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Chapra Steven C., Canale Raymond P. Numerical Methods for Engineers

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Chapra Steven C., Canale Raymond P. Numerical Methods for Engineers
Textbook. — 5th Edition, McGraw-Hill, 2006. — 926 p.
Applications continues its tradition of excellence.
The revision retains the successful pedagogy of the prior editions. Chapra and Canale's unique approach opens each part of the text with sections called Motivation, Mathematical Background, and Orientation, preparing the student for what is to come in a motivating and engaging manner. Each part closes with an Epilogue containing sections called Trade-Offs, Important Relationships and Formulas, and Advanced Methods and Additional References. Much more than a summary, the Epilogue deepens understanding of what has been learned and provides a peek into more advanced methods.
Mathematical modeling and engineering problem solving
Programming and software
Approximations and round-off errors
Truncation errors and the Taylor series
Bracketing methods
Open methods
Roots of polynomials
Case studies : roots of equations
Gauss elimination
LU decomposition and matrix inversion
Special matrices and Gauss-Seidel
Case studies : linear algebraic equations
One-dimensional unconstrained optimization
Multidimensional unconstrained optimization
Constrained optimization
Case studies : optimization
Least-squares regression
Fourier approximation
Case studies : curve fitting
Newton-Cotes integration formulas
Integration of equations
Numerical differentiation
Case studies : numerical integration and differentiation
Runge-Kutta methods
Stiffness and multistep methods
Boundary-value and eigenvalue problems
Case studies : ordinary differential equations
Finite difference : elliptic equations
Finite difference : parabolic equations
Finite-element method
Case studies : partial differential equations
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