Introduction To Calculus And Classical Analysis (undergraduate Texts In Mathematics)
by Omar Hijab /
2016 / English / PDF
6.5 MB Download
This text is intended for an honors calculus course or for an
introduction to analysis. Involving rigorous analysis,
computational dexterity, and a breadth of applications, it
is ideal for undergraduate majors. This third edition
includes corrections as well as some additional material.
This text is intended for an honors calculus course or for an
introduction to analysis. Involving rigorous analysis,
computational dexterity, and a breadth of applications, it
is ideal for undergraduate majors. This third edition
includes corrections as well as some additional material.
Some features of the text include: The text is completely
self-contained and starts with the real number axioms; The
integral is defined as the area under the graph, while the area
is defined for every subset of the plane; There is a heavy
emphasis on computational problems, from the high-school
quadratic formula to the formula for the derivative of the zeta
function at zero; There are applications from many parts of
analysis, e.g., convexity, the Cantor set, continued
fractions, the AGM, the theta and zeta functions,
transcendental numbers, the Bessel and gamma functions, and many
more; Traditionally transcendentally presented material, such as
infinite products, the Bernoulli series, and the zeta
functional equation, is developed over the reals; and There
are 385 problems with all the solutions at the back of the text.
Some features of the text include: The text is completely
self-contained and starts with the real number axioms; The
integral is defined as the area under the graph, while the area
is defined for every subset of the plane; There is a heavy
emphasis on computational problems, from the high-school
quadratic formula to the formula for the derivative of the zeta
function at zero; There are applications from many parts of
analysis, e.g., convexity, the Cantor set, continued
fractions, the AGM, the theta and zeta functions,
transcendental numbers, the Bessel and gamma functions, and many
more; Traditionally transcendentally presented material, such as
infinite products, the Bernoulli series, and the zeta
functional equation, is developed over the reals; and There
are 385 problems with all the solutions at the back of the text.