📐 Math for Physics
The mathematics physics runs on: vectors, trigonometry, graphs, scientific notation and calculus ideas.
What you will learn
- Add and resolve vectors
- Use trigonometry in force problems
- Interpret motion graphs
- Apply significant figures correctly
Study guide
Intermediate concepts
Complex Numbers in Physics — From AC Circuits to Quantum Waves
Why physicists use imaginary numbers: Euler's formula, phasors, complex impedance in AC circuits, and how a + bi simplifies waves and oscillations.
Differential Equations in Physics — A Beginner's Introduction
What differential equations are, why Newton's laws are really differential equations, and how to solve the two most important ones: exponential decay and…
Introductory College concepts
Derivatives in Physics — Instantaneous Rates of Change
Derivatives in physics: instantaneous rates of change, v = dx/dt and a = dv/dt, the power rule, and why calculus matters.
Integrals in Physics — Adding Up the Infinitely Small
Integrals in physics: accumulation, area under curves, displacement from velocity, work from force, and the +C constant.
High School concepts
Dimensional Analysis — Checking Physics with Units
Use base dimensions [M], [L], [T] to check equations, catch mistakes, and even derive formulas like the pendulum period — no memorization needed.
Error Analysis for Physics Labs — Uncertainty Done Right
Absolute vs relative uncertainty, random vs systematic error, propagation rules, and how to report measurements honestly in the lab.
Graphing Motion — Reading Position, Velocity and Acceleration Graphs
How to read motion graphs: position-time, velocity-time and acceleration-time, slope meanings, area meanings, and worked examples.
Logarithms in Physics — Decibels, Half-Life and the Richter Scale
Log rules that matter in physics, base-10 vs natural logs, and the famous log scales: decibels, pH, the Richter scale, and radioactive half-life.
Significant Figures — Reporting Measurements Honestly
Significant figures explained: counting rules, multiplication/division and addition/subtraction rules, and worked examples.
Trigonometry for Physics — SOHCAHTOA, Components and Angles
Trigonometry for physics: SOHCAHTOA, resolving vectors into components, finding angles, and the degrees-vs-radians trap.
Vector Addition — Tip-to-Tail, Components and Resultants
How to add vectors: tip-to-tail method, resolving into components with trigonometry, and worked examples.
Beginner concepts
Scientific Notation — Writing Very Big and Very Small Numbers
Scientific notation explained: writing huge and tiny numbers as a × 10^n, converting, multiplying powers, and order of magnitude.
Vectors vs Scalars — The Two Kinds of Quantities in Physics
Vectors vs scalars in physics: definitions, examples, notation, and why direction changes everything.
Practice
Algebra for Physics Practice
10 problems · 10 practice problems on the algebra skills physics demands — rearranging equations and solving for u…
Calculus for Physics Practice
10 problems · 10 practice problems on calculus for physics — derivatives as rates, integrals as accumulation.…
Graphing Motion Practice
10 problems · 10 practice problems on graphing motion — reading position, velocity and acceleration graphs.…
Significant Figures Practice 2
10 problems · 10 practice problems on significant figures and scientific notation — reporting measurements honestl…
Trigonometry for Physics Practice 2
10 problems · 10 practice problems on trigonometry for physics — SOHCAHTOA, components, and inverse trig.…
Vectors Practice — Vector Math for Physics
10 problems · 10 practice problems on the math of physics — vectors, scalars, trigonometry, graphs and significant…