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Programming in Python and Julia for Physics: High-Level Languages for Scientific Computing

Kumar Prafull -
Table of Contents Introduction Why Python and Julia for Physics? Core Language Features for Scientific Computing Numerical Computing in Python Symbolic and Analytical Computation in Python Visualization with Python Julia's Philosophy...

Visualizing Physical Systems: Turning Equations into Intuition

Kumar Prafull -
Table of Contents Introduction Why Visualization Matters in Physics Types of Physical Visualization Vector Fields and Scalar Fields Phase Space and Trajectory Plots Contour and Density Plots Animations of Time Evolution 3D...

Simulations of Classical Systems: Modeling Dynamics from First Principles

Kumar Prafull -
Table of Contents Introduction Why Simulate Classical Systems? Newtonian Mechanics and Time Integration Lagrangian and Hamiltonian Formulations Numerical Methods for Classical Simulations Simulating Rigid Body Dynamics Molecular Dynamics (MD) N-Body Simulations in...

Numerical Methods in Physics: Algorithms for Approximating the Physical World

Kumar Prafull -
Table of Contents Introduction Why Use Numerical Methods in Physics? Types of Numerical Problems Root-Finding Algorithms Numerical Differentiation and Integration Solving Ordinary Differential Equations (ODEs) Solving Partial Differential Equations (PDEs) Finite Difference...

Computational Tools for Physicists: Bridging Theory and Simulation

Kumar Prafull -
Table of Contents Introduction Why Computational Tools Matter in Physics Categories of Computational Methods Symbolic Computation Tools Numerical Libraries and Environments Data Visualization and Analysis Programming Languages Commonly Used Monte Carlo Simulations Differential...

Mathematical Rigor in Physics: Bridging Intuition and Formalism

Kumar Prafull -
Table of Contents Introduction What Does Mathematical Rigor Mean? The Role of Rigor in Theoretical Physics Historical Evolution: From Intuition to Formalism Common Tools Requiring Rigor: Limits, Derivatives, and...

Set Theory and Logic: The Foundations of Mathematics and Theoretical Reasoning

Kumar Prafull -
Table of Contents Introduction What Is Set Theory? Basic Set Operations Subsets, Power Sets, and Cartesian Products Relations and Functions Types of Sets: Finite, Infinite, Countable, and Uncountable Russell’s Paradox and...

Topology and Compactness: Foundations of Modern Mathematical Physics

Kumar Prafull -
Table of Contents Introduction What Is Topology? Topological Spaces and Open Sets Basis and Subbasis for a Topology Closed Sets and Limit Points Continuity in Topological Terms Homeomorphisms and Topological Invariants Compactness:...

Functional Analysis Basics: Infinite-Dimensional Vector Spaces and Operators

Kumar Prafull -
Table of Contents Introduction What Is Functional Analysis? Normed and Banach Spaces Inner Product and Hilbert Spaces Linear Operators and Functionals Bounded and Unbounded Operators Dual Spaces and the Hahn–Banach Theorem The...

Tensor Analysis: The Language of Modern Theoretical Physics

Kumar Prafull -
Table of Contents Introduction What Is a Tensor? Scalars, Vectors, and Higher-Rank Tensors Tensor Notation and Index Conventions Contravariant and Covariant Tensors The Metric Tensor and Index Raising/Lowering Tensor Transformation Laws Symmetry...

SU(2), SO(3), and U(1): Key Symmetry Groups in Physics

Kumar Prafull -
Table of Contents Introduction Overview of SU(2), SO(3), and U(1) U(1): The Simplest Lie Group U(1) in Physics: Electromagnetism and Phase Invariance SO(3): The Rotation Group in Three Dimensions Properties...

Lie Groups and Lie Algebras: Continuous Symmetries in Physics and Geometry

Kumar Prafull -
Table of Contents Introduction What Are Lie Groups? Examples of Lie Groups Smooth Manifolds and Group Structure What Is a Lie Algebra? The Lie Bracket and Commutators Matrix Lie Groups and...
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