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Lecturer:
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Alberto Corso,
POT 701, (859) 257-3167, corso@ms.uky.edu
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Office hours: MWF 2:00-2:50 pm and by appointment
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Teaching Assistant:
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Furuzan Ozbek, POT 718, fozbek@ms.uky.edu
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Office hours: TR 10:30-11:30 am and by appointment
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Text:
Calculus for Biology and Medicine (second edition),
by Claudia Neuhauser.
The book is published by Prentice Hall and it will be
the primary text for the course.
The book can be purchased from the bookstores or online.
It is very readable and has many worked out examples.
We shall cover the first six (6) chapters of this book.
Course Overview:
In Calculus I for the life sciences, we will learn about derivatives,
integrals and the fundamental theorems of calculus.
We begin by introducing the notion of a limit. Limits are essential to
defining derivatives and integrals. By the end of the semester students
should know precise definitions of the derivative and the integral
and the fundamental theorem of calculus which gives the
relation between the derivative and the integral.
We will illustrate the methods and ideas of calculus by studying
several problems from biology. We will study the interpretation
of the derivative as a rate of change, and model growth and
declines of populations.
Course Outline:
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Preview and review
Preliminaries, elementary Functions, and graphing
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Discrete time models, sequences, and difference equations
Exponential growth and decay
Sequences
More population models
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Limits and continuity
Limits
Continuity
Limits at infinity
The Sandwich Theorem and some trigonometric limits
Properties of continuous functions
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Differentiation
Formal definition of the derivative
The power rule, the basic rules of differentiation, and the
derivatives of polynomials
The product and quotient rules, and the derivatives
of rational and power functions
The chain rule and higher derivatives
Derivatives of trigonometric functions
Derivatives of exponential functions
Derivatives of inverse and logarithmic functions
Approximations and local linearity
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Applications of differentiation
Extrema and the Mean Value Theorem
Monotonicity and Concavity
Extrema, inflection points, and graphing
Optimization
L'Hospital's rule
Difference equations: stability
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Integration
The definite integral
The Fundamental Theorem of Calculus
Applications of integration
Student Learning Outcomes:
Students will compute fluently. Students will write correct
justifications for their solutions to problems.
Students will apply the methods of calculus in new contexts
to solve unfamiliar problems.
Corrections to: corso@ms.uky.edu