# 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 17B: 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 16A, 17A, or 21A with C- or above
Suggested Schedule:
1 4.6, 5.1 Antiderivatives, solutions of initial value problems, areas, distances
2-35.2 Definite integrals, midpoint rule
45.3 Fundamental Theorem of Calculus
5 5.4 Integration by substitution
65.5 Integration by parts
75.6 Partial fractions; mention tables of integrals (5.7) and software packages
85.8Improper integrals
96.1-6.2 Area between curves, average value
106.3 Further applications to biology
116.4Volumes
127.1Modeling with differential equations, solving pure-time differential equations
137.2 Phase plots, equilibria, stability of equilibria
147.4 Separable differential equations
15online notes Solving first-order linear non-autonomous differential equations using integrating factors
167.3 or
7.5
Direction fields and Euler's method or
Systems of autonomous ODEs
17-188.1-8.3 Coordinate systems, vectors, vector operations
198.4 Matrices, matrix multiplication
208.5 Systems of difference equations
218.6 Inverses and determinants of matrices
22-238.7 Eigenvalues and eigenvectors
248.8 Iterated matrix models
25-27Use remaining lectures as buffer for material above and/or to cover optional material from 7.3, 7.5, or 7.6
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 5-8: integration, differential equations, linear algebra, elements of analytic geometry.
Learning Goals:
Upon completion of this course, students will be able to
• understand the meaning of definite and indefinite integrals,
• understand the relationships between derivatives, antiderivatives, rates of change, indefinite integrals, definite integrals, distances, and areas,
• calculate definite and indefinite integrals using appropriate techniques,
• numerically approximate definite integrals,
• interpret integrals in a biological context, including ecological, physiological, and pharmacological models,
• model biological phenomena using differential equations,
• solve pure-time, separable, and first-order linear differential equations,
• use appropriate graphical techniques to visualize differential equations and their solutions,
• determine and analyze equilibria and their stability,
• visualize vectors and vector operations,
• perform basic operations on vectors and matrices, and
• calculate eigenvectors and eigenvalues.