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Multivariable Analysis
This book provides a rigorous treatment of multivariable differential and integral calculus. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connection to solving systems of equations. There is an extensive treatment of extrema, including constrained extrema and Lagrange multipliers, covering both first order necessary conditions and second order sufficient conditions. The material on Riemann integration in n dimensions, being delicate by its very nature, is discussed in detail. Differential forms and the general Stokes' Theorem are expounded in the last chapter. With a focus on clarity rather than brevity, thi...
Elements of Hilbert Spaces and Operator Theory
The book presents an introduction to the geometry of Hilbert spaces and operator theory, targeting graduate and senior undergraduate students of mathematics. Major topics discussed in the book are inner product spaces, linear operators, spectral theory and special classes of operators, and Banach spaces. On vector spaces, the structure of inner product is imposed. After discussing geometry of Hilbert spaces, its applications to diverse branches of mathematics have been studied. Along the way are introduced orthogonal polynomials and their use in Fourier series and approximations. Spectrum of an operator is the key to the understanding of the operator. Properties of the spectrum of different ...
Measure and Integration
This textbook provides a thorough introduction to measure and integration theory, fundamental topics of advanced mathematical analysis. Proceeding at a leisurely, student-friendly pace, the authors begin by recalling elementary notions of real analysis before proceeding to measure theory and Lebesgue integration. Further chapters cover Fourier series, differentiation, modes of convergence, and product measures. Noteworthy topics discussed in the text include Lp spaces, the Radon–Nikodým Theorem, signed measures, the Riesz Representation Theorem, and the Tonelli and Fubini Theorems. This textbook, based on extensive teaching experience, is written for senior undergraduate and beginning graduate students in mathematics. With each topic carefully motivated and hints to more than 300 exercises, it is the ideal companion for self-study or use alongside lecture courses.
Metric Spaces
One of the first books to be dedicated specifically to metric spaces Full of worked examples, to get complex ideas across more easily
Divine Proportions
"... introduces a remarkable new approach to trigonometry and Euclidean geometry, with dramatic implications for mathematics teaching, industrial applications and the direction of mathematical research in geometry" -- p. vii.
The Cartoon Introduction to Economics, Volume I: Microeconomics
The award-winning illustrator Grady Klein has paired up with the world's only stand-up economist, Yoram Bauman, PhD, to take the dismal out of the dismal science. From the optimizing individual to game theory to price theory, The Cartoon Introduction to Economics is the most digestible, explicable, and humorous 200-page introduction to microeconomics you'll ever read. Bauman has put the "comedy" into "economy" at comedy clubs and universities around the country and around the world (his "Principles of Economics, Translated" is a YouTube cult classic). As an educator at both the university and high school levels, he has learned how to make economics relevant to today's world and today's stude...
Matrix Algebra
Matrix Algebra is the first volume of the Econometric Exercises Series. It contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undergraduate or a postgraduate course in econometrics or statistics. The book contains a comprehensive collection of exercises, all with full answers. But the book is not just a collection of exercises; in fact, it is a textbook, though one that is organized in a completely different manner than the usual textbook. The volume can be used either as a self-contained course in matrix algebra or as a supplementary text.
