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)
Prerequisites:
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:
| Days | Sections | Topics |
|---|---|---|
| 1 | 1.1-1.2 | Review of functions (including linear, power, polynomial, rational); functions and models |
| 1 | 1.3-1.4 | Linear models & linear regression |
| 1 | 2.2-2.3 | Exponential & 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 | 10.5-10.6 | The derivative |
| 0.5 | 11.1 | Derivative rules |
| 1 | 11.2 | Marginal analysis |
| 1 | 11.3 | Product & quotient rules |
| 1.5 | 11.4 | Chain rule |
| 1 | 11.5 | Derivatives of exponential & logarithmic functions |
| 0.5 | 11.6 | Implicit differentiation |
| 2.5 | 12.1 | Extrema |
| 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.