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## 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.

## 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 and 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 [email protected], 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 Spring 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, meeting ID 874 4669 1935; passcode: 2023

Hours: Mon, Wed 10-6; Tue, Thur 10:30-8:30; Fri 12-5; Sat 12-5; Sun 5-10 pm

Tutoring sessions for Math 190, 195, 205, 209, 201, 212, and Eco 102

.- - - - - -

Marshak Center: In-person tutoring is available in Marshak, Room 106, Monday, Tuesday and Thursday 11am-6pm, Thursday 11am-5pm and Friday 11am-4pm. No appointment necessary. Available Jan 29 through May 22, except Feb 12, Feb 19, and Apr 22--Apr 30.

For more information please email the Tutor Coordinator, Andy Trafford, at [email protected]

- CLO.pdf : Course and Department Learning Objectoves
- Math212SampleFinalExamRevMay2024 : Sample Final Exam
- Math212SampleFinalExamSolutionsRevMay2024 : Sample Final Exam Solutions
- Math212-Syllabus-Homework2a : Math212-Syllabus-Homework Effective Spring 2024
- Math212-Syllabus-Homework3 : Math 212 Syllabus and Homework End After Fall 2023
- 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

For Spring 2024, the following sections are being offered:

Historical offerings

- 4/10/2024: CCNY Physics Club to host Integration Bee, April 16 and 18.
- 2/27/2024: Vladimir Shpilrain wins interdisciplinary grant
- 1/26/2024: New Faculty Member Dr. Sánchez-Muñiz for Spring 2024
- ... more news

## Course Resources

Problem sets.

This course contains problem sets that accompany each section and module. In these problem sets, students are given an opportunity to apply the quantitative-reasoning skills they learned throughout the module.

Answers are only available to the problems with “Show Solution” links below the question prompt.

## Module 1: Integration

- Problem Set: Approximating Areas
- Problem Set: The Definite Integral
- Problem Set: The Fundamental Theorem of Calculus
- Problem Set: Integration Formulas and the Net Change Theorem
- Problem Set: Substitution
- Problem Set: Integrals Involving Exponential and Logarithmic Functions
- Problem Set: Integrals Resulting in Inverse Trigonometric
- Module 1 Review Problems

## Module 2: Applications of Integration

- Problem Set: Areas Between Curves
- Problem Set: Determining Volumes by Slicing
- Problem Set: Volumes of Revolution: Cylindrical Shells
- Problem Set: Arc Length of a Curve and Surface Area
- Problem Set: Physical Applications
- Problem Set: Moments and Centers of Mass
- Problem Set: Integrals, Exponential Functions, and Logarithms
- Problem Set: Exponential Growth and Decay
- Problem Set: Calculus of the Hyperbolic Functions
- Module 2 Review Problems

## Module 3: Techniques of Integration

- Problem Set: Integration by Parts
- Problem Set: Trigonometric Integrals
- Problem Set: Trigonometric Substitution
- Problem Set: Partial Fractions
- Problem Set: Other Strategies for Integration
- Problem Set: Numerical Integration
- Problem Set: Improper Integrals
- Module 3 Review Problems

## Module 4: Differential Equations

- Problem Set: Basics of Differential Equations
- Problem Set: Direction Fields and Numerical Methods
- Problem Set: Separable Equations
- Problem Set: The Logistic Equation
- Problem Set: First-order Linear Equations
- Module 4 Review Problems

## Module 5: Sequences and Series

- Problem Set: Sequences
- Problem Set: Infinite Series
- Problem Set: The Divergence and Integral Tests
- Problem Set: Comparison Tests
- Problem Set: Alternating Series
- Problem Set: Ratio and Root Tests
- Module 5 Review Problems

## Module 6: Power Series

- Problem Set: Power Series and Functions
- Problem Set: Properties of Power Series
- Problem Set: Taylor and Maclaurin Series
- Problem Set: Working with Taylor Series
- Module 6 Review Problems

## Module 7: Parametric Equations and Polar Coordinates

- Problem Set: Parametric Equations
- Problem Set: Calculus of Parametric Curves
- Problem Set: Polar Coordinates
- Problem Set: Area and Arc Length in Polar Coordinates
- Problem Set: Conic Sections
- Module 7 Review Problems
- Problem Sets. Provided by : Lumen Learning. License : CC BY: Attribution
- Puzzle Pieces. Authored by : LAFS. Provided by : Noun Project. Located at : https://thenounproject.com/term/puzzle-pieces/963732/ . License : CC BY: Attribution

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