Practical MATLAB Modeling with Simulink: Programming and Simulating Ordinary and Partial Differential Equations

Table of Contents
About the Author
About the Technical Reviewer
Acknowledgments
Introduction
Part I: Ordinary Differential Equations
	Chapter 1: Analytical Solutions for ODEs
		Classifying ODEs
		Example 1
		Example 2
		Example 3
		Analytical Solutions of ODEs
			dsolve()
		Example 4
		Example 5
		Example 6
		Example 7
		Second-Order ODEs and a System of ODEs
		Example 8
		Example 9
		Example 10
		Example 11
		Example 12
		Example 13
		Laplace Transforms
		Example 14
			laplace/ilaplace
		Example 15
		Example 16
		Example 17
		Example 18
		Example 19
		Example 20
		Example 21
		References
	Chapter 2: Numerical Methods for First-Order ODEs
		Euler Method
		Example 1
		Improved Euler Method
		Backward Euler Method
		Example 2
		Midpoint Rule Method
		Example 3
		Ralston Method
		Runge-Kutta Method
		Example 4
		Runge-Kutta-Gill Method
		Runge-Kutta-Fehlberg Method
		Adams-Bashforth Method
		Example 5
		Milne Method
		Example 6
		Taylor Series Method
		Example 7
		Adams-Moulton Method
		Example 8
		MATLAB’s Built-in ODE Solvers
		Example 9
			The OPTIONS, ODESET, and ODEPLOT Tools of Solvers
		Example 10
		Example 11
		Simulink Modeling
		Example 12
		SIMSET
		References
	Chapter 3: Numerical Methods for Second-Order ODEs
		Euler Method
		Example 1
		Example 2
		Example 3
		Example 4
		Example 5
		Runge-Kutta Method
		Example 6
		Example 7
		Example 8
		Example 9
		Example 10
		Adams-Moulton Method
		Example 11
		Example 12
		Simulink Modeling
		Example 13
		Example 14
		Example 15
		Example 16
		Nonzero Starting Initial Conditions
		Example 17
		ODEx Solvers
		Example 18
		Example 19
		Example 20
		Example 21
		diff()
		Example 22
	Chapter 4: Stiff ODEs
		Example 1
		Example 2
		Example 3
		Example 4
		Jacobian Matrix
		Example 5
		Example 6
	Chapter 5: Higher-Order and Coupled ODEs
		Fourth-Order ODE Problem
		Robertson Problem
		Akzo-Nobel Problem
		HIRES Problem
		Reference
	Chapter 6: Implicit ODEs
		Example 1
		Example 2
		Example 3
		Example 4
		Example 5
		Example 6
		References
	Chapter 7: Comparative Analysis of ODE Solution Methods
		Example 1
		Drill Exercises
		Exercise 1
		Exercise 2
		Exercise 3
		Exercise 4
		Exercise 5
		Exercise 6
		Exercise 7
		Exercise 8
		Exercise 9
		Exercise 10
		Exercise 11
		Exercise 12
		Exercise 13
Part II: Boundary Value Problems in Ordinary Differential Equations
	Chapter 8: Boundary Value Problems
		Dirichlet Boundary Condition Problem
		Example 1
		Example 2
		Robin Boundary Condition Problem
		Example 3
		Sturm-Liouville Boundary Value Problem
		Example 4
		Stiff Boundary Value Problem
		Example 5
		References
		Drill Exercises
		Exercise 1
		Exercise 2
		Exercise 3
		Exercise 4
		Exercise 5
		Exercise 6
		Exercise 7
		Exercise 8
		Exercise 9
		Exercise 10
		Exercise 11
		Exercise 12
		Exercise 13
Part III: Applications of Ordinary Differential Equations
	Chapter 9: Spring-Mass-Damper Systems
		Single Degree of Freedom System
		Case 1: Free Vibration (Motion)
		Case 2: Forced Vibration (Motion)
		Two Degrees of Freedom System
		Three Degrees of Freedom System
		Matrix Approach for n-Degree of Freedom System
		References
	Chapter 10: Electromechanical and Mechanical Systems
		Modeling a DC Motor
		Modeling a DC Motor with Flexible Load
		Modeling a Microphone
		Modeling Motor: Pump Gear Box
			Modeling Double Pendulum
		Reference
	Chapter 11: Trajectory Problems
		Falling Object
		Thrown Ball Trajectories
		References
	Chapter 12: Simulation Problems
		Lorenz System
		Lotka-Voltera Problem
		References
		Drill Exercises
		Exercise 1
		Exercise 2
		Exercise 3
		Exercise 4
		Exercise 5
		Exercise 6
		Exercise 7
		Exercise 8
		Exercise 9
		Exercise 10
		Exercise 11
		Exercise 12
		Exercise 13
		Exercise 14
		Exercise 15
		Exercise 16
		Exercise 17
		Exercise 18
Part IV: Partial Differential Equations
	Chapter 13: Solving Partial Differential Equations
		pdepe()
		One-Dimensional Heat Transfer Problem
		Example 1
		Two-Dimensional Heat Transfer: Solving an Elliptic PDE with the Gauss-Seidel Method
		Example 2
		del2(): Laplace Operator
		Example 3
		Wave Equation
		Solving a One-Dimensional Wave Equation
		Example 4
		Solving a Two-Dimensional Wave Equation
		Example 5
		References
		Drill Exercises
		Exercise 1
		Exercise 2
		Exercise 3
		Exercise 4
		Exercise 5
		Exercise 6
		Exercise 7
		Exercise 8
		Exercise 9
		Exercise 10
		Exercise 11
		Exercise 12
		Exercise 13
Index