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Differential Equations - With MATLAB - 01 edition

ISBN13: 978-0130593184
ISBN10: 0130593184

Summary: A manual demonstrating the power and utility of MATLAB in a differential equations course.

Accompanying the text is some of the finest software available for use in a differential equations course. This software has been extensively tested in the classroom and students applaud its ease of use. The MATLAB function dfield5 is used to plot solutions of first order differential equations of the form using a variety of solvers: Euler, RK2, RK4, and Dormand-Princ
e. Direction fields can also be drawn. The MATLAB function pplane5 is used to draw solutions of planar, autonomous systems having the form. Solutions can be drawn in the phase plane, tx-plane, ty-plane, and there are 3-dimensional and compositive views available. Many advanced features are available, including: direction field, nullclines, equilibrium point analysis and linearization, and the ability to adjust the step size of fixed-step solvers and the error tolerances of the Dormand-Prince solver. Users can also build and save systems and galleries of systems for later use. MATLAB functions eul, rk2, and rk4 also accompany the text and are used to introduce readers to fixed-step solvers and error analysis.

An extensive treatment of MATLAB's suite of ODE solvers empowers students with the ability to apply powerful routines to the solution of higher order equations and systems.
Summary: A manual demonstrating the power and utility of MATLAB in a differential equations course.

Accompanying the text is some of the finest software available for use in a differential equations course. This software has been extensively tested in the classroom and students applaud its ease of use. The MATLAB function dfield5 is used to plot solutions of first order differential equations of the form using a variety of solvers: Euler, RK2, RK4, and Dormand-Prince. Direction fields can also be drawn. The MATLAB function pplane5 is used to draw solutions of planar, autonomous systems having the form. Solutions can be drawn in the phase plane, tx-plane, ty-plane, and there are 3-dimensional and compositive views available. Many advanced features are available, including: direction field, nullclines, equilibrium point analysis and linearization, and the ability to adjust the step size of fixed-step solvers and the error tolerances of the Dormand-Prince solver. Users can also build and save systems and galleries of systems for later use. MATLAB functions eul, rk2, and rk4 also accompany the text and are used to introduce readers to fixed-step solvers and error analysis.

An extensive treatment of MATLAB's suite of ODE solvers empowers students with the ability to apply powerful routines to the solution of higher order equations and systems. ...show less