MATH 1341 - Calculus
for Engineer/Sci I
Fall 2009
Course
Information
This is our premier calculus course
for engineers, math, science, and computer science majors. The goal is to
ensure that students know and are able to effectively use this subject which is
so vital to all those disciplines. Thus attention is given to the scientific
and technical uses of calculus, which are many indeed.
The topics considered in the course
include differentiation and integration of functions of one variable,
especially polynomial, exponential, and trigonometric functions and their
inverses. We study vectors and vector-valued functions with an eye on their use
in modeling a variety of physical processes. Proficiency with the rules of
differentiation is an important goal. We also begin the study of integration
and its connection with differentiation. We are concerned that students
understand what the subject is good for; this often requires understanding its
underlying principles.
Specific mathematical skills that
you will learn in this course are:
- Parametrizing curves in the plane and motion along a
straight line.
- Using
functions, derivatives and vectors to model physical processes (e.g.
velocities, accelerations and other rates of change).
- Applying
the definition of the derivative to calculate the instantaneous rate of
change as a limit of average rates of change.
- Visualizing
and interpreting derivatives geometrically as slopes of tangent lines to
graphs.
- Deriving,
learning, and using the rules of differentiation to calculate derivatives
of important functions, including polynomials, exponential and logarithmic
functions, trigonometric and inverse trigonometric functions, and
combinations of such functions using the product, quotient and chain
rules.
- Sketching
graphs of functions by analyzing the first and second derivatives.
- Modeling
physical problems with differential equations and vector-valued functions,
especially problems involving Newton's laws of motion.
- Solving
optimization (maximum-minimum) problems via derivatives.
- Calculating
the linearization of a function and using it to approximate changes in the
value of the function.
- Understanding
integrals as limits of sums and understanding the Fundamental Theorem of
Calculus.
- Calculating
antiderivatives of some important functions.
There is a free tutoring service
at Math Center.
Click here
for detailed information.
For Fall 2009, service starts September 16.
Syllabus
Final exams from past two years:
2007, 2008