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Jeffrey R. Chasnov’s Scientific Computing is a set of introductory lecture notes designed for mathematics students with no previous background in numerical analysis, combining numerical mathematics, MATLAB programming, dynamical systems, and computational physics. The book begins with core numerical methods—including IEEE floating-point arithmetic and round-off error, root-finding methods such as bisection and Newton’s method, numerical integration, Runge–Kutta methods for differential equations, Gaussian elimination and LU decomposition, finite differences, iterative methods, interpolation, and least-squares approximation.
It then applies these techniques to nonlinear dynamical systems and chaos, using the pendulum to introduce stability, bifurcations, phase portraits, limit cycles, Poincaré sections, fractals, period doubling, and the Feigenbaum constant. The final section develops computational fluid dynamics, deriving the continuity and Navier–Stokes equations and showing how numerical methods can model laminar flow, vorticity, and two-dimensional flow past rectangular and circular obstacles. Overall, it is a practical bridge between mathematical theory and computer-based experimentation, with a strong emphasis on learning numerical methods through concrete scientific applications.
LECTURE NOTES [PDF]
It then applies these techniques to nonlinear dynamical systems and chaos, using the pendulum to introduce stability, bifurcations, phase portraits, limit cycles, Poincaré sections, fractals, period doubling, and the Feigenbaum constant. The final section develops computational fluid dynamics, deriving the continuity and Navier–Stokes equations and showing how numerical methods can model laminar flow, vorticity, and two-dimensional flow past rectangular and circular obstacles. Overall, it is a practical bridge between mathematical theory and computer-based experimentation, with a strong emphasis on learning numerical methods through concrete scientific applications.
LECTURE NOTES [PDF]
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