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 (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); “Biocalculus,” 1st edition, by Stewart & Day (Cengage)
Prerequisites:
MAT 17B, 19B or 21B with C- or above
Course Description:
Calculus and other mathematical methods necessary in data driven analysis in social sciences, technology and humanities. Functions of several variables, partial derivatives, differential equations, systems of differential equations, and applications.
Suggested Schedule:
| Lecture | Sections | Textbook | Topics |
|---|---|---|---|
| 2 | 15.1 | WC | Functions of several variables, three-dimensional coordinate systems, and graphs of functions of two variables |
| 1 | 15.2 | WC | Partial derivatives |
| 3 | 15.3-15.4 | WC | Extrema, regression, and constrained optimization |
| 2 | 15.5 | WC | Double integrals |
| 2 | 14.6 | WC | Differential equations, modeling, and separation of variables |
| 1 | 7.2 | SD | Equilibria and stability |
| 1 | 7.3 | WC | Slope fields and Euler's method |
| 2 | 8.7 | SD | Eigenvalues and eigenvectors |
| 4 | 10.1-10.2 | SD | Systems of linear differential equations |
| 4 | 7.6, 10.4 | SD | Systems of non-linear differential equations |
| 2 | 8.7 | WC | Markov systems |
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
- use functions of several variables to model economic situations,
- plot and visualize functions of two variables,
- calculate partial derivatives,
- interpret partial derivatives in an economic context,
- solve optimization problems,
- calculate double integrals,
- interpret double integrals in an economic context,
- model economic phenomena using differential equations,
- solve and interpret separable differential equations,
- visualize differential equations and their solutions,
- determine and analyze equilibria and their stability,
- model economic phenomena using systems of differential equations,
- solve and interpret systems of differential equations,
- visualize and analyze solutions to systems of differential equations,
- model real-world situations using Markov systems,
- determine and interpret long-term behavior of Markov systems, and
- , use R to model and analyze data.