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Physics
119 topics across 7 chapters
Chapter 1
Mathematical Tools for Physics
1
Calculus and Vector Calculus
2 subtopics
2
Single-variable calculus refresh (derivatives, integrals, Taylor series) + problem set
3
Vector calculus drills: grad/div/curl, line & surface integrals, Gauss/Stokes theorems
4
Linear Algebra
2 subtopics
5
Matrix operations + eigenvalues/eigenvectors practice (including diagonalization)
6
Orthogonality, inner products, and change of basis (incl. least-squares intuition)
7
Differential Equations
2 subtopics
8
Solve common ODEs (first/second order), with physical examples (SHM, RC/RL)
9
Separation of variables for PDEs (wave/heat/Laplace) + boundary condition practice
10
Complex Numbers and Fourier Methods
2 subtopics
11
Complex exponentials and phasors (connect sinusoids ↔ exponentials) + exercises
12
Fourier series/transform practice on simple signals and waveforms
13
Probability and Statistics for Physics
2 subtopics
14
Random variables and key distributions (Gaussian, Poisson, exponential) + physics examples
15
Uncertainty propagation and least-squares estimation (derive and apply)
16
Numerical Methods Basics
2 subtopics
17
Numerical differentiation/integration (trapezoid/Simpson) + error behavior experiments
18
ODE solvers (Euler vs Runge–Kutta) mini-project on a physical system
Chapter 2
Measurement, Data, and Scientific Practice
19
Units, Dimensions, and Scaling
2 subtopics
20
SI units, dimensional analysis, and consistency checks (do 20+ quick drills)
21
Scaling and order-of-magnitude estimation (Fermi problems) for physical systems
22
Uncertainty and Error Analysis
2 subtopics
23
Significant figures, systematic vs random error, and reporting results correctly
24
Confidence intervals and combining uncertainties (incl. repeated measurements)
25
Data Visualization and Model Fitting
2 subtopics
26
Least-squares curve fitting (linear and nonlinear) using a real dataset
27
Residual plots and model checking: detect overfitting, bias, and outliers
28
Experimental Design and Lab Skills
2 subtopics
29
Lab notebook workflow, safety basics, and writing a clear experimental procedure
30
Calibration and instrument limits (resolution, drift, saturation) + short lab exercise
Chapter 3
Classical Mechanics
31
Kinematics and Newton’s Laws
2 subtopics
32
Free-body diagrams and Newton’s 2nd law setup (multi-step problems)
33
2D kinematics problems: projectile motion, uniform circular motion, relative motion
34
Work–Energy and Momentum
2 subtopics
35
Work–energy theorem + conservative potentials (solve and interpret)
36
Momentum and impulse problems: collisions, center-of-mass frame, rockets basics
37
Rotational Motion and Rigid Bodies
2 subtopics
38
Torque and angular momentum conservation problems (point mass and rigid body)
39
Moments of inertia + rolling without slipping (solve several canonical examples)
40
Gravitation and Orbits
2 subtopics
41
Gravitational potential energy, escape velocity, and effective potentials (problems)
42
Keplerian orbits: circular/elliptic parameters, energy and angular momentum relations
↗ Differential Equations (see Chapter 1)
43
Oscillations and Resonance
2 subtopics
44
SHM, damping, and driven oscillators (amplitude/phase) + problem set
45
Resonance, quality factor, and energy flow in oscillators (interpret experiments)
46
Lagrangian and Hamiltonian Mechanics
2 subtopics
47
Derive Euler–Lagrange equations for standard systems (pendulum, Atwood, central force)
48
Hamiltonian mechanics basics: phase space, canonical equations, Poisson brackets (intro)
Chapter 4
Electricity and Magnetism
49
Electrostatics
2 subtopics
50
Gauss’s law for symmetric charge distributions (spheres, cylinders, planes) + practice
51
Electric potential, capacitance, and stored energy (derive and solve problems)
52
Electric Circuits
2 subtopics
53
Kirchhoff’s laws: analyze DC networks and measure equivalent resistance
54
RC/RL/RLC circuits: transients, resonance, and AC impedance/phasors (problems)
55
Magnetostatics and Induction
2 subtopics
56
Compute magnetic fields with Biot–Savart and Ampère’s law (canonical geometries)
57
Faraday’s law and Lenz’s law: induction problems + inductance intuition
58
Fields in Matter (Dielectrics and Magnetics)
2 subtopics
