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Numerical Solutions of Initial Value Problems Using Mathematica

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The book contains a detailed account of numerical solutions of differential equations of a number of elementary problems of physics using Euler and second order Runge–Kutta methods using Mathematic...
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  • 31 May 2018
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The book contains a detailed account of numerical solutions of differential equations of a number of elementary problems of physics using Euler and second order Runge–Kutta methods using Mathematica 6.0. The problems are motion under constant force (free fall), motion under Hooke’s law force (simple harmonic motion), motion under combination of Hooke’s law force and a velocity dependent damping force (damped harmonic motion) and radioactive decay law. Also included are uses of Mathematica in dealing with complex numbers, in solving system of linear equations, in carrying out differentiation and integration, and in dealing with matrices.
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Price: £46.95
Pages: 56
Publisher: Morgan & Claypool Publishers
Imprint: Morgan & Claypool Publishers
Publication Date: 31 May 2018
Trim Size: 10.00 X 7.00 in
ISBN: 9780750329170
Format: Paperback
BISACs:

SCIENCE / Physics / General, Applied physics, SCIENCE / Applied Sciences, SCIENCE / Physics / Mathematical & Computational, Statistical physics, Mathematical physics

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Chapter I Numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods 1.1 Euler solution of differential equation 1.2 2nd order Runge-Kutta solution of differential equation
Chapter II Motion under constant force: numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods using Mathematica 2.1 Motion under constant force: the differential equations of themotion 2.2 Euler solution of free fall using Mathematica 6.0 2.3 Runge-Kutta solution of free fall using Mathematica 6.0
Chapter III Simple harmonic oscillator: numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods using Mathematica 3.1 Motion under Hooke’s law force: the differential equations of the motion 3.2 Euler solution of simple harmonic oscillation using Mathematica 6.0 3.3 Runge-Kutta solution of simple harmonic oscillation using Mathematica 6.0
Chapter IV Damped harmonic oscillator: numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods using Mathematica 4.1 Damped harmonic oscillator: the differential equations of the motion 4.2 Euler solution of damped harmonic oscillation using Mathematica 6.0 4.3 Runge-Kutta solution of damped harmonic oscillation using Mathematica 6.0
Chapter V Radioactive decay: numerical solution of differential equation using Euler and 2nd order Runge-Kutta methods using Mathematica 5.1 The differential equation for radioactive decay 5.2 Euler solution of radioactive decay law using Mathematica 6.0 5.3 Runge-Kutta solution of radioactive decay law using Mathematica 6.0
Chapter VI Miscellaneous use of Mathematica in computational Physics 6.1 Dealing with complex numbers using mathematica 6.2 Solution of a system of linear equations using mathematica 6.3 Differentiation and integration using mathematica 6.4 Dealing with matrices using Mathematica