# 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 19A: Calculus for Data-Driven Applications

**Approved:**2023-03-21, J. De Loera and R. Thomas

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

“Finite Mathematics & Applied Calculus,” 8th edition, by Waner & Costenoble (Cengage)

**Prerequisites:**

Two years of high school algebra, plane geometry, plane trigonometry, and analytical geometry, and satisfying the Mathematics Placement Requirement.

**Course Description:**

Calculus and other mathematical methods necessary in data driven analysis in the sciences, technology and the humanities.

**Suggested Schedule:**

Days | Sections | Topics |
---|---|---|

1 | 1.1-1.2 | Review of functions (including linear, power, polynomial, rational); functions and models |

1 | 1.3-1.4 | Linear models & linear regression |

1 | 2.2-2.3 | Exponential & logarithmic functions |

1 | 2.4 | Logistic functions |

1.5 | 10.1-10.3 | Limits and continuity |

0.5 | 10.4 | Average rate of change |

2 | 10.5-10.6 | The derivative |

0.5 | 11.1 | Derivative rules |

1 | 11.2 | Marginal analysis |

1 | 11.3 | Product & quotient rules |

1.5 | 11.4 | Chain rule |

1 | 11.5 | Derivatives of exponential & logarithmic functions |

0.5 | 11.6 | Implicit differentiation |

2.5 | 12.1 | Extrema |

1 | 12.3 | Higher-order derivatives, concavity |

2 | 12.4 | Curve sketching |

1.5 | 12.5 | Related rates |

0.5 | 12.6 | Elasticity |

1 | 8.1-8.3 | Events, sample spaces, probability |

1 | 8.5 | Conditional probability, independence |

1 | 8.6 | Bayes’ Theorem |

**Additional Notes:**

This course includes weekly 2-hour lab meetings in which students will use R to analyze real data in order to deepen their understanding of course material.

**Learning Goals:**

Upon completion of this course, students will be able to

- model data using functions,
- calculate derivatives,
- interpret derivatives in an economic or financial context,
- solve related rates and optimization problems,
- use calculus to sketch curves,
- calculate basic probabilities,
- determine whether events are independent, and
- use Bayes’ Theorem to calculate conditional probabilities.