Math 21200: Calculus II

Supervisor: Niel Shell

Techniques of integration, exponential growth and decay, separable differential equations, improper integrals, infinite sequences and series, polar coordinates, areas in polar coordinates, geometry of space, and quadric surfaces.

Prerequisite: Grade of C or higher in Math 20100 or placement by the Department. (Part of sequence 20100, 21200, 21300.) 4 hr./wk.; 4 cr.

CAREER: undergraduate

CATEGORY: regular

TERM OFFERED: Fall, Spring, Summer

Textbook: Calculus: Early Transcendentals (9th edition), Stewart, Clegg and Watson (Cengage)

This is the text, effective Spring 2024.

Important Supplements to Textbook: Notes1a and Notes5a and 5b

The following topics are in the syllabus, but are not discussed in the text:

Notes1a: The Limit Comparison Test for Improper Integrals is not in Section 7.8

Notes5a: Right-handed Coordinate Systems, Shifts, Reflections and Symmetry, the General Definition of Cones, and Intercepts are not in Section 12.1

Notes5b: A discussion of why the standard listing of the Quadric Surfaces are the only non-degenerate Quadric Surfaces is not in Section 12.6

These Notes in the Documents below are essential supplements to the text.

Syllabus and Homework

The syllabus that went into effect Fall 2022 has not changed. "Math 212 Syllabus and Homework Effective Spring 2024" document below has been updated for use with the current textbook. It consists of three parts:

First, a table in which the first three columns constitute the syllabus and in which the fourth column contains a suggested list of homework problems from the text.

Second, a supplementary set of suggested homework problems which are not from the text. The supplementary problem numbers are preceded by an "s." For example, in the suggested homework problems for Section 7.2, the entry s1 refers to supplementary problem 7.2/s1.

Third, answers and selected solutions to all even numbered suggested problems from the text and all supplementary problems.

For the convenience of students who have access to the Thomas's Calculus: Early Transcendentals, the "Math 212 Syllabus and Homework End After Fall 2023" pdf for that text has been kept to provide additional exercises. Copies of both the 14th or 15th edition will be placed on reserve at both the NAC library and the Marshak library.

All of the suggested problems from that text are in both the 14th and 15th editions, usually with the same number. If the 14th and 15th edition numbers for a problem are different, the listing shows, for example, 53(51), that the problem is listed as number 53 in the 15th edition and number 51 in the 14th edition. Information about online homework problems will be included when available.

ONLINE HOMEWORK: Ask your instructor for a link to your webwork online homework.

The login is the name of you CCNY mail address: For example, my email is nshell@ccny.cuny.edu, so my webwork name is nshell. The password is the same as your CCNY email password.

Spring 2019 through Summer 2022 Math 212 Calculus II with Introduction to Multivariate Functions

Math 212 (4 hours/4 credits) replaced Math 202 (4 hours/3 credits) as part of a plan to replace the previous calculus sequence consisting of Math 201, 202, 203 and part of 392 with a three semester sequence. This version of Math 212 was changed, effective Fall 2022, to make it comparable to Calculus II in other CUNY schools. Vectors, parametric equations and the introduction to multivariate functions were deleted from the syllabus, and exponential growth and decay, separable differential equations and areas using polar coordinates were added.

Tutoring for Fall 2024

There are two places on campus where you can find help, The Artino Math Tutoring Center and The Marshak Math/Physics Tutoring Center:

Artino Center: Monday-Friday, Room NAC 1/511; remote Saturday-Sunday; all days follow the college academic calendar meeting ID 874 4669 1935; passcode: 2023

Hours: Mon, Tue, Thur 11-6; Wed 11-5; Fri 11-4.

Tutoring sessions for Math 150, 173, 180/185, 190/195, 205/209, 201/212/213, 346 and 391

.- - - - - -

Marshak Center: From January 27 to May 22, in-person tutoring is available in Marshak, Room 106, Monday, Tuesday and Thursday 11am-6pm, Wednesday 11am-5pm and Friday 11am-4pm. No appointment necessary.

Exceptions to the above are as follows:

Wednesday, January 29th CLOSED

Wednesday, February 12th CLOSED Monday, February 17th CLOSED Tuesday, February 18th Monday Schedule

Thursday, March 6th Wednesday Schedule Monday, March 31st CLOSED

Monday, April 14th – Friday, April 18th CLOSED

For more information please email the Tutor Coordinator, Andy Trafford, at atrafford@ccny.cuny.edu

Documents

• CLO.pdf: Course and Department Learning Objectoves
• Math212SampleFinalExamRevMay2024: Sample Final Exam
• Math212SampleFinalExamSolutionsRevMay2024: Sample Final Exam Solutions
• Math212-Syllabus-Homework3: Math 212 Syllabus and Homework End After Fall 2023
• Math212-Syllabus-Homework-Current: Math 212 Syllabus-Homework Effective Spring 2024
• Notes1: Integration, Change of Base, Exponential Change, Rate of Growth of Functions
• Notes1a: Limit Comparison Test for Improper Integrals
• Notes2: Sequences, Series of Real Numbers
• Notes3a: Power Series: Interval of Convergence
• Notes3b: Power Series: Representing Functions, Numerical Approximation
• Notes4: Polar Coordinates
• Notes5a: 3-Dimensional Coordinate Systems
• Notes5b: Conic Sections and Quadric Surfaces

Sections

For Summer 2025, the following sections are being offered:

Historical offerings