Mathematik Mit Matlab

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Mathematical Explorations With Matlab

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Author : Ke Chen
language : en
Publisher: Cambridge University Press
Release Date : 1999-04-15

Mathematical Explorations With Matlab written by Ke Chen and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-15 with Computers categories.

This book is about the kind of mathematics usually encountered in first year university courses. A key feature of the book is that this mathematics is explored in depth using the popular and powerful package Matlab. The emphasis is on understanding and investigating the mathematics, and putting it into practice in a wide variety of modelling situations. In the process, the reader will gain some fluency with Matlab, no starting knowledge of the package being assumed.

Mathematik Mit Matlab

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Author : Hans Benker
language : de
Publisher: Springer-Verlag
Release Date : 2013-03-11

Mathematik Mit Matlab written by Hans Benker and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-11 with Mathematics categories.

MATLAB löst die Mathematikaufgaben der Technik und Naturwissenschaften. Dieses Buch eignet sich als Einführung für Einsteiger, begleitendes Übungsbuch für Hörer von Mathematikvorlesungen und Nachschlagewerk für Dozenten und Praktiker. Es enthält zu allen behandelten mathematischen Problemen typische mit MATLAB gelöste Beispiele. Der Leser erlernt so die Anwendung von MATLAB und die Interpretation der Ergebnisse. Die Beispiele beziehen sich auf Release 5.3.

Engineering Mathematics With Matlab

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Author : Won Y. Yang et. al
language : en
Publisher: Won Y. Yang
Release Date : 2019-02-01

Engineering Mathematics With Matlab written by Won Y. Yang et. al and has been published by Won Y. Yang this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-02-01 with Antiques & Collectibles categories.

