# 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 19B: 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:**

MAT 19A 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 | Topics |
---|---|---|

1-2 | 7.3-7.4 | Decision algorithms; permutations & combinations |

3 | 8.4 | Probability & counting techniques |

4 | 9.1 | Random variables & distributions |

5 | 9.2 | Bernoulli trials & binomial random variables |

6 | 9.3 | Measures of central tendency |

7 | 4.1 | Systems of two equations in two unknowns |

8-9 | 4.2 | Using matrices to solve systems of equations |

10 | 5.1-5.2 | Basic matrix operations |

11 | 5.3 | Matrix inversion |

5.4 | (Optional) Game theory | |

12-13 | Eigenvalues & eigenvectors | |

14 | 6.1 | Graphing linear inequalities |

15 | 6.2 | Solving linear programming problems graphically |

16-18 | 6.3-6.4 | The simplex method, maximization problems, general linear programming |

6.5 | (Optional) The simplex method and duality | |

19 | 13.1 | The indefinite integral |

20 | 13.2 | Substitution |

21 | 13.3 | The definite integral |

22 | 13.4 | The Fundamental Theorem of Calculus |

23 | 14.1 | Integration by parts |

14.2 | (Optional) Area between two curves & applications | |

24 | 14.3 | Averages & moving averages |

25 | 14.4 | Consumers’ surplus, producers’ surplus, continuous income streams |

14.5 | (Optional) Improper integrals and applications | |

26-27 | Use remaining lectures as buffer for material above and/or to cover optional material from 5.4, 6.5, 14.2, or 14.5 |

**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

- calculate probabilities,
- model random processes using random variables,
- simulate random processes using appropriate technology,
- use matrices to solve systems,
- calculate matrix inverses, eigenvalues, and eigenvectors,
- solve linear programming problems,
- use linear programs to model economic and financial situations,
- calculate definite and indefinite integrals, and
- interpret definite and indefinite integrals in an economic or financial context.