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 19A: 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)
Two years of high school algebra, plane geometry, plane trigonometry, and analytical geometry, and satisfying the Mathematics Placement Requirement.
Course Description:
Calculus and other mathematical methods necessary in data driven analysis in the sciences, technology and the humanities.
Suggested Schedule:
DaysSections Topics
1 1.1-1.2Review of functions (including linear, power, polynomial, rational);
functions and models
1 1.3-1.4 Linear models & linear regression
12.2-2.3Exponential & logarithmic functions
1 2.4 Logistic functions
1.5 10.1-10.3 Limits and continuity
0.5 10.4 Average rate of change
2 10.5-10.6The derivative
0.5 11.1 Derivative rules
1 11.2Marginal analysis
111.3Product & quotient rules
1.511.4 Chain rule
1 11.5Derivatives of exponential & logarithmic functions
0.5 11.6 Implicit differentiation
1 12.3 Higher-order derivatives, concavity
2 12.4 Curve sketching
1.5 12.5 Related rates
0.5 12.6 Elasticity
1 8.1-8.3 Events, sample spaces, probability
1 8.5 Conditional probability, independence
1 8.6 Bayes’ Theorem
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 data using functions,
  • calculate derivatives,
  • interpret derivatives in an economic or financial context,
  • solve related rates and optimization problems,
  • use calculus to sketch curves,
  • calculate basic probabilities,
  • determine whether events are independent, and
  • use Bayes’ Theorem to calculate conditional probabilities.