Chapter 1: Vectors and Matrices 1.1 Vectors 1.1.1 Geometry with Vector 1.1.2 Dot Product 1.1.3 Cross Product 1.1.4 Lines and Planes 1.1.5 Vector Space 1.1.6 Coordinate Systems 1.1.7 Gram-Schmidt Orthonolization 1.2 Matrices 1.2.1 Matrix Algebra 1.2.2 Rank and Row/Column Spaces 1.2.3 Determinant and Trace 1.2.4 Eigenvalues and Eigenvectors 1.2.5 Inverse of a Matrix 1.2.6 Similarity Transformation and Diagonalization 1.2.7 Special Matrices 1.2.8 Positive Definiteness 1.2.9 Matrix Inversion Lemma 1.2.10 LU, Cholesky, QR, and Singular Value Decompositions 1.2.11 Physical Meaning of Eigenvalues/Eigenvectors 1.3 Systems of Linear Equations 1.3.1 Nonsingular Case 1.3.2 Undetermined Case - Minimum-Norm Solution 1.3.3 Overdetermined Case - Least-Squares Error Solution 1.3.4 Gauss(ian) Elimination 1.3.5 RLS (Recursive Least Squares) Algorithm Problems Chapter 2: Vector Calculus 2.1 Derivatives 2.2 Vector Functions 2.3 Velocity and Acceleration 2.4 Divergence and Curl 2.5 Line Integrals and Path Independence 2.5.1 Line Integrals 2.5.2 Path Independence 2.6 Double Integrals 2.7 Green's Theorem 2.8 Surface Integrals 2.9 Stokes' Theorem 2.10 Triple Integrals 2.11 Divergence Theorem Problems Chapter 3: Ordinary Differential Equation 3.1 First-Order Differential Equations 3.1.1 Separable Equations 3.1.2 Exact Differential Equations and Integrating Factors 3.1.3 Linear First-Order Differential Equations 3.1.4 Nonlinear First-Order Differential Equations 3.1.5 Systems of First-Order Differential Equations 3.2 Higher-Order Differential Equations 3.2.1 Undetermined Coefficients 3.2.2 Variation of Parameters 3.2.3 Cauchy-Euler Equations 3.2.4 Systems of Linear Differential Equations 3.3 Special Second-Order Linear ODEs 3.3.1 Bessel's Equation 3.3.2 Legendre's Equation 3.3.3 Chebyshev's Equation 3.3.4 Hermite's Equation 3.3.5 Laguerre's Equation 3.4 Boundary Value Problems Problems Chapter 4: Laplace Transform 4.1 Definition of the Laplace Transform 4.1.1 Laplace Transform of the Unit Step Function 4.1.2 Laplace Transform of the Unit Impulse Function 4.1.3 Laplace Transform of the Ramp Function 4.1.4 Laplace Transform of the Exponential Function 4.1.5 Laplace Transform of the Complex Exponential Function 4.2 Properties of the Laplace Transform 4.2.1 Linearity 4.2.2 Time Differentiation 4.2.3 Time Integration 4.2.4 Time Shifting - Real Translation 4.2.5 Frequency Shifting - Complex Translation 4.2.6 Real Convolution 4.2.7 Partial Differentiation 4.2.8 Complex Differentiation 4.2.9 Initial Value Theorem (IVT) 4.2.10 Final Value Theorem (FVT) 4.3 The Inverse Laplace Transform 4.4 Using of the Laplace Transform 4.5 Transfer Function of a Continuous-Time System Problems 300 Chapter 5: The Z-transform 5.1 Definition of the Z-transform 5.2 Properties of the Z-transform 5.2.1 Linearity 5.2.2 Time Shifting - Real Translation 5.2.3 Frequency Shifting - Complex Translation 5.2.4 Time Reversal 5.2.5 Real Convolution 5.2.6 Complex Convolution 5.2.7 Complex Differentiation 5.2.8 Partial Differentiation 5.2.9 Initial Value Theorem 5.2.10 Final Value Theorem 5.3 The Inverse Z-transform 5.4 Using The Z-transform 5.5 Transfer Function of a Discrete-Time System 5.6 Differential Equation and Difference Equation Problems Chapter 6: Fourier Series and Fourier Transform 6.1 Continuous-Time Fourier Series (CTFS) 6.1.1 Definition and Convergence Conditions 6.1.2 Examples of CTFS 6.2 Continuous-Time Fourier Transform (CTFT) 6.2.1 Definition and Convergence Conditions 6.2.2 (Generalized) CTFT of Periodic Signals 6.2.3 Examples of CTFT 6.2.4 Properties of CTFT 6.3 Discrete-Time Fourier Transform (DTFT) 6.3.1 Definition and Convergence Conditions 6.3.2 Examples of DTFT 6.3.3 DTFT of Periodic Sequences 6.3.4 Properties of DTFT 6.4 Discrete Fourier Transform (DFT) 6.5 Fast Fourier Transform (FFT) 6.5.1 Decimation-in-Time (DIT) FFT 6.5.2 Decimation-in-Frequency (DIF) FFT 6.5.3 Computation of IDFT Using FFT Algorithm 6.5.4 Interpretation of DFT Results 6.6 Fourier-Bessel/Legendre/Chebyshev/Cosine/Sine Series 6.6.1 Fourier-Bessel Series 6.6.2 Fourier-Legendre Series 6.6.3 Fourier-Chebyshev Series 6.6.4 Fourier-Cosine/Sine Series Problems Chapter 7: Partial Differential Equation 7.1 Elliptic PDE 7.2 Parabolic PDE 7.2.1 The Explicit Forward Euler Method 7.2.2 The Implicit Forward Euler Method 7.2.3 The Crank-Nicholson Method 7.2.4 Using the MATLAB Function 'pdepe()' 7.2.5 Two-Dimensional Parabolic PDEs 7.3 Hyperbolic PDES 7.3.1 The Explict Central Difference Method 7.3.2 Tw-Dimensional Hyperbolic PDEs 7.4 PDES in Other Coordinate Systems 7.4.1 PDEs in Polar/Cylindrical Coordinates 7.4.2 PDEs in Spherical Coordinates 7.5 Laplace/Fourier Transforms for Solving PDES 7.5.1 Using the Laplace Transform for PDEs 7.5.2 Using the Fourier Transform for PDEs Problems Chapter 8: Complex Analysis 509 8.1 Functions of a Complex Variable 8.1.1 Complex Numbers and their Powers/Roots 8.1.2 Functions of a Complex Variable 8.1.3 Cauchy-Riemann Equations 8.1.4 Exponential and Logarithmic Functions 8.1.5 Trigonometric and Hyperbolic Functions 8.1.6 Inverse Trigonometric/Hyperbolic Functions 8.2 Conformal Mapping 8.2.1 Conformal Mappings 8.2.2 Linear Fractional Transformations 8.3 Integration of Complex Functions 8.3.1 Line Integrals and Contour Integrals 8.3.2 Cauchy-Goursat Theorem 8.3.3 Cauchy's Integral Formula 8.4 Series and Residues 8.4.1 Sequences and Series 8.4.2 Taylor Series 8.4.3 Laurent Series 8.4.4 Residues and Residue Theorem 8.4.5 Real Integrals Using Residue Theorem Problems Chapter 9: Optimization 9.1 Unconstrained Optimization 9.1.1 Golden Search Method 9.1.2 Quadratic Approximation Method 9.1.3 Nelder-Mead Method 9.1.4 Steepest Descent Method 9.1.5 Newton Method 9.2 Constrained Optimization 9.2.1 Lagrange Multiplier Method 9.2.2 Penalty Function Method 9.3 MATLAB Built-in Functions for Optimization 9.3.1 Unconstrained Optimization 9.3.2 Constrained Optimization 9.3.3 Linear Programming (LP) 9.3.4 Mixed Integer Linear Programing (MILP) Problems Chapter 10: Probability 10.1 Probability 10.1.1 Definition of Probability 10.1.2 Permutations and Combinations 10.1.3 Joint Probability, Conditional Probability, and Bayes' Rule 10.2 Random Variables 10.2.1 Random Variables and Probability Distribution/Density Function 10.2.2 Joint Probability Density Function 10.2.3 Conditional Probability Density Function 10.2.4 Independence 10.2.5 Function of a Random Variable 10.2.6 Expectation, Variance, and Correlation 10.2.7 Conditional Expectation 10.2.8 Central Limit Theorem - Normal Convergence Theorem 10.3 ML Estimator and MAP Estimator 653 Problems

