Syllabus Detail

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)
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.