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001452422 001__ 1452422
001452422 003__ OCoLC
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001452422 020__ $$a9783031215025$$q(electronic bk.)
001452422 020__ $$a3031215028$$q(electronic bk.)
001452422 020__ $$z303121501X
001452422 020__ $$z9783031215018
001452422 0247_ $$a10.1007/978-3-031-21502-5$$2doi
001452422 035__ $$aSP(OCoLC)1366124399
001452422 040__ $$aYDX$$beng$$cYDX$$dGW5XE$$dEBLCP
001452422 049__ $$aISEA
001452422 050_4 $$aQA39.3
001452422 08204 $$a510$$223
001452422 1001_ $$aPopescu, Sever Angel,$$eauthor.
001452422 24510 $$aAdvanced mathematics for engineers and physicists/$$cSever Angel Popescu, Marilena Jianu.
001452422 260__ $$aCham, Switzerland :$$bSpringer,$$c[2022]
001452422 300__ $$a1 online resource :$$billustrations
001452422 504__ $$aIncludes bibliographical references and index.
001452422 5050_ $$aIntro -- Preface -- Contents -- Basic Notations -- Sets -- Hyperbolic Functions -- Euler Integrals -- 1 First-Order Differential Equations -- 1.1 Introduction to Ordinary Differential Equations -- 1.2 Separable Equations -- 1.3 Homogeneous Equations -- 1.4 First-Order Linear Differential Equations -- 1.5 Bernoulli Equations -- 1.6 Riccati Equations -- 1.7 Exact Differential Equations -- 1.8 Lagrange Equations and Clairaut Equations -- 1.9 Existence and Uniqueness of Solution of the Cauchy Problem -- 1.10 Exercises -- 2 Higher-Order Differential Equations -- 2.1 Introduction
001452422 5058_ $$a2.2 Homogeneous Linear Differential Equations of Order n -- 2.3 Non-Homogeneous Linear Differential Equations of Order n -- 2.4 Homogeneous Linear Equations with Constant Coefficients -- 2.5 Nonhomogeneous Linear Equations with Constant Coefficients -- 2.6 Euler Equations -- 2.7 Exercises -- 3 Systems of Differential Equations -- 3.1 Introduction -- 3.2 First-Order Systems and Differential Equations of Order n -- 3.3 Linear Systems of Differential Equations -- 3.4 Linear Systems with Constant Coefficients -- 3.4.1 The Homogeneous Case (the Algebraic Method)
001452422 5058_ $$a3.4.2 The Non-Homogeneous Case (the Method of Undetermined Coefficients) -- 3.4.2.1 The Diagonalizable Case -- 3.4.2.2 The Non-Diagonalizable Case -- 3.4.3 Matrix Exponential and Linear Systems with Constant Coefficients -- 3.4.3.1 Fundamental Matrix -- 3.4.3.2 Matrix Exponential -- 3.4.3.3 The Exponential of a Diagonalizable Matrix -- 3.4.3.4 The Exponential of a Nondiagonalizable Matrix -- 3.4.4 Elimination Method for Linear Systems with Constant Coefficients -- 3.5 Autonomous Systems of Differential Equations -- 3.6 First-Order Partial Differential Equations
001452422 5058_ $$a3.6.1 Linear Homogeneous First-Order PDE -- 3.6.2 Quasilinear First-Order Partial Differential Equations -- 3.7 Exercises -- 4 Fourier Series -- 4.1 Introduction: Periodic, Piecewise Smooth Functions -- 4.1.1 Periodic Functions -- 4.1.2 Piecewise Continuous and Piecewise Smooth Functions -- 4.2 Fourier Series Expansions -- 4.2.1 Series of Functions -- 4.2.2 A Basic Trigonometric System -- 4.2.3 Fourier Coefficients -- 4.3 Orthogonal Systems of Functions -- 4.3.1 Inner Product -- 4.3.2 Best Approximation in the Mean: Bessel's Inequality -- 4.4 The Convergence of Fourier Series
001452422 5058_ $$a4.5 Differentiation and Integration of the Fourier Series -- 4.6 The Convergence in the Mean: Complete Systems -- 4.7 Examples of Fourier Expansions -- 4.8 The Complex form of the Fourier Series -- 4.9 Exercises -- 5 Fourier Transform -- 5.1 Improper Integrals -- 5.2 The Fourier Integral Formula -- 5.3 The Fourier Transform -- 5.4 Solving Linear Differential Equations -- 5.5 Moments Theorems -- 5.6 Sampling Theorem -- 5.7 Discrete Fourier Transform -- 5.8 Exercises -- 6 Laplace Transform -- 6.1 Introduction -- 6.2 Properties of the Laplace Transform -- 6.3 Inverse Laplace Transform
001452422 506__ $$aAccess limited to authorized users.
001452422 520__ $$aThis book is designed to be an introductory course to some basic chapters of Advanced Mathematics for Engineering and Physics students, researchers in different branches of Applied Mathematics and anyone wanting to improve their mathematical knowledge by a clear, live, self-contained and motivated text. Here, one can find different topics, such as differential (first order or higher order) equations, systems of differential equations, Fourier series, Fourier and Laplace transforms, partial differential equations, some basic facts and applications of the calculus of variations and, last but not least, an original and more intuitive introduction to probability theory. All these topics are carefully introduced, with complete proofs, motivations, examples, applications, problems and exercises, which are completely solved at the end of the book. We added a generous supplementary material (11.1) with a self-contained and complete introduction to normed, metric and Hilbert spaces. Since we used some topics from complex function theory, we also introduced in Chapter 11 a section (11.2) with the basic facts in this important field. What a reader needs for a complete understanding of this book? For a deep understanding of this book, it is required to take a course in undergraduate calculus and linear algebra. We mostly tried to use the engineering intuition instead of insisting on mathematical tricks. The main feature of the material presented here is its clarity, motivation and the genuine desire of the authors to make extremely transparent the "mysterious" mathematical tools that are used to describe and organize the great variety of impressions that come to the searching mind, from the infinite complexity of Nature. The book is recommended not only to engineering and physics students or researchers but also to junior students in mathematics because it shows the connection between pure mathematics and physical phenomena, which always supply motivations for mathematical discoveries.
001452422 650_0 $$aMathematics.
001452422 650_0 $$aEngineering mathematics.
001452422 650_0 $$aMathematical physics.
001452422 655_0 $$aElectronic books.
001452422 7001_ $$aJianu, Marilena,$$eauthor.
001452422 77608 $$iPrint version: $$z303121501X$$z9783031215018$$w(OCoLC)1347781821
001452422 852__ $$bebk
001452422 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-031-21502-5$$zOnline Access$$91397441.1
001452422 909CO $$ooai:library.usi.edu:1452422$$pGLOBAL_SET
001452422 980__ $$aBIB
001452422 980__ $$aEBOOK
001452422 982__ $$aEbook
001452422 983__ $$aOnline
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