Mathematical Analysis
Title | Mathematical Analysis PDF eBook |
Author | Andrew Browder |
Publisher | Springer Science & Business Media |
Pages | 348 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 1461207150 |
Among the traditional purposes of such an introductory course is the training of a student in the conventions of pure mathematics: acquiring a feeling for what is considered a proof, and supplying literate written arguments to support mathematical propositions. To this extent, more than one proof is included for a theorem - where this is considered beneficial - so as to stimulate the students' reasoning for alternate approaches and ideas. The second half of this book, and consequently the second semester, covers differentiation and integration, as well as the connection between these concepts, as displayed in the general theorem of Stokes. Also included are some beautiful applications of this theory, such as Brouwer's fixed point theorem, and the Dirichlet principle for harmonic functions. Throughout, reference is made to earlier sections, so as to reinforce the main ideas by repetition. Unique in its applications to some topics not usually covered at this level.
Introduction to Mathematical Analysis
Title | Introduction to Mathematical Analysis PDF eBook |
Author | William R. Parzynski |
Publisher | McGraw-Hill Companies |
Pages | 376 |
Release | 1982 |
Genre | Mathematics |
ISBN |
Introduction to Analysis
Title | Introduction to Analysis PDF eBook |
Author | Maxwell Rosenlicht |
Publisher | Courier Corporation |
Pages | 270 |
Release | 2012-05-04 |
Genre | Mathematics |
ISBN | 0486134687 |
Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.
Introduction to Real Analysis
Title | Introduction to Real Analysis PDF eBook |
Author | William F. Trench |
Publisher | Prentice Hall |
Pages | 0 |
Release | 2003 |
Genre | Applied mathematics |
ISBN | 9780130457868 |
Using an extremely clear and informal approach, this book introduces readers to a rigorous understanding of mathematical analysis and presents challenging math concepts as clearly as possible. The real number system. Differential calculus of functions of one variable. Riemann integral functions of one variable. Integral calculus of real-valued functions. Metric Spaces. For those who want to gain an understanding of mathematical analysis and challenging mathematical concepts.
An Introduction to Mathematical Analysis for Economic Theory and Econometrics
Title | An Introduction to Mathematical Analysis for Economic Theory and Econometrics PDF eBook |
Author | Dean Corbae |
Publisher | Princeton University Press |
Pages | 696 |
Release | 2009-02-17 |
Genre | Business & Economics |
ISBN | 1400833086 |
Providing an introduction to mathematical analysis as it applies to economic theory and econometrics, this book bridges the gap that has separated the teaching of basic mathematics for economics and the increasingly advanced mathematics demanded in economics research today. Dean Corbae, Maxwell B. Stinchcombe, and Juraj Zeman equip students with the knowledge of real and functional analysis and measure theory they need to read and do research in economic and econometric theory. Unlike other mathematics textbooks for economics, An Introduction to Mathematical Analysis for Economic Theory and Econometrics takes a unified approach to understanding basic and advanced spaces through the application of the Metric Completion Theorem. This is the concept by which, for example, the real numbers complete the rational numbers and measure spaces complete fields of measurable sets. Another of the book's unique features is its concentration on the mathematical foundations of econometrics. To illustrate difficult concepts, the authors use simple examples drawn from economic theory and econometrics. Accessible and rigorous, the book is self-contained, providing proofs of theorems and assuming only an undergraduate background in calculus and linear algebra. Begins with mathematical analysis and economic examples accessible to advanced undergraduates in order to build intuition for more complex analysis used by graduate students and researchers Takes a unified approach to understanding basic and advanced spaces of numbers through application of the Metric Completion Theorem Focuses on examples from econometrics to explain topics in measure theory
Introduction to Calculus and Analysis II/1
Title | Introduction to Calculus and Analysis II/1 PDF eBook |
Author | Richard Courant |
Publisher | Springer Science & Business Media |
Pages | 585 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 3642571492 |
From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991
Real Mathematical Analysis
Title | Real Mathematical Analysis PDF eBook |
Author | Charles Chapman Pugh |
Publisher | Springer Science & Business Media |
Pages | 445 |
Release | 2013-03-19 |
Genre | Mathematics |
ISBN | 0387216847 |
Was plane geometry your favourite math course in high school? Did you like proving theorems? Are you sick of memorising integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is Pure Mathematics, and it is sure to appeal to the budding pure mathematician. In this new introduction to undergraduate real analysis the author takes a different approach from past studies of the subject, by stressing the importance of pictures in mathematics and hard problems. The exposition is informal and relaxed, with many helpful asides, examples and occasional comments from mathematicians like Dieudonne, Littlewood and Osserman. The author has taught the subject many times over the last 35 years at Berkeley and this book is based on the honours version of this course. The book contains an excellent selection of more than 500 exercises.