# 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 16B: Short Calculus

**Approved:**1999-09-01 (revised 2005-09-01, 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 |

1.5 |
4.1 – 4.3 |
Exponential functions and their derivatives. Note: You may want to skip the “proof” on page 273 that the exponential function is its own derivative, and justify this after you show in section 4.5 how to differentiate y = ln x, using the def. of the derivative). |

1 |
4.4 |
Logarithmic functions |

1.5 |
4.5 |
Derivatives of logarithmic functions Note: Show how to differentiate functions of the form y = [f(x)] ^ [g(x)] |

1 |
4.6 |
Exponential growth and decay Note: notice that the proof on page 299 is incomplete. |

1 |
5.1 |
Antiderivatives and indefinite integrals |

1 |
5.2 |
The General Power Rule Note: Use this section as a simple introduction to substitution, rather than emphasizing the general power rule itself. |

0.5 |
8.5 |
Simple trig integrals Note: Introduce the integration rules on page 588. Point out that the substitution u = x in example one is never needed. |

1 |
5.3 |
Exponential and logarithmic integrals |

1.5 |
5.4 |
Definite integrals and the Fundamental Theorem of Calculus Note: Mention that a more standard approach to definite integrals is presented in Appendix A. |

1 |
5.5 |
Area of a region Note: Present some examples of regions bounded by graphs of functions of y, since these are not included in the examples. |

1.5 |
5.7 |
Volumes of solids of revolution (disc/washer method). Note: You may want to show how to find the volume when a region is revolved around a general vertical or horizontal line. |

1 |
6.1 |
Integration by substitution |

1.5 |
6.2 |
Integration by parts Note: you may want to introduce tabular integration (vertical integration by parts). |

1 |
8.5 |
Trigonometric integrals Note: Introduce the integrals on page 592. Mention that there are two common ways to write the anti-derivative of the tangent function. |

1 |
6.3 |
Partial fractions Note: Make it clear when division is necessary. |

1.5 |
6.6 |
Improper integrals |

1 |
9.1 |
Discrete probability Note: This section is meant to motivate the ideas in the next two sections. |

1 |
9.2 |
Continuous random variables |

1.5 |
9.3 |
Mean and median; variance and standard deviation; uniform, normal, and exponential probability density functions. |

0.5 |
5.6 |
The midpoint rule Note: Point out that any integrals cannot be evaluated using the Fundamental Theorem of Calculus. |

1 |
6.5 |
The trapezoidal rule and Simpson’s rule. Note: do not require memorization of the error formulas on page 431. |

0.5 |
6.4 |
Integration tables and completing the square. Note: Make it clear that the formulas on pages 417-419 do not have to be memorized. |

**Additional Notes:**