Foundations of Computational Thinking for Physics: Volume III - Numerical Methods for Physics Using C: Modeling the Physical World Through Simulation

Feb 2026 · Kamsali Nagaraja

Ebook

296

Pages

About this ebook

Numerical Methods for Physics Using C constitutes the modelling and simulation core of the trilogy Foundations of Computational Thinking for Physics. This volume advances beyond algorithmic description into disciplined numerical practice, where approximation is controlled, verified, and interpreted within physical context. The architecture of the book unfolds in four integrated layers. The first establishes the necessity of numerical methods by examining the limits of analytic closure and the transition from continuous formulation to structured discretisation. The second develops the principal computational engines - root finding, numerical integration, differential equation solvers, linear systems, boundary value problems, and data fitting, each presented through mathematical formulation, algorithmic structure, and systematic implementation in C. The third layer extends these methods into physics modelling systems, emphasising stability, invariant preservation, conditioning, convergence under refinement, and sensitivity analysis. The fourth consolidates learning through structured computational laboratories in which physical interpretation, error behaviour, and verification discipline are explicitly examined.

Throughout the volume, computation is treated not as mechanical calculation but as structured scientific reasoning. Truncation error, round-off effects, phase drift, resonance behaviour, matrix conditioning, and perturbation amplification are analysed as measures of credibility rather than technical details. Students are guided to compare methods, monitor conserved quantities, perform refinement studies, and distinguish physical sensitivity from numerical artefact.

This volume completes the trilogy by unifying conceptual foundations, algorithmic construction, modelling practice, and scientific judgment into a coherent computational framework suitable for advanced undergraduate and postgraduate physics education. It affirms computation as a disciplined extension of physical reasoning capable of modelling complexity, quantifying uncertainty, and transforming controlled approximation into structured insight.

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About the author

Dr Kamsali Nagaraja is a Professor of Physics at Bangalore University, India, with expertise in Atmospheric, Space, and Planetary Physics. His work integrates analytical modelling, mathematical methods, and computational simulation for complex dynamical systems. As principal architect of the trilogy, he has shaped its synthesis of mathematical structure, algorithmic formulation, and disciplined scientific modelling in contemporary physics education.

Dr Susheela KL is an Assistant Professor of Physics at Bangalore University, specializing in Solid State Physics and Materials Science. With interdisciplinary training in Education and Computer Applications, she brings a structured pedagogical perspective to computational modelling and simulation-based learning. Her work strengthens the integration of mathematical methods, numerical implementation, and conceptual clarity in education.

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