# 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 19C: 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); “Biocalculus,” 1st edition, by Stewart & Day (Cengage)

**Prerequisites:**

MAT 19B with C- or above

**Course Description:**

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

**Suggested Schedule:**

Lecture | Sections | Textbook | Topics |
---|---|---|---|

1-3 | 15.1 | WC | Functions of several variables |

4 | 15.2 | WC | Partial derivatives |

5-6 | 15.3 | WC | Maxmima & minima |

7-8 | 15.4 | WC | Constrained maxima and minima |

9-11 | Logistic regression, least squares, machine learning models | ||

12-13 | 14.6 | WC | Solutions of elementary & separable differential equations |

14 | 14.6 | WC | Linear first-order differential equations |

15 | 7.3 | SD | Euler’s method |

16-18 | 10.1-10.3 | SD | Linear systems of differential equations |

19-22 | 10.4, 7.6 | SD | Non-linear systems of differential equations |

23-24 | Applications of differential equations | ||

25-27 | Use remaining lectures as buffer for material above and/or to cover optional material from 15.5: Double integrals & applications |

**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 financial and economic processes using functions of several variables,
- use functions of several variables to model and understand data,
- calculate and interpret partial derivatives,
- identify extrema of functions of several variables,
- model financial and economic processes using differential equations,
- solve differential equations,
- determine equilibria of systems of differential equations and analyze their stability,
- interpret solutions to differential equations in an economic or financial context, and
- use differential equations to model and understand data.