Theoretical Principles & Computational Physics Guide
Mathematical Operations: Arithmetic Expressions & Operator Precedence
Dr. Alorika Chatterjee & Dr. Anirban Shaw
Science & Physics Learners
Python 3 / NumPy / SciPy
1. Core Principles & Theoretical Framework
Algebraic Expressions: Translates algebraic force laws, kinetic energies, and kinematic equations directly into executable code.
Operator Precedence: Follows standard algebraic hierarchy: Exponentiation (
**) > Multiplication/Division (*, /, //, %) > Addition/Subtraction. Modular Arithmetic: Modulo operator
% implements periodic boundary conditions in spatial lattices and particle simulations.2. Mathematical Formulation & Algorithmic Pipeline
Newtonian gravitational and electrostatic inverse-square forces:
$$ F = G \frac{m_1 m_2}{r^2} \quad \implies \quad \texttt{F = G * m1 * m2 / r**2} $$
3. Numerical Mechanics & Implementation Logic
- Explicit Parentheses: Always parenthesize fractional denominators (e.g.
a / (b * c)rather thana / b * c). - True vs Floor Division: Use
/for exact physical quantities and//for discrete indices and lattice sites. - Exponentiation: Prefer
x**2overmath.pow(x, 2)in core loops for speed and exact integer types.
4. Relevant Computational Practice Exercises
Exercise 1
Calculate the gravitational attraction between Earth and the Moon using astronomical parameters in SI units.
Exercise 2
Evaluate the relativistic Lorentz factor $\gamma = 1 / \sqrt{1 - v^2/c^2}$ for speeds $v = 0.5c, 0.9c, 0.99c$.
Exercise 3
Simulate 1D periodic boundary wrapping for a particle moving on a ring of circumference $L = 10.0\text{ m}$.
- Hans Petter Langtangen, "A Primer on Scientific Programming with Python", Springer (2016).