English | 2022 | ISBN: 1470465655, 978-1470465650 | 456 pages | True PDF | 22.73 MB
The book introduces complex analysis as a natural extension of the calculus of real-valued functions. The mechanism for doing so is the extension theorem, which states that any real analytic function extends to an analytic function defined in a region of the complex plane. The connection to real functions and calculus is then natural. The introduction to analytic functions feels intuitive and their fundamental properties are covered quickly. As a result, the book allows a surprisingly large coverage of the classical analysis topics of analytic and meromorphic functions, harmonic functions, contour integrals and series representations, conformal maps, and the Dirichlet problem. It also introduces several more advanced notions, including the Riemann hypothesis and operator theory, in a manner accessible to undergraduates. The last chapter describes bounded linear operators on Hilbert and Banach spaces, including the spectral theory of compact operators, in a way that also provides an excellent review of important topics in linear algebra and provides a pathway to undergraduate research topics in analysis.
The book allows flexible use in a single semester, full-year, or capstone course in complex analysis. Prerequisites can range from only multivariate calculus to a transition course or to linear algebra or real analysis. There are over one thousand exercises of a variety of types and levels. Every chapter contains an essay describing a part of the history of the subject and at least one connected collection of exercises that together comprise a project-level exploration.

MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz, 2 Ch
Genre: eLearning | Language: English + srt | Duration: 52 lectures (8h 8m) | Size: 1.16 GB
Differentiation Course : A Self-Paced High-Quality Study Guide - Complete preparation with Tasks & Quizzes

100+1 Problems in Advanced Calculus | 9.69 MB
English | 233 Pages

Title: 100+1 Problems in Advanced Calculus: A Creative Journey through the Fjords of Mathematical Analysis for Beginners (Problem Books in Mathematics)
Author: Paolo Toni
Year: 2022

English | 2022 | ISBN: 3030918629 | 233 pages | True PDF EPUB | 21.8 MB
This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques. With eight chapters, this work guides the student through the basic principles of the subject, with a level of complexity that requires good use of imagination.
In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and l'Hospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found at the end of each chapter.

Calculus: Single Variable By Deborah Hughes-Hallett, William G. McCallum, Andrew M. Gleason, Eric Connally, David O. Lomen, Douglas Quinney, Daniel E. Flath, David Lovelock, Karen Rhea, Selin Kalayciôglu, Guadalupe I. Lozano, Adam H. Spiegler, Brigitte Lahme, Brad G. Osgood, Jef
2013 | 771 Pages | ISBN: 0470888539 | PDF | 24 MB

Paolo Toni, "100+1 Problems in Advanced Calculus: A Creative Journey through the Fjords of Mathematical Analysis for Beginners "
English | ISBN: 3030918629 | 2022 | 237 pages | PDF | 4 MB

English | 2022 | ISBN: 1032047798 | 318 pages | True PDF | 38.45 MB
Fractional calculus is used to model many real-life situations from science and engineering. The book includes different topics associated with such equations and their relevance and significance in various scientific areas of study and research. In this book readers will find several important and useful methods and techniques for solving various types of fractional-order models in science and engineering. The book should be useful for graduate students, PhD students, researchers and educators interested in mathematical modelling, physical sciences, engineering sciences, applied mathematical sciences, applied sciences, and so on.

MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz, 2 Ch
Genre: eLearning | Language: English + srt | Duration: 115 lectures (21h 22m) | Size: 2 GB
Become an Expert on a Wide Range of Functions, Trigonometry, Sequence & Series, Conic Sections and other Precalc topics

MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz, 2 Ch
Genre: eLearning | Language: English | Duration: 87 lectures (7h 52m) | Size: 1.76 GB
Learn Calculus 1 and understand insights about it

Fractional Calculus Applications
pdf | 10.62 MB | English | Isbn:‎ 978-0486450018 | Author: author unknown | Year: 2006