MATH162 -Calculus II, Summer 2025 (MATH 162-01)
Course Information.
Course Blackboard.
Instructor:
Debanshu Ghosh.
Email: dghosh5@ur.rochester.edu
Office: Hylan 910.
Lecture: MTWTh, 9:00 AM - 11:30 AM.
Office Hours: MW 2:00 PM - 4:00 PM and by appointment.
Delivery Mode: We will use the same Zoom link for the lectures, recitations, and office hours. See Blackboard for the meeting link.
Course Description: Applications of integration, including areas, volumes, and arc length; techniques of integration such as partial fractions and improper integrals; calculus of parametric curves and polar coordinates; sequences and series, with convergence tests including comparison, integral, alternating series, ratio, and root tests; Taylor and Maclaurin series.
Learning Outcomes: This course provides an introductory exploration of integral calculus and infinite series, helping students build intuition and problem-solving skills by computing areas, volumes, and arc lengths; applying integration techniques; working with parametric and polar curves; and analyzing the convergence of sequences and series, including Taylor and Maclaurin expansions.
Attendance and Course Access: Attendance is not mandatory but strongly recommended. All lecture recordings and handwritten notes will be provided to support your learning. However, during exams, all students must be present on Zoom. Please see the course information for detailed requirements.
Prerequisites: Successful Completion of MATH 161 or MATH 171 with a C- or better is required.
Textbook: Calculus: Early Transcendentals by James Stewart
Grading: WeBWorK (30%), Midterm (30%), Final (40%).
See the course information for more details.
Important Dates:
First day of Class: Monday, May 19th.
Midterm: Monday, June 2 (2 hours during class).
Final Exam: Monday, June 23 (During class hour, this is also the last day of class).
WeBWorK: A total of 9 sets will be assigned throughout the course. Those will typically be due on Tuesdays and Fridays at 11:59 PM. Your lowest individual WeBWorK score will be dropped from the final grade calculation.
Lecture notes: These notes closely follow the 8th edition of Calculus: Early Transcendentals, the official textbook for this course. I have kept the section numbering aligned with the book so you can easily refer to it for more detailed explanations. The handwritten notes may contain typos; please let me know if you spot any. Class recordings are available on Blackboard.
Lec 1.2 Applications of Integration.
Lec 1.4 Average length and Integration by Parts.
Lec 2.1 Trigonometric substitution and Partial Fractions.
Lec 2.2 Partial fractions and Arc length.
Lec 3.1 Parametric Equations and Polar Coordinates.
Lec 3.2 Polar Coordinates and Introduction to Sequences.
Lec 4.1 Introduction to Series.
Lec 4.2 Test of Divergence and Integral Test.
Lec 4.3 p-Test and Comparison Test.
Lec 4.4 Alternating Series Test and Conditionally Convergent.
Lec 5.1 Root and Ratio Test and Introduction to Power Series.
Lec 5.2 Taylor and Maclaurin Series.
Lec 5.3 Application of Taylor Series and Review of what we did so far.
Exam Paper: Midterm Paper [Solution], Final Paper [Solution].
Many additional materials are available on Blackboard, including past exam papers and recitation questions.