# Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

## MAT 16C: Short Calculus

**Approved:**2000-09-01 (revised 2013-12-01, D.A. Kouba)

**ATTENTION:**

**Suggested Textbook:**(actual textbook varies by instructor; check your instructor)

Search by ISBN on Amazon: 9781133115007

**Prerequisites:**

**Suggested Schedule:**

Lecture(s) |
Sections |
Comments/Topics |

0.5 |
C.1 |
Introduction to differential equations |

1 |
C.2 |
Separation of variables (Show how to derive the exponential growth and decay formula). |

1.5 |
C.3 |
First order linear DE’s (Give students practice solving a mixture of separable and linear De’s). |

1.5 |
C.4 |
Applications of DE’s (You may want to cover logistic growth on page 410; Notice the error in the Study Tip) |

0.5 |
7.1 |
3-dimensional coordinates |

1.5 |
7.2 |
Planes and quadric surfaces |

0.5 |
7.3 |
Functions of several variables, level curves. |

1.5 |
7.4 |
Partial derivatives |

2 |
7.5 |
Relative extrema for functions of two variables. |

1.5 |
7.6 |
Lagrange multipliers |

1.5 |
7.8 |
Double integrals |

1.5 |
7.9 |
Applications of double integrals: volume and average value (You may want to show how to find the volumes of solids bounded by 2 surfaces). |

1 |
10.1 |
Sequences |

1.5 |
10.2 |
Definition of infinite series, Divergence test, geometric series. |

2 |
10.3 |
P-series, Ratio test (You may want to introduce the Comparison Test). |

2 |
10.4 |
Power series, Taylor’s Theorem. |

0.5 |
10.4 |
Maclaurin series for sine and cosine, binomial series (Assign problems to estimate function values and definite integrals using these series) |

1 |
10.5 |
Taylor polynomials (Taylor’s Theorem with Remainder, page 694, is optional). |

1 |
10.6 |
Newton’s Method |

**Learning Goals:**

**Assessment:**