59
Polarization/magnetization: bound charge/current, susceptibility concepts (problems)
60
Boundary conditions at material interfaces (E, D, B, H) + worked examples
61
Maxwell’s Equations and Electromagnetic Waves
2 subtopics
62
Translate Maxwell’s equations between integral and differential forms + interpret each term
63
Derive EM wave equation; compute Poynting vector and radiation pressure basics
↗ Differential Equations (see Chapter 1)
Chapter 5
Thermodynamics and Statistical Mechanics
64
Thermodynamic Systems and the First Law
2 subtopics
65
First law practice: sign conventions, PV work, and energy bookkeeping in processes
66
Heat capacities, calorimetry, and phase changes (solve multi-step problems)
67
Second Law and Entropy
2 subtopics
68
Entropy calculations for ideal gases and phase changes (reversible vs irreversible)
69
Carnot cycle and efficiency limits (engines and refrigerators) + problems
70
Thermodynamic Potentials and Maxwell Relations
2 subtopics
71
Thermodynamic potentials (F, G) and Legendre transforms: derive key identities
72
Maxwell relations and phase equilibrium/chemical potential basics (apply to examples)
73
Kinetic Theory and the Ideal Gas
2 subtopics
74
Kinetic theory derivations: pressure, temperature, equipartition (work through steps)
75
Mean free path and transport estimates (diffusion/viscosity) at order-of-magnitude level
76
Statistical Mechanics Foundations
2 subtopics
77
Compute partition functions for simple systems (two-level, harmonic oscillator)
78
Classical vs quantum statistics: when Maxwell–Boltzmann fails; intro to Bose/Fermi
↗ Probability and Statistics for Physics (see Chapter 1)
Chapter 6
Waves, Optics, and Acoustics
79
Wave Basics (Wave Equation, Boundary Conditions)
2 subtopics
80
Derive the 1D wave equation and write traveling-wave solutions; interpret parameters
81
Standing waves and normal modes on strings and air columns (boundary conditions)
↗ Differential Equations (see Chapter 1)
↗ Complex Numbers and Fourier Methods (see Chapter 1)
82
Superposition, Fourier Analysis, and Dispersion
2 subtopics
83
Superposition + Fourier decomposition to build signals and wave packets (practice)
84
Dispersion, group velocity, beats; connect math to real wave phenomena
85
Geometric Optics
2 subtopics
86
Ray tracing: reflection/refraction, Snell’s law, and sign conventions (problem set)
87
Thin lens equation, magnification, and optical instruments (microscope/telescope basics)
88
Physical Optics (Interference, Diffraction, Polarization)
2 subtopics
89
Interference: double-slit and thin-film interference (predict fringe patterns)
90
Diffraction: single-slit and gratings; resolving power and aperture limits (problems)
91
Acoustics and Sound
2 subtopics
92
Sound intensity, decibel scale, Doppler effect (solve and interpret)
93
Resonance in cavities + acoustic impedance basics (connect to reflections/transmission)
Chapter 7
Modern Physics (Relativity, Quantum, and Matter)
94
Special Relativity
2 subtopics
95
Lorentz transformations and spacetime diagrams (events, simultaneity) + exercises
96
Relativistic energy–momentum, invariants, and collision kinematics (problems)
97
Quantum Mechanics Fundamentals
2 subtopics
98
Solve Schrödinger equation in 1D: infinite well, finite step/barrier, tunneling
99
Operators and commutators; uncertainty principle; spin-1/2 and measurement postulates
100
Atomic Physics
2 subtopics
101
Hydrogen atom qualitative structure + spectra (n, l, m, orbitals conceptually)
102
Fine structure and Zeeman effect overview; selection rules basics + simple exercises
103
Nuclear and Particle Physics
2 subtopics
104
Radioactive decay (exponential law, half-life chains) + nuclear binding energy basics
105
Particle physics survey (quarks/leptons/interactions) + detector/accelerator fundamentals
106
Condensed Matter and Materials
2 subtopics
107
Crystals and band structure intuition; semiconductors (pn junction concepts)
108
Superconductivity and magnetism survey (key phenomena) + short conceptual problem set
109
Modern Experiments and Applications
2 subtopics
110
Photoelectric and Compton effects: experimental signatures and interpretations
111
Modern physics applications case study (choose one: MRI, GPS, lasers, quantum tech)

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