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 19B: 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)
MAT 19A 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 Topics
1-2 7.3-7.4 Decision algorithms; permutations & combinations
3 8.4 Probability & counting techniques
4 9.1 Random variables & distributions
5 9.2 Bernoulli trials & binomial random variables
6 9.3 Measures of central tendency
7 4.1 Systems of two equations in two unknowns
8-9 4.2 Using matrices to solve systems of equations
10 5.1-5.2 Basic matrix operations
11 5.3 Matrix inversion
5.4 (Optional) Game theory
12-13 Eigenvalues & eigenvectors
14 6.1 Graphing linear inequalities
15 6.2 Solving linear programming problems graphically
16-18 6.3-6.4 The simplex method, maximization problems, general linear programming
6.5 (Optional) The simplex method and duality
19 13.1 The indefinite integral
20 13.2 Substitution
21 13.3 The definite integral
22 13.4 The Fundamental Theorem of Calculus
23 14.1 Integration by parts
14.2 (Optional) Area between two curves & applications
24 14.3 Averages & moving averages
25 14.4 Consumers’ surplus, producers’ surplus, continuous income streams
14.5 (Optional) Improper integrals and applications
26-27 Use remaining lectures as buffer for material above and/or to cover optional material from 5.4, 6.5, 14.2, or 14.5
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,
  • simulate random processes using appropriate technology,
  • use matrices to solve systems,
  • calculate matrix inverses, eigenvalues, and eigenvectors,
  • solve linear programming problems,
  • use linear programs to model economic and financial situations,
  • calculate definite and indefinite integrals, and
  • interpret definite and indefinite integrals in an economic or financial context.