Calculus Without Derivatives expounds the foundations and recent advances in nonsmooth analysis, a powerful compound of mathematical tools that obviates the usual smoothness assumptions. This textbook also provides significant tools and methods towards applications, in particular optimization problems. Whereas most books on this subject focus on a particular theory, this text takes a general approach including all main theories. In order to be self-contained, the book includes three chapters of preliminary material, each of which can be used as an independent course if needed. The first chapter deals with metric properties, variational principles, decrease principles, methods of error bounds, calmness and metric regularity. The second one presents the classical tools of differential calculus and includes a section about the calculus of variations. The third contains a clear exposition of convex analysis.

First time author Ledesma sets his adventure tale in early America. Antonios' travels and adventures carry him across two continents, Europe and America in his quest for a new life. He leaves the safety and love of his family in Italy for uncertain life in a far off land. His dreams, anxieties and fears are borne out as he encounters and conquers the harsh strange and challenging world that surrounds him. Each tantalizing adventure brings our hero closer to maturity, self-esteem and the molding of his character. He experiences love; fear and death on his long journey and witnesses the history that shaped early America. 1n 1846 he becomes an early pioneer by joining a wagon train bound for California. During the trip he experiences encounters with Indians, death, accidents and newly establishes a long lasting friendship. He wanders around California finding romance and land. He eventually starts a grape vineyard and establishes himself as a rancher, husband and father. His life in early California is entwined with such history making events as the Gold Rush, statehood, the Pony Express, building of the Transcontinental Railroad and many more historical events. Reading this heart warming young mans story will enrich the readers to understand the personal triumphs, hardships and the west's rich history

Calculus is a subject that needs to be studied many times over, ideally with a different book in each new round. Using Ezra Pound’s analogy (in ABC of Reading), we may think of the learner as an apprentice carpenter, and of calculus as a stool or table; the learner must keep going until the piece of furniture has three legs and will stand up, or four legs and won’t tip over too easily. Most people cannot follow this plan, because life is short and the list of other demands on their time just too long. This book has been written with a view to making calculus more interesting and intelligible to those who left college, recently or a long time ago, without becoming an adept; those who are familiar with the contents of undergraduate calculus, but not altogether content with their own grasp of the central concepts; those who are aware that the structure put together by them during their apprenticeship is too wobbly, and liable to tip over when the number of independent variables is increased from one to just two. An absurd simile? Not in the opinion of a distinguished mathematician and educator (quoted verbatim in the preface), who acknowledged that the customary definition of a differential in the theory of functions of a single variable breaks down when one extends it to functions of several variables and considers double integrals. He continued: “Students are rightly baffled when they attempt to convert such an integral to polar coordinates and are told that no longer is it permissible to [apply a straightforward extension of the relevant formula for a change of variable in a single integral]. The Jacobian must be used instead, and at this point the logical structure which was built so carefully collapses entirely. If we wish to make calculus an intellectually honest subject and not a collection of convenient tricks, it is time we made a fresh start.” Calculus Without Hocus Pocus aims to elucidate those (and only those) issues that are not treated adequately in standard textbooks. It offers more cogent explanations of the conundrums and paradoxes which have been nagging the minds of students and teachers of calculus for generations. The author, who has been using calculus as a teacher and researcher for over fifty years, has tried to produce a condensed and readable book that throws light from various directions upon the difficult parts of this very technical (and somewhat unpopular) subject; to show some of the reasons why calculus has been cast in the mould in which we find it; and to recommend some minor changes in notation and nomenclature that would remove nearly all of the hocus-pocus which almost every learner of calculus has had to endure so far.

The Greek of the classical age, with Euclid and Archimedes, have conceived very next ideas to those that have allowed the invention of the Infinitesimal and Integral calculation. The author thinks how just Euclide has grazed the concept of infinitesimal, with his theorem related to the "horn angle". It was then in 1600 that Leibniz and Newton they created the Infinitesimal Calculus and that Integral. But the infinitesimals have always elicited criticisms for their logical contradictions, immediately stigmatized by the bishop Berkeley. With the method of the double limit of Weierstrass, the problem apparently, seems overcome. Then in the 1900 Robinson overcome the impasse from the logical point of view, but resorting to the Analysis not-standard, in the sphere of not Archimedean fields. With this work the author overcomes the issue of the infinitesimals, adopting a very classical methodology and, above all, of easy understanding.

The Greek of the classical age, with Euclid and Archimedes, have conceived very next ideas to those that have allowed the invention of the Infinitesimal and Integral calculation. The author thinks how just Euclide has grazed the concept of infinitesimal, with his theorem related to the "horn angle". It was then in 1600 that Leibniz and Newton they created the Infinitesimal Calculus and that Integral. But the infinitesimals have always elicited criticisms for their logical contradictions, immediately stigmatized by the bishop Berkeley. With the method of the double limit of Weierstrass, the problem apparently, seems overcome. Then in the 1900 Robinson overcome the impasse from the logical point of view, but resorting to the Analysis not-standard, in the sphere of not Archimedean fields. With this work the author overcomes the issue of the infinitesimals, adopting a very classical methodology and, above all, of easy understanding.

Students no longer have anything to fear: The Complete Idiot's Guide to Calculus, Second Edition is here. Like its predecessor, it was created with an audience of students working toward a non-science related degree in mind. A non-intimidating, easy-to-understand textbook companion, this new edition has more explanatory graphs and illustrations and double the number of practice problems. First edition of this book has sold more copies than any of the other 70+ books on the subjsect. Twice as many practice problems in the second edition. More college students are now required to take calculus in college than ever before. Author is an award-winning calculus teacher praised for his ability to make this topic fun and approachable. His website, calculus-help.com, reaches thousands of students every month.

This book brings together eleven topics on different aspects of fractional calculus in a single volume. It provides readers the basic knowledge of fractional calculus and introduces advanced topics and applications. The information in the book is presented in four parts: 1. Fractional Diffusion Equations: (i) solutions of fractional diffusion equations using wavelet methods, (ii) the maximum principle for time fractional diffusion equations, (iii) nonlinear sub-diffusion equations. 2. Mathematical Analysis: (i) shifted Jacobi polynomials for solving and identifying coupled fractional delay differential equations, (ii) the monotone iteration principle in the theory of Hadamard fractional delay differential equations, (iii) dynamics of fractional order modified Bhalekar-Gejji System, (iv) Grunwald-Letnikov derivatives. 3. Computational Techniques: GPU computing of special mathematical functions used in fractional calculus. 4. Reviews: (i) the popular iterative method NIM, (ii) fractional derivative with non-singular kernels, (iii) some open problems in fractional order nonlinear system This is a useful reference for researchers and graduate level mathematics students seeking knowledge about of fractional calculus and applied mathematics.

This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.

Let's face it, most students don't take calculus because they find it intellectually stimulating. It's not . . . at least for those who come up on the wrong side of the bell curve! There they are, minding their own business, working toward some non-science related degree, when . . . BLAM! They get next semester's course schedule in the mail, and first on the list is the mother of all loathed college courses . . . CALCULUS! Not to fear—Idiot's Guides®: Calculus I is a curriculum-based companion book created with this audience in mind. This new edition continues the tradition of taking the sting out of calculus by adding more explanatory graphs and illustrations and doubling the number of practice problems! By the time readers are finished, they will have a solid understanding (maybe even a newfound appreciation) for this useful form of math. And with any luck, they may even be able to make sense of their textbooks and teachers.