This textbook provides a compact but comprehensive treatment that guides students through applied numerical analysis, using MATLAB®/Simulink®. Ideal as a hands-on source for courses in Numerical Analysis, this text focuses on solving problems using market-standard software, corresponding to all key concepts covered in the classroom. The author uses his extensive classroom experience to guide students toward deeper understanding of key concepts, while they gain facility with software they will need to master for later studies and practical use in their engineering careers.
Author(s): Farzin Asadi
Series: Synthesis Lectures on Engineering, Science, and Technology
Publisher: Springer
Year: 2022
Language: English
Pages: 326
City: Cham
Preface
Contents
1 Essential of MATLAB®
1.1 Introduction
1.2 MATLAB Environment
1.3 Basic Operation with MATLAB
1.4 Clearing the Screen and Variables
1.5 Basic Matrix Operations
1.6 Trigonometric Functions
1.7 Hyperbolic Functions
1.8 Logarithmic and Exponential Function
1.9 Rounding Functions
1.10 Colon Operator
1.11 Linspace and Logspace Commands
1.12 Ones, Zeros and Eye Commands
1.13 Format Command
1.14 Polynomial Functions
1.15 Solution of Nonlinear Systems
1.16 Eigen Values and Eigen Vectors
1.17 Reduced Echelon Form of a Matrix
1.18 Norm of Vectors and Matrices
1.19 Condition Number of a Matrix
1.20 Tic and Toc Commands
1.21 Getting Help in MATLAB
References for Further Study
2 Symbolic Calculations in MATLAB®
2.1 Introduction
2.2 Calculation of Limit, Derivative and Integral
2.3 Solving the Ordinary Differential Equations
2.4 Partial Fraction Expansion and Laplace Transform
2.5 Fourier Transform
2.6 Taylor Series
2.7 Expansion of an Algebraic Expression
Reference for Further Study
3 Numerical Integration and Derivation
3.1 Introduction
3.2 Trapezoidal Rule
3.3 Simpson’s 1/3 Rule
3.4 Simpson 3/8 Rule
3.5 Double Integrals
3.6 Triple Integrals
3.7 Derivative
References for Further Study
4 Statistics with MATLAB®
4.1 Introduction
4.2 Sum of Elements
4.3 Average
4.4 Variance and Standard Deviation
4.5 Factorial
4.6 Combination
4.7 Random Numbers
4.8 Normal Probability Density Function
4.9 Cumulative Distribution Function
References for Further Study
5 Impulse and Step Response of Linear Systems
5.1 Introduction
5.2 Impulse Response of Dynamical Systems
5.3 Step Response of Dynamical Systems
Reference for Further Study
6 Solving Differential Equations in Simulink®
6.1 Introduction
6.2 Solving a Linear Differential Equation in Simulink
6.3 Multiplexer Block
6.4 Giving Name to Scope Blocks
6.5 Selection of Solver
6.6 Transferring the Results from Simulink Environment to MATLAB®
6.7 Transfer Function Block
6.8 State Space Block
6.9 Nonlinear Models
6.10 Van Der Pol Equation
References for Further Study
7 Solving Difference Equations in Simulink®
7.1 Introduction
7.2 Solving the Difference Equations: Example 1
7.3 Solving the Difference Equations: Example 2
7.4 Solving the Difference Equations: Example 3
References for Further Study
8 Curve Fitting with MATLAB®
8.1 Introduction
8.2 Example 1: Linear Curve Fitting
8.3 Graphical Comparison of Estimation with Measured Data
8.4 Quantitative Comparison of Estimation with Data
8.5 Example 2: Nonlinear Curve Fitting
8.6 Example 3: Export the Obtained Equation to the MATLAB Workspace
References for Further Study
9 Drawing Graphs with MATLAB®
9.1 Introduction
9.2 fplot Command
9.3 Plotting the Graph of a Numeric Data
9.4 Addition of Labels and Title to the Drawn Graph
9.5 Exporting the Drawn Graph as a Graphical File
9.6 Drawing Two or More Graphs on the Same Axis
9.7 Logarithmic Axis
9.8 Drawing 2D and 3D Parametric Graphs
9.9 Polar Plot
9.10 3D Surfaces
9.11 Pie Chart
9.12 Exploded Pie Chart
9.13 Export the Drawn Pie Chart as a Graphical File
9.14 Bar Graphs
References for Further Study
10 MATLAB® Programming
10.1 Introduction
10.2 MATLAB Editor
10.3 Simple Game
10.4 Switch-Case Control Statement
10.5 fprintf and disp Command
10.6 Functions
10.7 Calculation of Fourier Series Coefficients
10.8 Newton–Raphson Method
10.9 Bisection Method
10.10 Taking the Equation of the Function from the User
10.11 Range-Kutta 45
10.12 Code for 4th Order Range-Kutta Method
References for Further Study
11 Optimization with MATLAB®
11.1 Introduction
11.2 Local Minimum
11.3 Global Minimum
11.4 fminsearch Function
11.5 Constrained Optimization
References for Further Study
