THE
UNIVERSITY OF HAWAI'I AT HILO - MATHEMATICS DEPARTMENT
Course
Description:
This course delves into the elegant worlds of differential and integral
calculus. We will begin with a review of functions of real
numbers, their properties, and their graphs. To more deeply
understand functions, we will investigate the notion of a limit and use
it to define the infamous derivative. Using both conceptual
and computational aspects of the derivative, we will expand our
qualitative and quantitative understanding of how (differentiable)
functions may be described via their rates of changes. We will
find and explore numerous applications of the derivative and relate
this essential tool to fields such as Physics, Chemistry, and
Economics. We will then investigate the notion of area bound by a
graph via the definite integral. Using the Fundamental Theorem of
Calculus, we will then bridge the seemingly disparate concepts of the
derivative and the integral to obtained a more unified understanding of
real functions. Learning
Outcomes:
Students
successfully completing the course should be able to:
Compute
limits both graphically and symbolically
Determine
if a function is continuous at each point
Compute
the derivative of a function using the definition of a derivative
Become
proficient at using all rules of differentiation (e.g., product rule,
quotient rule, chain rule) to compute global derivative and know when
and when not to apply each rule
Apply
the derivative to linearly approximate functions
Utilize
the symbolic derivative to find the equation for a tangent link
Utilize
implicit differentiation to solve related rates problems
Utilize
the derivative to optimize functions
Understand
and apply higher order derivatives to model problems and graph functions
Understand
the definition of a definite integral and apply it to basic functions
Understand
and apply integration
Utilize
the Fundamental Theorem of Calculus to compute definite integrals using
anti-derivatives
Homework:
This
course will have frequent homework (HW) assignments. Most
HW assignments will be hosted on the MyMathLab portal. It is the
students' responsibility to have access to internet and a computer with
the appropriate software to complete the HW assignments. Non-MML
homework and other assignments are also posted online on this
website.
Quizzes:
There
will be frequent short quizzes given during the course to verify that
the contents of the course have been absorbed. These
quizzes will be
announced beforehand.
Grading:
The final
grade will be based largely on homework, midterms, final, and frequent
quizzes. Furthermore, class participation (e.g., asking questions
in
class, going to the Math Lab, going to office hours, asking Bob email
questions, etc) will also be used in this computation. The
lecture portion grade breakdown is given below.
Your
lecture grade will be computed using the following weights:
25% - Homework
40% - Midterms & Final
25% - Quizzes
10% - Participation