# Rutgers Math 136 -- The standard syllabus

Textbook for Summer 2003/Fall 2003:
*Soo T. Tan*; **Applied Calculus**; Brooks/Cole (Fifth edition),
2002 (976 pp.);(ISBN# 0-534-37843-9)

The textbook starting in Spring 2004:
*Strauss, Bradley, Smith*; **Calculus**; Prentice-Hall.

Syllabus: This syllabus divides the material of Math 136 into 26 lectures, leaving two lectures free for in-class midterm exams. Problems using trigonometric functions (see Chapter 12) will be introduced in lectures.

Lecture | Topic | Sections (Tan) |

1 | Integration review: Substitution, the Definite Integral | 6.2, 6.3, 12.4 |

2 | Fundamental Theorem of Calculus, Evaluation of Definite Integrals | 6.4, 6.5 |

3 | Applications of the Definite Integral, Areas by Definite Integrals | 6.6, 6.7 |

4 | Volumes of Solids by Definite Integrals | 6.8 |

5 | Integration by Parts; Integration Tables | 7.1, 7.2 |

6 | Numerical Integration; Improper Integrals | 7.3, 7.4 |

7 | Differential Equations, introduction | 9.1 |

8 | Differential Equations: Separation of Variables | 9.2 |

9 | Separable Differential Equations: Applications | 9.3 |

10 | Differential Equations: Approximate Solutions | 9.4 |

11 | Probability Distributions; Expected Value and Standard Deviation | 10.1, 10.2 |

12 | Normal Distributions | 10.3 |

13 | Taylor polynomials | 11.1 |

14 | Infinite Sequences and Infinite Series | 11.2, 11.3 |

15 | Infinite Series with positive terms | 11.4 |

16 | Power Series and Taylor Series | 11.5 |

17 | Power Series and Taylor Series | 11.6 |

18 | Newton Raphson Method | 11.7 |

19 | Functions of several Variables | 8.1 |

20 | Partial Derivatives | 8.2 |

21 | Maximizing or minimizing functions of several variables | 8.3 |

22 | The Least Squares Method of Curve-Fitting | 8.4 |

23 | Constrained Optimization by Lagrange Multipliers | 8.5 |

24 | Total Differentials | 8.6 |

25 | Double Integrals; Definition and calculuation | 8.7 |

26 | Double integrals; Applications | 8.8 |