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 (revised 2025-02-21, DeLorea/Thomas)
Suggested Textbook: (actual textbook varies by instructor; check your
instructor)
“Finite Mathematics & Applied Calculus,” 8th edition, by Waner & Costenoble (Cengage)
Prerequisites:
MAT 17A, 19A, or 21A with C- or above
Course Description:
Calculus and other mathematical methods necessary in data driven analysis in the social sciences, technology and humanities. Probability, linear algebra, linear programming, integrals and applications.
Suggested Schedule:
| Lecture | Sections | Topics |
|---|---|---|
| 2 | 7.3-7.4 | Decision algorithms; permutations & combinations |
| 1 | 8.4 | Probability & counting techniques |
| 1 | 9.1-9.2 | Random variables & distributions |
| 1 | 9.3 | Measures of central tendency |
| 2 | 4.1-4.3 | Systems of linear equations |
| 1 | 5.1-5.2 | Matrix operations |
| 1 | 5.3 | Matrix inversion |
| 1 | 5.4 | Game theory |
| 1 | 6.1-6.2 | Graphing inequalities and linear programming |
| 3 | 6.3-6.4 | The simplex method |
| 1 | 6.5 | The simplex method and duality |
| 1 | 13.1 | The indefinite integral |
| 1 | 13.2 | Substitution |
| 1 | 13.3 | Definite integrals |
| 1 | 13.4 | The Fundamental Theorem of Calculus |
| 1 | 14.1 | Integration by parts |
| .5 | 14.2 | Area between two curves |
| 1.5 | 14.3 | Averages & moving averages |
| 1 | 14.4 | Consumers’ surplus, producers’ surplus, continuous income streams |
| 1 | 14.5 | Improper integrals |
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,
- use R to simulate simulate random processes,
- use matrices to solve systems of linear equations
- perform basic matrix operations,
- calculate optimal strategies for two-player zero-sum games,
- solve linear programming problems,
- use linear programs to model economic situations,
- calculate definite and indefinite integrals, and
- interpret definite and indefinite integrals in an economic context, and
- use R to model and analyze data.