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Foundations Of Differential Calculus

Author: Euler
Publisher: Springer Science & Business Media
ISBN: 0387226451
Size: 50.90 MB
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The positive response to the publication of Blanton's English translations of Euler's "Introduction to Analysis of the Infinite" confirmed the relevance of this 240 year old work and encouraged Blanton to translate Euler's "Foundations of Differential Calculus" as well. The current book constitutes just the first 9 out of 27 chapters. The remaining chapters will be published at a later time. With this new translation, Euler's thoughts will not only be more accessible but more widely enjoyed by the mathematical community.

Local Analysis Part A Foundations And Differential Calculus Part B First Order Differential Equations And Differential Forms

Author: Carl-Heinz Schriba
Publisher: Wiley-VCH
ISBN: 9783527400638
Size: 77.12 MB
Format: PDF, ePub, Mobi
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The first part of the "Local Analysis" textbook is self-consistent & provides a detailed introduction to those parts of finite-dimensional real calculus which go with multi-dimensional differentiation & only one-dimensional integration. The second part is based upon the first one & gives a detailed introduction to the initial value problems of certain systems of first order ordinary & partial differential equations as well as to the theory of differential forms.

Introduction To Differential Calculus

Author: Ulrich L. Rohde
Publisher: John Wiley & Sons
ISBN: 1118130146
Size: 39.19 MB
Format: PDF
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Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications. The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Subsequent chapters present a broad range of theories, methods, and applications in differential calculus, including: Concepts of function, continuity, and derivative Properties of exponential and logarithmic function Inverse trigonometric functions and their properties Derivatives of higher order Methods to find maximum and minimum values of a function Hyperbolic functions and their properties Readers are equipped with the necessary tools to quickly learn how to understand a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine-tuning of various calculus skills. Introduction to Differential Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals alike who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.

Introduction To Analysis Of The Infinite

Author: Leonhard Euler
Publisher: Springer Science & Business Media
ISBN: 1461210216
Size: 50.49 MB
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From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."

Shapes And Geometries

Author: M. C. Delfour
Publisher: SIAM
ISBN: 0898719364
Size: 10.89 MB
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Presents the latest groundbreaking theoretical foundation to shape optimization in a form accessible to mathematicians, scientists and engineers.

The Absolute Differential Calculus

Author: Tullio Levi-Civita
Publisher: Dover Publications
ISBN: 9780486446370
Size: 18.88 MB
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A chief requirement in the study of relativity is knowledge of the absolute differential calculus, the subject that Einstein found necessary for developing his ideas mathematically. Tullio Levi-Civita was one of the founders of this field of mathematics, and he presents a clear, detailed exposition of the subject in this classic book. The first section of the three-part treatment examines functional determinants and matrices; systems of total differential equations; linear partial differential equations in complete systems; and algebraic foundations of the absolute differential calculus, concluding with a geometrical introduction to the theory of differential quadratic forms. Part two, a study of the fundamental quadratic form and the absolute differential calculus, focuses on covariant differentiation, invariants and differential parameters, and locally geodesic coordinates; Riemann's symbols and properties relating to curvature, Ricci's and Einstein's symbols, and geodesic deviation; relations between two different metrics referred to the same parameters, manifolds of constant curvature; and differential quadratic forms of class zero and class one; and some applications of intrinsic geometry. The third and final section explores physical applications, including the evolution of mechanics and geometrical optics and their relation to a four-dimensional world according to Einstein; and gravitational equations and general relativity.

Fundamentals Of Calculus

Author: Carla C. Morris
Publisher: John Wiley & Sons
ISBN: 1119015316
Size: 22.42 MB
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Features the techniques, methods, and applications of calculus using real-world examples from business and economics as well as the life and social sciences An introduction to differential and integral calculus, Fundamentals of Calculus presents key topics suited for a variety of readers in fields ranging from entrepreneurship and economics to environmental and social sciences. Practical examples from a variety of subject areas are featured throughout each chapter and step-by-step explanations for the solutions are presented. Specific techniques are also applied to highlight important information in each section, including symbols interspersed throughout to further reader comprehension. In addition, the book illustrates the elements of finite calculus with the varied formulas for power, quotient, and product rules that correlate markedly with traditional calculus. Featuring calculus as the “mathematics of change,” each chapter concludes with a historical notes section. Fundamentals of Calculus chapter coverage includes: Linear Equations and Functions The Derivative Using the Derivative Exponents and Logarithms Differentiation Techniques Integral Calculus Integrations Techniques Functions of Several Variables Series and Summations Applications to Probability Supplemented with online instructional support materials, Fundamentals of Calculus is an ideal textbook for undergraduate students majoring in business, economics, biology, chemistry, and environmental science.