# 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 17C: Calculus for Biology and Medicine

Approved: 2019-09-03, R. Thomas and K. Burke
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
Prerequisites:
MAT 17B with C- or above
Suggested Schedule:
1-2 9.1 Functions of several variables, limits, continuity (briefly)
3 9.2 Partial derivatives
4 9.3 Tangent planes and linear approximations, differentiability (briefly)
5 9.4 Chain rule, optional: implicit differentiation
7-8 9.6 Maxima and minima (local and global)
9-10 online notes Double integrals
11-15 10.1-10.3 Systems of linear ODEs: theory, modeling, and examples
16-19 10.4, 7.6 Systems of nonlinear ODEs: theory, modeling, and examples
20-21 12.1 Counting: permutations and combinations
22 12.2 Basic probability: definitions and examples
23 12.3 Conditional probability, law of total probability
24 12.3 Independent events, Bayes' rule
25-27 Use remaining lectures as buffer for material above and/or to cover optional material: more complicated problems using Bayes' rule, discrete random variables (12.4), Lagrange multipliers
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.

Covering the optional material in 12.4 would work best if spread over two lectures.

This course covers chapters 9, 10, and 12: functions of several variables, double integrals, systems of differential equations, discrete probability.
Learning Goals:
Upon completion of this course, students will be able to
• use appropriate techniques to visualize functions of several variables,
• model biological phenomena using functions of several variables,
• calculate limits of functions of several variables,
• calculate partial derivatives, directional derivatives, and gradients,
• understand the meaning of partial derivatives, directional derivatives, and gradients,
• interpret partial derivatives, directional derivatives, and gradients in a biological context, - approximate functions using partial derivatives,
• determine extrema of functions of several variables,
• calculate double integrals,
• model biological phenomena using systems of differential equations,
• use appropriate graphical techniques to visualize systems of two differential equations,
• determine and analyze equilibria and their stability,
• interpret qualitative behavior of solutions to systems of differential equations in a biological context,
• calculate probabilities using discrete probability models and Bayes' theorem, - determine whether events are independent, and
• understand the meaning of independence.