





Goal: To achieve a thorough understanding of vector
calculus, including both problem solving and theoretical aspects. The
orientation of the course is toward the problem aspects, though we go into
great depth concerning the theory behind the computational skills that are
developed. This goal shows itself in that we present no
“hard” proofs, though we do present “hard” theorems.
This means that you are expected to understand these theorems as to their
hypotheses and conclusions, but not to understand or even see their proofs.
However, “easy” theorems are discussed throughout the course, and
you are expected to understand their proofs completely. For example, it is a
hard theorem that a continuous realvalued function defined on a closed
interval of the real numbers attains its maximum value. But it is an easy
theorem that if that maximum value is taken at an interior point of the
interval and if the function is differentiable there, then its derivative
equals zero at that point. You also will learn to grasp quite a large number of
important definitions. For instance, one of the most important definitions,
the differentiability of a function of several real variables, is utterly
important, and you’ll confront it right away in Chapter 2. Since we are discussing vector calculus throughout the
year, and a great deal of what we do takes place in ndimensional Euclidean
space, a large amount of basic linear algebra will need to be developed as we
go along. In fact, a The first semester is mainly restricted to
“differential” calculus, and the second semester treats
“integral” calculus. The combination MATH 321/322, Introduction to Analysis, treats in great detail the proofs of the hard theorems alluded to above. Prerequisites: A good oneyear course in singlevariable calculus, and especially a genuine love for mathematics.
Grading: I shall take all aspects into consideration, especially
your progress during the semester. 

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