Scientific Computing With Matlab

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Author : Dingyu Xue
language : en
Publisher: CRC Press
Release Date : 2018-09-03

Scientific Computing With Matlab written by Dingyu Xue and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-03 with Mathematics categories.

Scientific Computing with MATLAB®, Second Edition improves students’ ability to tackle mathematical problems. It helps students understand the mathematical background and find reliable and accurate solutions to mathematical problems with the use of MATLAB, avoiding the tedious and complex technical details of mathematics. This edition retains the structure of its predecessor while expanding and updating the content of each chapter. The book bridges the gap between problems and solutions through well-grouped topics and clear MATLAB example scripts and reproducible MATLAB-generated plots. Students can effortlessly experiment with the scripts for a deep, hands-on exploration. Each chapter also includes a set of problems to strengthen understanding of the material.

Exercises In Computational Mathematics With Matlab

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Author : Tom Lyche
language : en
Publisher: Springer
Release Date : 2014-09-02

Exercises In Computational Mathematics With Matlab written by Tom Lyche and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-02 with Mathematics categories.

Designed to provide tools for independent study, this book contains student-tested mathematical exercises joined with MATLAB programming exercises. Most chapters open with a review followed by theoretical and programming exercises, with detailed solutions provided for all problems including programs. Many of the MATLAB exercises are presented as Russian dolls: each question improves and completes the previous program and results are provided to validate the intermediate programs. The book offers useful MATLAB commands, advice on tables, vectors, matrices and basic commands for plotting. It contains material on eigenvalues and eigenvectors and important norms of vectors and matrices including perturbation theory; iterative methods for solving nonlinear and linear equations; polynomial and piecewise polynomial interpolation; Bézier curves; approximations of functions and integrals and more. The last two chapters considers ordinary differential equations including two point boundary value problems, and deal with finite difference methods for some partial differential equations. The format is designed to assist students working alone, with concise Review paragraphs, Math Hint footnotes on the mathematical aspects of a problem and MATLAB Hint footnotes with tips on programming.

Numerical And Analytical Methods With Matlab

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Author : William Bober
language : en
Publisher: CRC Press
Release Date : 2009-08-11

Numerical And Analytical Methods With Matlab written by William Bober and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-11 with Technology & Engineering categories.

Numerical and Analytical Methods with MATLAB® presents extensive coverage of the MATLAB programming language for engineers. It demonstrates how the built-in functions of MATLAB can be used to solve systems of linear equations, ODEs, roots of transcendental equations, statistical problems, optimization problems, control systems problems, and stress analysis problems. These built-in functions are essentially black boxes to students. By combining MATLAB with basic numerical and analytical techniques, the mystery of what these black boxes might contain is somewhat alleviated. This classroom-tested text first reviews the essentials involved in writing computer programs as well as fundamental aspects of MATLAB. It next explains how matrices can solve problems of linear equations, how to obtain the roots of algebraic and transcendental equations, how to evaluate integrals, and how to solve various ODEs. After exploring the features of Simulink, the book discusses curve fitting, optimization problems, and PDE problems, such as the vibrating string, unsteady heat conduction, and sound waves. The focus then shifts to the solution of engineering problems via iteration procedures, differential equations via Laplace transforms, and stress analysis problems via the finite element method. The final chapter examines control systems theory, including the design of single-input single-output (SISO) systems. Two Courses in One Textbook The first six chapters are appropriate for a lower level course at the sophomore level. The remaining chapters are ideal for a course at the senior undergraduate or first-year graduate level. Most of the chapters contain projects that require students to write a computer program in MATLAB that produces tables, graphs, or both. Many sample MATLAB programs (scripts) in the text provide guidance on completing these projects.

