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About this book :-
Advanced Calculus (5E) written by Wilfred Kaplan.
The background assumed is that usually obtained in the freshman-sophomore calculus sequence. Linear algebra is not assumed to be known but is developed in the first chapter. Subjects discussed include all the topics usually found in texts on advanced calculus. However. there is more than the usual emphasis on applications and on physical motivation. Vectors are introduced at the outset and serve at many points to indicate geometrical and physical significance of mathematical relations. Numerical methods are touched upon at various points, both because of their practical value and because of the insights they give into the theory. A sound level of rigor is maintained throughout. Definitions are clearly labeled as such and all important results are formulated as theorems. A few of the finer points of real variable theory are treated at the ends of Chapters 2, 4, and 6. A large number of problems (with answers) are distributed throughout the text. These include simple exercises as well as complex ones planned to stimulate critical reading. Some -points of the theory are relegated to the problems. with hints given where appropriate. Generous references to the literature are given, and each chapter concludes with a list of books for supplementary reading. Starred sections are less essential in a first course.
Book Detail :-
Title: Advanced Calculus
Author(s): Wilfred Kaplan
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About Author :-
The author Wilfred Kaplan (1915–2007) was a professor of mathematics at the University of Michigan for 46 years, from 1940 through 1986. His research focused on dynamical systems, the topology of curve families, complex function theory, and differential equations. In total, he authored over 30 research papers and 11 textbooks.
Wilfred Kaplan was born in Boston, Massachusetts to Jacob and Anne Kaplan. He attended Boston Latin School and furthered his education at Harvard University, where he was granted his A.B. in mathematics in 1936 and graduated summa cum laude. Later that same year he received his master's degree at Harvard. Kaplan received a Rogers Fellow scholarship to study in Europe from 1936-1937, during his second year of graduate school. He was based out of Zürich, Switzerland where many of the mathematicians working on the applications of topology to differential equations were located. He also spent a month in Rome to work with famous mathematician Tullio Levi-Civita. Upon returning to the United States, Kaplan accepted a yearlong teaching fellowship at Rice Institute for the 1938-1939 school year, thus completing his graduate program. He received his Ph.D. from Harvard in 1939 under the advisement of Hassler Whitney. His dissertation covered regular curve families filling the plane.
All Famous Books of this Author :-
Here is list all books, text books, editions, versions or solution manuals avaliable of this author, We recomended you to download all.
• Download PDF Calculus and Linear Algebra Vol-1 by Wilfred Kaplan, Donald J Lewis
• Download PDF Calculus and Linear Algebra Vol-2 by Wilfred Kaplan, Donald J Lewis
• Download PDF Advanced Calculus (5E) by Wilfred Kaplan
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Book Contents :-
Advanced Calculus (5E) written by Wilfred Kaplan cover the following topics.
1. Vectors and Matrices
2. Differential Calculus of Functions of Several Variables
3. Vector Differential Calculus
4. Integral Calculus of Functions of Several Variables
5. Vector Integral Calculus Two-Dimensional Theory
6. Infinite Series
7. Fourier Series and Orthogonal Functions
8. Functions of a Complex Variable
9. Ordinary Differential Equations
10. Partial Differential Equations
Answers to Problems
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