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Author: John B. Conway Publisher: Cambridge University Press ISBN: 1107173140 Category : Mathematics Languages : en Pages : 357
Book Description
This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.
Author: John B. Conway Publisher: Cambridge University Press ISBN: 1107173140 Category : Mathematics Languages : en Pages : 357
Book Description
This concise text clearly presents the material needed for year-long analysis courses for advanced undergraduates or beginning graduates.
Author: M.H. Protter Publisher: Springer Science & Business Media ISBN: 1461599903 Category : Mathematics Languages : en Pages : 520
Book Description
The first course in analysis which follows elementary calculus is a critical one for students who are seriously interested in mathematics. Traditional advanced calculus was precisely what its name indicates-a course with topics in calculus emphasizing problem solving rather than theory. As a result students were often given a misleading impression of what mathematics is all about; on the other hand the current approach, with its emphasis on theory, gives the student insight in the fundamentals of analysis. In A First Course in Real Analysis we present a theoretical basis of analysis which is suitable for students who have just completed a course in elementary calculus. Since the sixteen chapters contain more than enough analysis for a one year course, the instructor teaching a one or two quarter or a one semester junior level course should easily find those topics which he or she thinks students should have. The first Chapter, on the real number system, serves two purposes. Because most students entering this course have had no experience in devising proofs of theorems, it provides an opportunity to develop facility in theorem proving. Although the elementary processes of numbers are familiar to most students, greater understanding of these processes is acquired by those who work the problems in Chapter 1. As a second purpose, we provide, for those instructors who wish to give a comprehen sive course in analysis, a fairly complete treatment of the real number system including a section on mathematical induction.
Author: Dorairaj Somasundaram Publisher: ISBN: 9788173190643 Category : Mathematics Languages : en Pages : 616
Book Description
Intends to serve as a textbook in Real Analysis at the Advanced Calculus level. This book includes topics like Field of real numbers, Foundation of calculus, Compactness, Connectedness, Riemann integration, Fourier series, Calculus of several variables and Multiple integrals are presented systematically with diagrams and illustrations.
Author: Sterling K. Berberian Publisher: Springer Science & Business Media ISBN: 1441985484 Category : Mathematics Languages : en Pages : 249
Book Description
Mathematics is the music of science, and real analysis is the Bach of mathematics. There are many other foolish things I could say about the subject of this book, but the foregoing will give the reader an idea of where my heart lies. The present book was written to support a first course in real analysis, normally taken after a year of elementary calculus. Real analysis is, roughly speaking, the modern setting for Calculus, "real" alluding to the field of real numbers that underlies it all. At center stage are functions, defined and taking values in sets of real numbers or in sets (the plane, 3-space, etc.) readily derived from the real numbers; a first course in real analysis traditionally places the emphasis on real-valued functions defined on sets of real numbers. The agenda for the course: (1) start with the axioms for the field ofreal numbers, (2) build, in one semester and with appropriate rigor, the foun dations of calculus (including the "Fundamental Theorem"), and, along the way, (3) develop those skills and attitudes that enable us to continue learning mathematics on our own. Three decades of experience with the exercise have not diminished my astonishment that it can be done.
Author: Anthony Ralston Publisher: Courier Corporation ISBN: 9780486414546 Category : Mathematics Languages : en Pages : 644
Book Description
Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.
Author: David Alexander Brannan Publisher: Cambridge University Press ISBN: 1139458957 Category : Mathematics Languages : en Pages : 103
Book Description
Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject.
Author: Andrew Browder Publisher: Springer Science & Business Media ISBN: 1461207150 Category : Mathematics Languages : en Pages : 348
Book Description
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.
Author: Frank R. Giordano Publisher: Cengage Learning ISBN: 9780495011590 Category : Mathematics Languages : en Pages : 640
Book Description
Offering a solid introduction to the entire modeling process, A FIRST COURSE IN MATHEMATICAL MODELING, 4th Edition delivers an excellent balance of theory and practice, giving students hands-on experience developing and sharpening their skills in the modeling process. Throughout the book, students practice key facets of modeling, including creative and empirical model construction, model analysis, and model research. The authors apply a proven six-step problem-solving process to enhance students' problem-solving capabilities -- whatever their level. Rather than simply emphasizing the calculation step, the authors first ensure that students learn how to identify problems, construct or select models, and figure out what data needs to be collected. By involving students in the mathematical process as early as possible -- beginning with short projects -- the book facilitates their progressive development and confidence in mathematics and modeling. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
Author: J. C. Burkill Publisher: Cambridge University Press ISBN: 9780521294683 Category : Mathematics Languages : en Pages : 200
Book Description
This course is intended for students who have acquired a working knowledge of the calculus and are ready for a more systematic treatment which also brings in other limiting processes, such as the summation of infinite series and the expansion of trigonometric functions as power series.
Author: John B. Conway
Author: John B. Conway
Author: M.H. Protter
Author: Dorairaj Somasundaram
Author: J. C. Burkill
Author: Sterling K. Berberian
Author: Anthony Ralston
Author: David Alexander Brannan
Author: Andrew Browder
Author: Frank R. Giordano
Author: J. C. Burkill