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.