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 (revised 2025-02-21, DeLorea/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 social sciences, technology and humanities. Functions, limits, derivatives, probability, and applications.
Suggested Schedule:
| Days | Sections | Topics | ||
|---|---|---|---|---|
| 1 | 1.1-1.3 | Review of functions (including linear, power, polynomial, rational); functions and models |
||
| 1 | 2.2-2.3 | Review of exponential functions | ||
| 1 | .9, 2.4 | Logarithmic functions | ||
| 2 | 10.1-10.3 | Limits and continuity | ||
| 2 | 10.4-10.6 | Average rate of change and the derivative | ||
| 1 | 11.1 | Basic derivative rules and L'Hospital's rule | ||
| 1 | 11.2 | Marginal analysis | ||
| 1 | 11.3 | The product & quotient rules | ||
| 1 | 11.4 | The chain rule | ||
| 1 | 11.5 | Derivatives of exponential & logarithmic functions | ||
| 1 | 11.6 | Implicit differentiation | ||
| 1 |
|
Maxima and minima | ||
| 1 | 12.2 | Optimization | ||
| 1 | 12.3 | Higher-order derivatives, concavity, nad diminishing returns | ||
| 2 | 12.4 | Analyzing and sketching graphs | ||
| 1 | 12.5 | Differentials, linearization, and error estimation | ||
| 1 | 12.6 | Related rates | ||
| 1 | 12.7 | 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 limits and derivatives of functions,
- interpret derivatives in an economic or financial context,
- approximate functions and bound error using derivatives,
- solve related rates and optimization problems,
- use derivatives to predict the behavior of and graph functions,
- calculate basic probabilities,
- determine whether events are independent,
- calculate conditional probabilities using Bayes’ Theorem and
- use R to model and analyze data.