Computational Physics Course Description

Based on the methodology of Nicholas J. Giordano

Course Overview

This course introduces students to computational techniques and numerical methods for solving diverse physics problems that go beyond analytical approaches. The curriculum uses the pedagogical framework of Nicholas J. Giordano, focusing on how computation can expand and deepen physical understanding through simulation and analysis¹.

Learning Objectives

Upon completion, students will:

• Understand the role of computation in modern physics.
• Develop the ability to translate physical problems into algorithms.
• Apply standard numerical methods (e.g., root finding, integration, differentiation, differential equations, Monte Carlo methods) to solve physical systems.
• Visualize and interpret computational results.
• Gain proficiency in scientific programming and computational thinking².

Course Content

Module	Topics and Skills
Introduction & Programming	Basics of computational thinking in physics. Introduction to programming languages (typically Python or MATLAB). Algorithms, data visualization.
Numerical Methods	Root-finding (bisection, Newton-Raphson), interpolation (polynomials, Lagrange), least squares and data fitting, numerical integration (trapezoidal, Simpson’s rule), ordinary differential equations (Euler, Runge-Kutta).
Classical Mechanics	Applications: projectile motion, oscillatory systems, planetary motion, chaos, and dynamical systems. Simulation of Newtonian and nonlinear systems34.
Random Processes	Monte Carlo simulations, random walks, diffusion, nuclear decay, statistical mechanics foundations.
Electromagnetism & Quantum	Simulation of electrostatics, fields, basic quantum systems (time-dependent and independent Schrödinger equations).
Advanced Topics	Fourier transforms, partial differential equations, complex systems (e.g., Ising model, cellular automata, phase transitions)1.

Teaching Methods

• Interactive lectures on physical and numerical concepts.
• Hands-on programming labs and coding assignments.
• Guided projects replicating textbook simulations and exploring new scenarios.
• Visualization of results to develop intuition for numerical solutions².

Evaluation

• Problem sets and coding assignments
• Mid-term exam on theory and implementation
• Project: formulation, coding, and reporting of a computational solution to a relevant physical problem

Recommended Text

• Computational Physics (2nd Ed.), Nicholas J. Giordano & Hisao Nakanishi¹

Typical Applications

• Classical and quantum simulations are not solvable analytically
• Visualization of complex system behavior
• Statistical and stochastic physics
• Project-based investigations in modern research topics

Prerequisites

• Introductory physics
• Calculus (single and multivariable)
• Basic programming (not mandatory, but helpful; the course often includes a rapid introduction to coding fundamentals)²

This course leverages computation to make physical concepts tangible and equips students for advanced careers or research in physics and related disciplines¹².

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Footnotes

1. https://www.mathworks.com/academia/books/computational-physics-giordano.html ↩ ↩² ↩³ ↩⁴

2. https://class-descriptions.northwestern.edu/4930/WCAS/PHYSICS/28874 ↩ ↩² ↩³ ↩⁴

3. https://nust.edu.pk/wp-content/uploads/course_content_files/340753870_PHY-930%20%20%20Computational%20Physics%20.pdf ↩

4. https://www.ndsu.edu/fileadmin/physics.ndsu.edu/PDF_FILES/Detailed_Course_Descriptions/Phys370.pdf ↩