Math 152 (Calculus II for Math and Physical Sciences) is a continuation of Math 151, and is part of the three-semester calculus sequence for the mathematical and physical sciences at Rutgers University, New Brunswick. Math 152 covers the integral calculus and its applications, the theory of infinite series and power series, parametric curves, polar coordinates, and complex numbers.

All sections of Math 152 (other than asynchronous online sections) will have two lecture meetings and one workshop meeting per week. The Lecturer presents the course material during the lecture meetings. The workshop class is a smaller meeting with a Workshop Instructor (WI), where students engage in group work to solve in-depth problems related to the content delivered in the lectures. Workshops typically require students to complete a pre-class assignment, a write-up of their in-class activity results, and a short quiz following the problem-solving session. The workshop problems will form the basis for some of the problems that students will encounter on midterm quizzes and on the final exam.

The required textbook is *Thomas' Calculus: Early Transcendentals* (15th edition), by Hass, et al. with MyMathLab access code. You may use either the hardcover edition or the eBook; they contain exactly the same material. Both are available through the Rutgers bookstore, and the eBook can be purchased directly through the course canvas page.

- The ISBN for the
**physical textbook**with MyMathLab access is 978-0137559756. - The ISBN for the
**eBook**with MyMathLab access is 978-0137560103.

Math 152 covers parts of Chapters 5, 6, 8, 10, 11 and 18 of the textbook. The course sets the following learning goals for each student:

- To use integrals to find volumes, arc lengths, and surfaces of revolution.
- To find antiderivatives using techniques including u-substitution, integration by parts, and trigonometric substitution.
- To determine whether an infinite series converges, and to find and user Taylor series and Taylor polynomials.
- To use derivatives and integrals with parametric equations, and with equations defined in polar coordinates.
- To use polar and exponential forms of a complex number.

A more detailed list of learning goals can be found here.

**Typical Lecture Schedule **(may vary slightly by semester)

Lecture | Textbook Sections | Topics |

1 | 5.3, 5.5, 5.6, 8.1 | Review of basic integration formulas, average value, u-substitution, and area under curves |

2 | 6.1 | Volume by cross-sections (including disk/washer method) |

3 | 6.2 | Volume by shells; other applications |

4 | 6.3 | Arc length and surface area |

5 | 6.4 | Arc length and surface area |

6 | 8.2 | Integration by Parts |

7 | Midterm Exam 1 | |

8 | 8.3 | Trigonometric integrals |

9 | 8.4 | Trigonometric substitution |

10 | 8.8 | Improper Integrals |

11 | 10.1 | Sequences |

12 | 10.2 | Infinite series |

13 | 10.3 | The Integral Test |

14 | Midterm Exam 2 | |

15 | 10.4 | Comparison tests |

16 | 10.5 | Ratio/Root tests and absolute convergence |

17 | 10.6 | Alternating series and conditional convergence |

18 | 10.7 | Power series |

19 | 10.8 | Taylor and Maclaurin series |

20 | 10.9 | Convergence of Taylor series |

21 | 10.1 | Applications of Taylor series |

22 | Midterm Exam 3 | |

23 | 11.1, 11.2 | Parametrizations of plane curves; Calculus with parametric curves |

24 | 11.3,11.4 | Polar coordinates; graphing polar equations |

25 | 11.5 | Areas and lengths in polar coordinates |

26 | 18.1 | Arithmetic and Geometry of Complex Numbers |

27 | 18.1 | Euler's Theorem and Polar Forms of Complex Numbers; Finding complex roots of polynomials. |

Specific course information, resources, and policies for the current semester are available to course registrants through the Math 152: All Sections Canvas site.