Scientific Computing With Matlab And Octave

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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-20

Scientific Computing With Matlab And Octave written by Alfio Quarteroni and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-20 with Computers categories.

This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer-based solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros, the extrema, and the integrals of continuous functions, solve linear systems, approximate functions using polynomials and construct accurate approximations for the solution of ordinary and partial differential equations. To make the format concrete and appealing, the programming environments Matlab and Octave are adopted as faithful companions. The book contains the solutions to several problems posed in exercises and examples, often originating from important applications. At the end of each chapter, a specific section is devoted to subjects which were not addressed in the book and contains bibliographical references for a more comprehensive treatment of the material. From the review: ".... This carefully written textbook, the third English edition, contains substantial new developments on the numerical solution of differential equations. It is typeset in a two-color design and is written in a style suited for readers who have mathematics, natural sciences, computer sciences or economics as a background and who are interested in a well-organized introduction to the subject." Roberto Plato (Siegen), Zentralblatt MATH 1205.65002.

Statistics In Matlab

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Author : MoonJung Cho
language : en
Publisher: CRC Press
Release Date : 2014-12-15

Statistics In Matlab written by MoonJung Cho and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-15 with Business & Economics categories.

This primer provides an accessible introduction to MATLAB version 8 and its extensive functionality for statistics. Fulfilling the need for a practical user's guide, the book covers capabilities in the main MATLAB package, the Statistics Toolbox, and the student version of MATLAB, presenting examples of how MATLAB can be used to analyze data. It explains how to determine what method should be used for analysis, and includes figures, visual aids, and access to a companion website with data sets and additional examples.

Numerical And Analytical Methods With Matlab For Electrical Engineers

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Author : William Bober
language : en
Publisher: CRC Press
Release Date : 2012-08-27

Numerical And Analytical Methods With Matlab For Electrical Engineers written by William Bober and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-27 with Mathematics categories.

Combining academic and practical approaches to this important topic, Numerical and Analytical Methods with MATLAB® for Electrical Engineers is the ideal resource for electrical and computer engineering students. Based on a previous edition that was geared toward mechanical engineering students, this book expands many of the concepts presented in that book and replaces the original projects with new ones intended specifically for electrical engineering students. This book includes: An introduction to the MATLAB programming environment Mathematical techniques for matrix algebra, root finding, integration, and differential equations More advanced topics, including transform methods, signal processing, curve fitting, and optimization An introduction to the MATLAB graphical design environment, Simulink Exploring the numerical methods that electrical engineers use for design analysis and testing, this book comprises standalone chapters outlining a course that also introduces students to computational methods and programming skills, using MATLAB as the programming environment. Helping engineering students to develop a feel for structural programming—not just button-pushing with a software program—the illustrative examples and extensive assignments in this resource enable them to develop the necessary skills and then apply them to practical electrical engineering problems and cases.

Statics With Matlab

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Author : Dan B. Marghitu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-13

Statics With Matlab written by Dan B. Marghitu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-13 with Science categories.

Engineering mechanics involves the development of mathematical models of the physical world. Statics addresses the forces acting on and in mechanical objects and systems. Statics with MATLAB® develops an understanding of the mechanical behavior of complex engineering structures and components using MATLAB® to execute numerical calculations and to facilitate analytical calculations. MATLAB® is presented and introduced as a highly convenient tool to solve problems for theory and applications in statics. Included are example problems to demonstrate the MATLAB® syntax and to also introduce specific functions dealing with statics. These explanations are reinforced through figures generated with MATLAB® and the extra material available online which includes the special functions described. This detailed introduction and application of MATLAB® to the field of statics makes Statics with MATLAB® a useful tool for instruction as well as self study, highlighting the use of symbolic MATLAB® for both theory and applications to find analytical and numerical solutions