Introduction:
What is Calculus About?

The
seeds for the main
ideas
of calculus go back to ancient times but calculus itself, as we think
of
it today, was invented (or discovered?--which?) during the 17th century
as part of an explosion of interest and discovery in the physical
sciences.
Its invention is usually attributed to the English mathematician Sir
Isaac Newton and the German mathematician Gottfried
Leibniz, working independently. As its power developed, calculus
gave
scientists a tool to generate remarkable new understandings of the
world.
Its creation is considered one of the great intellectual
accomplishments
of the human mind. This sweeping assertion is justified not only
by the beauty of the subject, but also by the fact that it still
retains
its fundamental importance, even several centuries after its
birth.
In fact, its role has become more important than ever as the use of
mathematical
models has reached beyond areas such as physics and engineering and
into
such different fields as biology, economics and business.
Of course there are also other important mathematical tools. Algebra, discrete mathematics, probability and statistics, topology, and computer science all have roles to play as research areas and as tools in applications. These diverse parts of mathematics complement each other. The increasing power and availability of technology enhances their usefulness and doesn't replace the need for any of them. Graphing
calculators are now good enough to be really helpful with numeric
calculations
and graphical interpretations of
what's
happening in calculus. The more powerful calculators (such as the
TI-89, TI-92, HP-48 and HP-49) contain a Computer
Algebra
System (CAS) that can do complex symbolic manipulations.
Computers,
of course, can do even better and with much
prettier
output. Technology makes it possible to explore calculus
numerically
and graphically in ways which were impractical
even
a decade ago, but There are lots of details and techniques for us to learn, but in the big picture there are only two "great ideas" in calculus. Both of them are illustrated on the dashboard of your car. 1) The first idea concerns "how fast is a quantity changing?" For example, if you're driving down the highway andMost of Math 131-132 consists of - developing
the
*background*for these ideas - developing
the
*mathematical concepts of derivative and integral* - seeing
*how the two ideas are connected* - learning
*techniques*for applying the ideas efficiently.
please,
put
them on the spot and ask!! ) For now, try to learn to
appreciate
the subject itself, its beauty, and how the pieces fit together. |