Matematické Fórum

Skrytý text:

Classic text leads from elementary calculus into more theoretic problems. Precise approach with definitions, theorems, proofs, examples and exercises. Topics include partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Numerous graded exercises with selected answers. 1961 edition.

Reviewer:
I bought this textbook as a supplementary resource book for an advanced calculus class I once took although I ended up using it for a Differential Equations II class instead (in particular the partial differential equation and fourier series sections). This book does not present proofs as one might expect from many of today's Advanced Calculus classes. It does not present abstract theorems but rather applied Calculus and Differential Equations. You will not find logical connectives, quantifiers, techniques of proofs, set operations, induction, or completeness axioms in this book. What you will find is partial differentiation, line and surface integrals, definite integrals, fourier series, infinite series, etc. Electrical and Computer Engineers will find that they may benefit from the Vector, Fourier Series, and Laplace Transform chapters of this book. Physics majors are more likely to profit from the chapters on Partial Differentiation and Fourier Series.

Here's the textbook's chapter titles: 1) Partial Differentiation, 2) Vectors, 3) Differential Geometry', 4) Applications of Partial Differentation, 5) Stieltjes Integral, 6) Multiple Integrals, 7) Line and Surface Integrals, 8) Limits and Indeterminate Forms, 9) Infinite Series, 10) Convergence of Improper Integrals, 11) The Gamma Function. Evaluation of Definite Integrals, 12) Fourier Series, 13) The Laplace Transform, 14) Applications of the Laplace Transform.

The book may be considered as being written in the ole' school style. It was written by a former Professor of Mathematics at Harvard and was first printed in 1947. The relatively low cost of the textbook may be attributed to it not having been `updated' for a while, being devoid of any color, and being softbound. It has some worked out examples but focuses more on established theorems and lemmas to solve problems. The book is fairly well organized and is overall a good reference book.

Reviewer:
I really believe that this book does an excellent job at teaching such a difficult topic. "Advanced Calculus" is just packed with proofs and stimulating problems. This should be the text used to teach the subject. If you intend to tutor yourself on the topic or you are actually taking the class, this book is a must. I am currently using this as a secondary text to an advanced calculus class I am taking, and, as far as I'm concerned, this is the only text I need. This book does, in such a small package, more than you'll ever need. I recommend one purchases this book at the multi-varialbe calculus level and use it through your time in analysis courses. This is a must have for all math majors.