Advanced Calculus: An Introduction to Linear Analysis.DUBLIN, Ireland -- Research and Markets (http://www.researchandmarkets.com/research/3d1413/advanced_calculus calculus, branch of mathematics that studies continuously changing quantities. The calculus is characterized by the use of infinite processes, involving passage to a limit—the notion of tending toward, or approaching, an ultimate value. ) has announced the addition of the "Advanced Calculus: An Introduction to Linear Analysis" report to their offering. Advanced Calculus highlights the connections between calculus and linear algebra linear algebra Branch of algebra concerned with methods of solving systems of linear equations; more generally, the mathematics of linear transformations and vector spaces. and provides a mathematically sophisticated introduction to functional analytic concepts. The book stresses that proofs must be written down, scrutinized step-by-step and rewritten whenever there is doubt. Unlike the competition, this book approaches the rigorous foundations of calculus in a manner that reorients thinking in the directions taken by modern analysis. Key Topics Covered: Preface. Acknowledgments. Introduction. PART I. ADVANCED CALCULUS IN ONE VARIABLE. 1. Real Numbers and Limits of Sequences. 2. Continuous Functions. 3. Rieman Integral. 4. The Derivative. 5. Infinite Series infinite series In mathematics, the sum of infinitely many numbers, whose relationship can typically be expressed as a formula or a function. An infinite series that results in a finite sum is said to converge (see convergence). One that does not, diverges. . PART II. ADVANCED TOPICS IN ONE VARIABLE. 6. Fourier Series Fourier series In mathematics, an infinite series used to solve special types of differential equations. It consists of an infinite sum of sines and cosines, and because it is periodic (i.e. . 7. The Riemann-Stieltjes Integral In mathematics, the Riemann-Stieltjes integral is a generalization of the Riemann integral, named after Bernhard Riemann and Thomas Joannes Stieltjes. Definition The Riemann-Stieltjes integral of a real-valued function f . PART III. ADVANCED CALCULUS IN SEVERAL VARIABLES. 8. Euclidean Space Euclidean space In geometry, a two- or three-dimensional space in which the axioms and postulates of Euclidean geometry apply; also, a space in any finite number of dimensions, in which points are designated by coordinates (one for each dimension) and the distance between . 9. Continuous Functions on Euclidean Space. 10. The Derivative in Euclidean Space. 11. Riemann Integration in Euclidean Space. Appendix A. Set Theory. Problem Solutions. References. Index For more information visit http://www.researchandmarkets.com/research/3d1413/advanced_calculus |
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