office Hour Participation: Attend office hours and ask math-related questions to earn 1 point per session.
• Extra Credit Problem on Exams: Each exam will include an extra credit problem worth 1 point.
• More extra credit opportunities might pop up during the semester (no promises though :))

Grading Scale