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| موضوع: كتاب Symbolic Math Toolbox - User's Guide 2023 الأربعاء 28 فبراير 2024, 1:16 am | |
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أخواني في الله أحضرت لكم كتاب Symbolic Math Toolbox - User's Guide 2023 MathWorks
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Contents Symbolic Computations in MATLAB Find Symbolic Variables in Expressions, Functions, and Matrices 2-2 Find a Default Symbolic Variable . 2-2 Choose syms or sym Function 2-4 Change Output Format of Symbolic and Variable-Precision Arithmetic 2-8 Change Output Display Format of Symbolic Results in the Live Editor . 2-11 Add Subscripts, Superscripts, and Accents to Symbolic Variables in the Live Editor 2-14 Copy and Paste Symbolic Output in Live Editor 2-18 Check Symbolic Equations, Inequalities, and Conditional Statements . 2-23 Numeric to Symbolic Conversion 2-29 Choose Numeric or Symbolic Arithmetic . 2-32 Double-Precision Arithmetic 2-32 Variable-Precision Arithmetic . 2-32 Symbolic Arithmetic 2-33 Comparisons of Numeric and Symbolic Arithmetic . 2-34 Increase Precision of Numeric Calculations . 2-36 Compute Binomial Coefficients Exactly . 2-38 Find Almost Integers with High-Precision Arithmetic . 2-41 Decimal Digits of PI 2-45 Units of Measurement Tutorial . 2-47 Unit Conversions and Unit Systems 2-53 Convert Units . 2-53 Temperature Unit Conversion . 2-54 Convert to SI, CGS, or US Unit Systems . 2-54 Define Custom Unit System from Existing System 2-56 Define Custom Unit System Directly 2-57 Unit System Definition 2-58 Units and Unit Systems List 2-60 Units List 2-60 SI Unit Prefixes List 2-70 Unit Systems List 2-71 Defining Constants of SI Units 2-72 Units in Physics Calculations . 2-74 vi ContentsThe Physics of the Damped Harmonic Oscillator . 2-78 Evaluating the Average Power Delivered by a Wind Turbine 2-88 Developing an Algorithm for Undistorting an Image 2-93 Electric Dipole Moment and Radiation Power . 2-99 Validate Simulink Model Using Symbolic Math Toolbox 2-102 Mathematics 3 Solve Algebraic Equations 3-3 Solve an Equation . 3-3 Return the Full Solution to an Equation 3-3 Work with the Full Solution, Parameters, and Conditions Returned by solve 3-4 Visualize and Plot Solutions Returned by solve . 3-5 Simplify Complicated Results and Improve Performance 3-6 Solve System of Algebraic Equations 3-7 Troubleshoot Equation Solutions from solve Function 3-17 Return Only Real Solutions . 3-17 Apply Simplification Rules . 3-17 Use Assumptions to Narrow Results 3-18 Simplify Solutions 3-19 Tips 3-19 Solve Equations Numerically . 3-21 Solve System of Linear Equations . 3-30 Solve System of Linear Equations Using linsolve . 3-30 Solve System of Linear Equations Using solve 3-31 Select Numeric or Symbolic Solver 3-33 Solve Parametric Equations in ReturnConditions Mode . 3-34 Solve Algebraic Equation Using Live Editor Task . 3-36 Solve Differential Equation . 3-43 First-Order Linear ODE . 3-43 Solve Differential Equation with Condition . 3-43 Nonlinear Differential Equation with Initial Condition . 3-44 Second-Order ODE with Initial Conditions . 3-44 Third-Order ODE with Initial Conditions . 3-44 More ODE Examples 3-45 Solve a System of Differential Equations 3-47 viiSolve a Second-Order Differential Equation Numerically 3-52 Solve Partial Differential Equation of Tsunami Model . 3-54 Solve Differential Algebraic Equations (DAEs) . 3-61 Solve Semilinear DAE System . 3-70 Solve DAEs Using Mass Matrix Solvers . 3-77 Step 1. Convert DAEs to Function Handles . 3-77 Step 2. Find Initial Conditions 3-78 Step 3. Solve DAE System . 3-79 Analyze and Manipulate Differential Algebraic Equations . 3-82 Derive and Apply Inverse Kinematics to Two-Link Robot Arm 3-89 Gauss-Laguerre Quadrature Evaluation Points and Weights 3-96 Simulate a Stochastic Process Using the Feynman–Kac Formula . 3-106 The Black–Scholes Formula for Call Option Price . 3-114 Choose Function to Rearrange Expression . 3-119 Combine Terms of Same Algebraic Structures . 3-119 Expand Expressions . 3-120 Factor Expressions 3-121 Extract Subexpressions from Expression . 3-123 Collect Terms with Same Powers . 3-123 Rewrite Expressions in Terms of Other Functions . 3-124 Compute Partial Fraction Decompositions of Expressions . 3-125 Compute Normal Forms of Rational Expressions 3-125 Represent Polynomials Using Horner Nested Forms . 3-126 Extract Numerators and Denominators of Rational Expressions . 3-127 Simplify Symbolic Expressions . 3-129 Simplify Using Options . 3-130 Simplify Using Assumptions . 3-132 Simplify Fractions 3-132 Simplify Symbolic Expressions Using Live Editor Task . 3-134 Substitute Variables in Symbolic Expressions 3-140 Substitute Elements in Symbolic Matrices . 3-142 Substitute Scalars with Matrices . 