# 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 17A: Calculus for Biology and Medicine
Approved: 2019-09-03, R. Thomas and K. Burke

This course requires the Math Placement Exam. Read More.

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
"Biocalculus: Calculus, Probability, and Statistics for the Life Sciences," 1​st​ edition, by Stewart/Day (Cengage)
Search by ISBN on Amazon: 9781305114036

Suggested Schedule:

1-31.1-1.5Preliminaries: Elementary functions and graphing.
Include one full lecture on transformation of functions, log transforms, and log-log/semi-log plot
4-51.6, 2.1Sequences, discrete-time models, and limits of sequences
6-82.2-2.5Limits of functions: limit laws, limits at infinity, algebraic methods, continuity
93.1Derivatives as rates of change, tangent lines
10-123.2, 3.3Derivatives as functions, differentiability, higher derivatives, power rule, basic differentiation rules, derivatives of exponential functions, derivatives of sine and cosine
133.4Product and quotient rules
14-153.5Chain rule, implicit differentiation, related rates
163.6Exponential growth and decay
173.7Derivatives of inverse and logarithmic functions
183.8Linear approximation (Optional: Newton's method, Taylor polynomials)
194.1Extrema
204.2Monotonicity and concavity (Optional: Mean Value Theorem)
214.2Graphing – Examples including sigmoidal curves
224.3L'Hospital's rule
23-244.4Optimization
254.5Stability of fixed points in recursions
26-27Use remaining lectures as buffer for material above and/or to cover optional material in 3.8

This course is part of the Inclusive Access program, in which your textbook and other course resources will be made available online. Please consult your instructor on the FIRST DAY of instruction.

This course covers chapters 1-4: limits and derivatives; applications of differentiation in biology; recursions.

Learning Goals:

Upon completion of this course, students will be able to
• use appropriate transformations to find power law and exponential relationships,
• create discrete-time models of biological phenomena and analyze their behavior,
• understand the meaning of limits and derivatives of functions,
• calculate limits and derivatives of functions using appropriate techniques,
• interpret derivatives in a biological context, including ecological, physiological, and pharmacological models,
• approximate functions and bound error using derivatives,
• apply problem-solving skills and knowledge of calculus to solve related rates and optimization problems, and
• use derivatives to predict the behavior of and graph functions.