sing the Symbolic Math Toolbox 10 Calculus 0-2 Differentiation 10-2 Limits Int 1018 Taylor Series 10-18 Calculus Example Extended Calculus Example 10-28 Simplifications and Substitutions 10-41 Substitutions 10-50 Variable-Precision arithmetic 10-57 Example: Using the different Kinds of Arithmetic 10-58 Another Example 10-60 Linear Algebra Linear Algebraic Operations 10-63 Eigenvalues 1067 Jordan canonical form 10.73 Singular Value Decomposition Eigenvalue Trajectories 10·77 Solving Equations 1086 Solving Algebraic Equations 10-86 Several Algebraic Equations Single Differential Equation 10-90 Several Differential Equations 1092 Inde
viii Contents 10 Using the Symbolic Math Toolbox Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-2 Differentiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-2 Limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-8 Integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-11 Symbolic Summation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-18 Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-18 Calculus Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-20 Extended Calculus Example . . . . . . . . . . . . . . . . . . . . . . . . . . 10-28 Simplifications and Substitutions . . . . . . . . . . . . . . . . . . . . 10-41 Simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-41 Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-50 Variable-Precision Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . 10-57 Example: Using the Different Kinds of Arithmetic . . . . . . . . 10-58 Another Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-60 Linear Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-62 Basic Algebraic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-62 Linear Algebraic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . 10-63 Eigenvalues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-67 Jordan Canonical Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-73 Singular Value Decomposition . . . . . . . . . . . . . . . . . . . . . . . . 10-74 Eigenvalue Trajectories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-77 Solving Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10-86 Solving Algebraic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 10-86 Several Algebraic Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 10-87 Single Differential Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 10-90 Several Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . 10-92 Index
Introducing the MATLAB simulink StudentⅤ ersion This chapter introduces the matlaB simulink Student Version and provides resources for using quick Start(p. 1-2) Syllabus for new users of MATLAB About the Student Version (p. 1-3) Description of the matlaB Simulink Student Version Obtaining Additional Math Work How to acquire other products for use with the mAtLAB Products(p. 1-5) simulink student version Getting Started with MATLAB(p. 1-6) Basic steps for using MATLAB Finding Reference Information(p. 1-7) How to learn more about MATLAB and related products Troubleshooting(p. 1-8) Getting information and reporting problems Other resources(. 1-9) Additional sources of information for the matlab Simulink student version Differences between the Student and Product differences Professional Versions(p. 1-11)
1 Introducing the MATLAB & Simulink Student Version This chapter introduces the MATLAB & Simulink Student Version and provides resources for using it. Quick Start (p. 1-2) Syllabus for new users of MATLAB About the Student Version (p. 1-3) Description of the MATLAB & Simulink Student Version Obtaining Additional MathWorks Products (p. 1-5) How to acquire other products for use with the MATLAB & Simulink Student Version Getting Started with MATLAB (p. 1-6) Basic steps for using MATLAB Finding Reference Information (p. 1-7) How to learn more about MATLAB and related products Troubleshooting (p. 1-8) Getting information and reporting problems Other Resources (p. 1-9) Additional sources of information for the MATLAB & Simulink Student Version Differences Between the Student and Professional Versions (p. 1-11) Product differences
1 Introducing the MATLAB Simulink Student Version uick start If you need help installing the software, see Chapter 2, "Installing the MATLAB simulink Student version At the heart of MaTLAB is a programming language you must learn before you can fully exploit its power. You can learn the basics of MATLAB quickly and mastery comes shortly after. You will be rewarded with high-productivity high-creativity computing power that will change the way you work. f you are new to MATLAB, you should start by reading Chapter 4, "Matrices and arrays The most important things to learn are how to enter matrices how to use the: (colon)operator, and how to invoke functions. After you master the basics, you should read the rest of the matlab chapters in this book and run the de · Chapter3,"“ Introduction Introduces MATLAB and the matlaB desktop. Chapter4,“ Matrices and arrays” Introduces matrices and arrays, how to enter and generate them, how to operate on them, and how to control Command window input and output Chapter5,“ Graphics” Introduces MatlAB graphic capabilities and the tools that let you · Chapter6,“ Programming Describes how to use the MatlAB language to create scripts and functions and manipulate data structures, such as cell arrays and multidimensional 1-2