3-144 Evaluate Symbolic Expressions Using subs . 3-146 Abbreviate Common Terms in Long Expressions 3-147 Harmonic Analysis of Transfer Function Output 3-150 viii ContentsExplore Single-Period Asset Arbitrage 3-156 Analytical Solutions of the Inverse Kinematics of a Humanoid Robot 3-160 Differentiation 3-171 Derivatives of Expressions with Several Variables . 3-172 More Examples 3-173 Integration . 3-176 Integration with Real Parameters . 3-178 Integration with Complex Parameters 3-179 High-Precision Numerical Integration Using Variable-Precision Arithmetic 3-180 Taylor Series . 3-182 Fourier and Inverse Fourier Transforms . 3-184 Fourier Transform Definition 3-184 Concept: Using Symbolic Workflows . 3-184 Calculate Beam Deflection Using Fourier Transform . 3-184 Solve Differential Equations of RLC Circuit Using Laplace Transform 3-188 Solve Difference Equations Using Z-Transform 3-195 Symbolic Summation 3-200 Comparing symsum and sum 3-200 Computational Speed of symsum versus sum 3-200 Output Format Differences Between symsum and sum . 3-201 Padé Approximant . 3-202 Limits . 3-209 One-Sided Limits . 3-209 Find Asymptotes, Critical, and Inflection Points 3-212 Functional Derivatives Tutorial 3-217 Learn Calculus in the Live Editor . 3-222 Differentiation 3-227 Integration . 3-235 Interactive Calculus in Live Editor . 3-239 Maxima, Minima, and Inflection Points 3-241 Find Extremum of Multivariate Function and Its Approximation . 3-250 Padé Approximant of Time-Delay Input 3-254 Solve Partial Differential Equation of Nonlinear Heat Transfer 3-260 ixSymbolic Matrix Computation . 3-267 Linear Algebraic Operations . 3-274 Symbolic Hilbert Matrix 3-274 Symbolic Linear Algebra Operations . 3-274 Variable-Precision Arithmetic 3-275 Symbolic Investigation of Singular Value . 3-276 Basic Algebraic Operations . 3-278 Singular Value Decomposition . 3-280 Eigenvalues 3-282 Jordan Canonical Form . 3-286 Eigenvalues of the Laplace Operator 3-288 Hilbert Matrices and Their Inverses 3-298 Markov Chain Analysis and Stationary Distribution . 3-302 Matrix Rotations and Transformations 3-307 Clear Assumptions and Reset the Symbolic Engine 3-314 Check Assumptions Set on Variables . 3-315 Effects of Assumptions on Computations 3-316 Recognize and Avoid Round-Off Errors 3-317 Use Symbolic Computations When Possible . 3-317 Perform Calculations with Increased Precision . 3-317 Compare Symbolic and Numeric Results 3-319 Plot the Function or Expression 3-319 Increase Speed by Reducing Precision 3-321 Prime Factorizations . 3-323 Handling Large Integers to Solve the 196 Problem 3-326 Graphics 4 Create Plots of Symbolic Expressions . 4-2 Transform Spherical Coordinates to Cartesian Coordinates and Plot Analytically 4-10 Tangent Plane and Normal Line of Implicit Surface 4-17 Analytical Plotting with Symbolic Math Toolbox . 4-21 x ContentsSimulate the Motion of the Periodic Swing of a Pendulum . 4-38 Animation and Solution of Double Pendulum Motion . 4-53 Animation and Model of Automotive Piston . 4-60 Code Generation 5 Generate C or Fortran Code from Symbolic Expressions 5-2 Generate MATLAB Functions from Symbolic Expressions . 5-3 Generating a Function Handle . 5-3 Control the Order of Variables . 5-3 Generate a File . 5-4 Name Output Variables . 5-5 Generate MATLAB Function Blocks from Symbolic Expressions . 5-6 Generate and Edit a Block 5-6 Control the Order of Input Ports 5-6 Name the Output Ports . 5-7 Generate Simscape Equations from Symbolic Expressions 5-8 Convert Algebraic and Differential Equations 5-8 Limitations 5-9 Deploy Generated MATLAB Functions from Symbolic Expressions with MATLAB Compiler 5-10 Generate C Code from Symbolic Expressions Using the MATLAB Coder App 5-16 Derive Quadrotor Dynamics for Nonlinear Model Predictive Control . 5-30 Using Symbolic Mathematics with Optimization Toolbox Solvers 5-37 Improving Accuracy and Performance in Optimization 5-46 Analytical Model of Cantilever Truss Structure for Simscape . 5-52 Customize and Extend Simscape Libraries for a Custom DC Motor 5-60 Estimate Model Parameters of a Symbolically Derived Plant Model in Simulink 5-69 xiMuPAD to MATLAB Migration 6 MuPAD Engines and MATLAB Workspace 6-2 Convert MuPAD Notebooks to MATLAB Live Scripts . 6-3 Convert a MuPAD Notebook .mn to a MATLAB Live Script .mlx . 6-3 Convert MuPAD Graphics to MATLAB Graphics 6-4 Known Issues 6-4 Troubleshoot MuPAD to MATLAB Translation Errors . 6-8 Troubleshoot MuPAD to MATLAB Translation Warnings . 6-15 Differences Between MATLAB and MuPAD Syntax 6-20 Call Built-In MuPAD Functions from MATLAB . 6-22 evalin . 6-22 feval 6-22 evalin vs. feval 6-23 Floating-Point Arguments of evalin and feval . 6-23 Functions #ماتلاب,#متلاب,#Matlab,#مات_لاب,#مت_لاب,
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