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Exterior calculus is a branch of mathematics which involves differential geometry. In Exterior calculus the concept of differentiations is generalized to antisymmetric exterior derivatives and the notions of ordinary integration to differentiable manifolds of arbitrary dimensions. It therefore generalizes the fundamental theorem of calculus to Stokes' theorem. This textbook covers the fundamental requirements of exterior calculus in curricula for college students in mathematics and engineering programs. Chapters start from Heaviside-Gibbs algebra, and progress to different concepts in Grassman algebra. The final section of the book covers applications of exterior calculus with solutions. Readers will find a concise and clear study of vector calculus and differential geometry, along with several examples and exercises. The solutions to the exercises are also included at the end of the book. This is an ideal book for students with a basic background in mathematics who wish to learn about exterior calculus as part of their college curriculum and equip themselves with the knowledge to apply relevant theoretical concepts in practical situations.

Calculus.

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"This book is devoted to some recent aspects of calculus. The book contains seven chapters. Chapter 1 introduces the conception for conformable delta (Hilger) derivative and some of its properties. Results in this chapter include basic conformable delta derivative, the conformable exponential function, conformable trigonometric and hyperbolic functions, conformable delta integral and integral rules and Taylor's formula. They are considered first order conformable dynamic equations on time scales. Chapter 2 is devoted to some classes second order quadratic difference equations. They are given criteria for existence of a unique equilibrium point that is stable and unstable, existence of prime period-two solutions. Chapter 3 is aimed to develop two calculi over the specific algebraic operations, preserving the preceding relativistic addition formula and having all ordinary properties. Chapter 4 is devoted to principles of hypercomplex random function calculus. Generalized Gaussian-type hypercomplex valued measures are studied. Random functions controlled by these measures are investigated. Solutions of hyperbolic PDEs over hypercomplex numbers such as the octonion algebra and Cayley-Dickson algebras are scrutinized. Chapter 5 covers the interesting historical aspects of the spreadsheets and their distinct advantages. It is described how the ubiquitous Microsoft Excel spreadsheets can be used to implement well-known numerical methods such as Simpson's Rule and Trapezoidal Rules. Appropriate examples are presented in substantial detail. The aim of Chapter 6 is to show some didactic tools that can be suggested by professors so that students can recall those issues saved in the deepest part of their minds. In Chapter 7, based on fractional differences, a fractional calculus is developed which complies with most of the properties that is to say non-differentiability, non-commutativity of derivative and long-range memory. The book is addressed to a wide audience of specialists such as mathematicians, physicists, engineers and biologists"--

Calculus

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Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible. This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.

Calculus.

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Calculus

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Calculus.