1 Introducing the MATLAB & Simulink Student Version 1-2 Quick Start If you need help installing the software, see Chapter 2, “Installing the MATLAB & Simulink Student Version.” At the heart of MATLAB® is a programming language you must learn before you can fully exploit its power. You can learn the basics of MATLAB quickly, and mastery comes shortly after. You will be rewarded with high-productivity, high-creativity computing power that will change the way you work. If you are new to MATLAB, you should start by reading Chapter 4, “Matrices and Arrays.” The most important things to learn are how to enter matrices, how to use the : (colon) operator, and how to invoke functions. After you master the basics, you should read the rest of the MATLAB chapters in this book and run the demos: • Chapter 3, “Introduction” Introduces MATLAB and the MATLAB desktop. • Chapter 4, “Matrices and Arrays” Introduces matrices and arrays, how to enter and generate them, how to operate on them, and how to control Command Window input and output. • Chapter 5, “Graphics” Introduces MATLAB graphic capabilities and the tools that let you customize your graphs to suit your specific needs. • Chapter 6, “Programming” Describes how to use the MATLAB language to create scripts and functions, and manipulate data structures, such as cell arrays and multidimensional arrays
About the student Version About the student version MATLAB and Simulink@ are the premier software packages for technical computing in education and industry. The MatlAB Simulink Student Version provides all of the features of professional MaTLAB, with no limitations, and the full functionality of professional Simulink, with model sizes up to 1000 blocks. The Student version gives you immediate access to high-performance numeric computing, modeling, and simulation power MATLAB allows you to focus on your course work and applications rather than on programming details. It enables you to solve many numerical problems in a fraction of the time it would take you to write a program in a lower-level language such as C, C++, or Fortran. matlAb helps you better understand and apply concepts in applications ranging from engineering and mathematics to chemistry, biology, and economics Simulink is an interactive tool for modeling, simulating, and analyzing dynamic systems, including controls, signal processing, communications, and complex The Symbolic Math Toolbox, also included with the Student Version, is based on the Maple8 symbolic math engine and lets you perform symbolic computations and variable-precision arithmetic MatLAB products are used in a broad range of industries, including automotive, aerospace electronics, environmental, telecommunications computer peripherals, finance, and medicine. More than one million technical professionals at the world, s most innovative technology companies government research labs, financial institutions, and at more than 3, 500 universities, rely on MatLAB and Simulink as the fundamental tools for their engineering and scientific work. Student use polic This MATLAB& Simulink Student Version License is for use in conjunction with courses offered at degree-granting institutions. The Math Works offers this license as a special service to the student community and asks your help in seeing that its terms are not abused To use this Student License, you must be a student either enrolled in a legree-granting institution or participating in a continuing education program t a degree-granting educational university. 1-3
About the Student Version 1-3 About the Student Version MATLAB and Simulink® are the premier software packages for technical computing in education and industry. The MATLAB & Simulink Student Version provides all of the features of professional MATLAB, with no limitations, and the full functionality of professional Simulink, with model sizes up to 1000 blocks. The Student Version gives you immediate access to high-performance numeric computing, modeling, and simulation power. MATLAB allows you to focus on your course work and applications rather than on programming details. It enables you to solve many numerical problems in a fraction of the time it would take you to write a program in a lower-level language such as C, C++, or Fortran. MATLAB helps you better understand and apply concepts in applications ranging from engineering and mathematics to chemistry, biology, and economics. Simulink is an interactive tool for modeling, simulating, and analyzing dynamic systems, including controls, signal processing, communications, and other complex systems. The Symbolic Math Toolbox, also included with the Student Version, is based on the Maple® 8 symbolic math engine and lets you perform symbolic computations and variable-precision arithmetic. MATLAB products are used in a broad range of industries, including automotive, aerospace, electronics, environmental, telecommunications, computer peripherals, finance, and medicine. More than one million technical professionals at the world’s most innovative technology companies, government research labs, financial institutions, and at more than 3,500 universities, rely on MATLAB and Simulink as the fundamental tools for their engineering and scientific work. Student Use Policy This MATLAB & Simulink Student Version License is for use in conjunction with courses offered at degree-granting institutions. The MathWorks offers this license as a special service to the student community and asks your help in seeing that its terms are not abused. To use this Student License, you must be a student either enrolled in a degree-granting institution or participating in a continuing education program at a degree-granting educational university
1 Introducing the MATLAB Simulink Student Version You may not use this Student License at a company or government lab also you may not use it for commercial or industrial purposes. In these cases, you can acquire the appropriate professional version of the software by contacting The math Works 1-4
1 Introducing the MATLAB & Simulink Student Version 1-4 You may not use this Student License at a company or government lab. Also, you may not use it for commercial or industrial purposes. In these cases, you can acquire the appropriate professional version of the software by contacting The MathWorks