# 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 16A: Short Calculus

**Approved:**2005-09-01 (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 |

1 |
1.1 – 1.3 |
Cartesian plane, distance formula, midpoint formula, graphs, intercepts, circles, and lines (Review the definition of absolute value on page O-8). |

1.5 |
1.4 |
Functions, composition of functions, and inverse. |

1.5 |
1.5 |
Limits |

1 |
3.6 |
Vertical asymptotes and finite limits; horizontal asymptotes and limits of infinity. |

1 |
1.6 |
Continuity |

2 |
2.1 |
Slope of the tangent line, definition of the derivative, differentiability and continuity. |

1 |
8.1 – 8.3 |
Trigonometry review |

0.5 |
2..2 |
Constant rule, power rule, constant multiple rule, sum and differences rules. |

1 |
2.3 |
Average rate change, instantaneous rate of change, velocity, marginals in economics. |

1 |
2.4 |
Product and quotient rules. |

1 |
8.4 |
Derivatives or trig functions. |

1 |
2.5 |
Chain rule, general power rule (Include relevant problems from section 8.4). |

0.5 |
2.6 |
Higher order derivatives, acceleration. |

1 |
2.7 |
Implicit differentiation (Include relevant problems from Section 8.4). |

1.5 |
2.8 |
Related rates. |

1 |
3.1 |
Increasing and decreasing functions, critical numbers. |

1.5 |
3.2 |
Relative extrema, the first-derivative test, absolute extrema (Include relevant problems from section 8.4 and page 612). |

1 |
3.3 |
Concavity, points of inflection, the second-derivative test. |

2 |
3.4 |
Optimization problems (You may want to assign some problems from section 3.5). |

2 |
3.7 |
Sketching graphs (You may want to assign some problems from section 3.6). |

1 |
3.8 |
Differentials (Explain estimating function values using differentials). |

**Additional Notes:**

This course is a pre-requisite for integral and mult-variable calculus. Mastery of this course will be reflected in improved reading and logical thinking skills, as well as enhanced algebraic, analytic, and general problem-solving skills, especially in the context of related rates and maximum-minimum word problems.

**Assessment:**