🦖 Bellaziraptor

AP Physics 2

Algebra-based second-year physics: fluids, thermodynamics, electricity and magnetism, optics, and modern physics. Eight units, one folder each. Unit 2 is fully written and comes with a lab you can actually run; the rest are queued.

Units

Unit 1 · Planned

Fluids

Density, pressure with depth, buoyancy and Archimedes, continuity, Bernoulli.

Unit 2 · Written

Thermodynamics

Ideal gases, kinetic theory, thermal expansion, specific heat, PV diagrams, the two laws, entropy.
Unit 3 · Planned

Electric Force, Field, and Potential

Charge, Coulomb’s law, electric fields and field lines, potential and potential energy, conductors.

Unit 4 · Planned

Electric Circuits

Resistivity, Ohm’s law, series and parallel, Kirchhoff’s rules, capacitors, RC behavior.

Unit 5 · Planned

Magnetism & EM Induction

Magnetic fields, force on moving charges and wires, magnetic flux, Faraday’s and Lenz’s laws.

Unit 6 · Planned

Geometric Optics

Reflection, refraction, Snell’s law, total internal reflection, mirrors and lenses, ray diagrams.

Unit 7 · Planned

Waves, Sound & Physical Optics

Wave properties, superposition, standing waves, double-slit interference, diffraction, thin films.

Unit 8 · Planned

Modern Physics

Photons and the photoelectric effect, atomic energy levels and spectra, nuclear decay, mass–energy.

Unit 2 lessons

Overview & formula sheet 1 · Thermal expansion 2 · Heat & specific heat 3 · First law & work 4 · PV diagrams 5 · Second law & entropy Lab · Boyle’s law Interactive lab · gas & PV
Check against your syllabus

This unit list follows the redesigned AP Physics 2 framework — the one with fluids as Unit 1 and thermodynamics as Unit 2. Some teachers still use the older ordering, and some reorder to fit the school year. If your class numbers them differently the content is the same; only the labels move.

How to use these notes

  1. Read the unit page first. It gives the study order and the formula sheet in one screen.
  2. Work the topic pages in order. Each ends with worked examples — try them before opening the solution.
  3. Do the lab. The exam asks experimental-design questions, and having actually taken the data makes those much easier.
  4. Come back to the formula sheet and check you can say what each symbol means and when the equation applies. That, not memorisation, is what the free-response section tests.

Open the standalone course page →

Calculus II for Engineers

Integration techniques, applications, infinite series, parametric and polar curves, and a first pass at differential equations — with every unit pointed at where an electrical engineer actually meets it. Partial fractions exist so you can invert a Laplace transform. Series exist so you can linearise a diode. Polar coordinates exist so you can read a Nyquist plot.

Units

Unit 1

Techniques of Integration

Parts, trig integrals, trig substitution, partial fractions, improper integrals, numerical quadrature.

 Unit 2

Applications of Integration

Area, volume, arc length, work, centroids — and RMS, average power, charge and stored energy.

 Unit 3

Sequences & Infinite Series

Convergence tests end to end, geometric series, and the strategy for choosing a test under pressure.

 Unit 4

Power Series & Taylor Expansions

Radius of convergence, the seven series worth memorising, error bounds, linearisation, Euler’s formula.

 Unit 5

Parametric, Polar & Complex

Parametric calculus, polar area and arc length, complex arithmetic, De Moivre, roots of unity, phasors.

 Unit 6

Intro to Differential Equations

Separable, first-order linear, integrating factors, second-order constant-coefficient — solved as RC, RL and RLC.

Practice exams

Exam 1

Integration techniques

10 questions · 90 min

 Exam 2

Applications

10 questions · 90 min

 Exam 3

Sequences & series

10 questions · 90 min

 Exam 4

Power & Taylor series

10 questions · 90 min

 Exam 5

Parametric, polar, complex

10 questions · 90 min

 Exam 6

Differential equations

10 questions · 90 min

What you need coming in

  • The derivative rules cold, especially chain rule and implicit differentiation. Integration is pattern-matching against derivatives you already know.
  • The Fundamental Theorem of Calculus, both parts, and what each is for.
  • u-substitution — the one Calc I technique you will use in every single unit.
  • Limits, including L’Hôpital’s rule. Half the series unit is limits in disguise.
  • Trig identities: Pythagorean, double-angle, half-angle. Unit 1 leans on them hard.
  • Algebra with exponentials and logs. ea+b = eaeb is not optional in EE.

Where each unit lands in the EE curriculum

UnitWhat it buys you
1 — Integration techniques Partial fractions is inverse Laplace. You will run it hundreds of times in Signals & Systems and Control Theory. Parts on eatcos bt is transient circuit response.
2 — Applications RMS voltage and average power. Every AC calculation, every spec sheet, every meter reading. Plus charge as ∫i dt and energy as ∫p dt.
3 — Series convergence Geometric series is feedback and the z-transform. Closed-loop gain, ladder networks, whether a discrete filter is stable.
4 — Taylor series Small-signal analysis. Every transistor and diode model is a first-order Taylor expansion about an operating point. Plus Euler’s formula, the whole basis of phasors.
5 — Parametric, polar, complex Impedance lives in the complex plane. Nyquist and polar plots, antenna patterns, Lissajous figures, roots of unity behind the DFT.
6 — Differential equations Every circuit with a capacitor or inductor is an ODE. RC time constants, RL current build-up, and the three damping regimes of RLC.
The three that get memorised wrong
  • ∫ sec x dx — the answer is a logarithm, not a power of sec. Nobody derives this mid-exam; memorise it.
  • ∫ dx/(a²+x²) has a 1/a out front; ∫ dx/√(a²−x²) does not. Losing that factor is the most common slip in Unit 1.
  • ∫ x−1 dx is the exception to the power rule. Applying xn+1/(n+1) here divides by zero.
How to work through it

Read the unit page, then close it and do the practice exam cold — no notes, timed. Grade honestly, and send every miss back to the section it came from rather than just reading the solution. Each question maps to exactly one section, which makes that loop fast.

Open the standalone course page, with the full antiderivative table →

Calculus III for Engineers

Multivariable and vector calculus: the geometry of space, curves and motion, partial derivatives and optimisation, multiple integrals, vector fields, and the three big theorems that turn into Maxwell’s equations. Every unit is pointed at where an electrical engineer meets it — gradients give you E = −∇V, flux integrals give you Gauss’s law, Stokes’ theorem gives you Faraday’s. The lessons that need spatial intuition carry interactive 3D labs built right into the page.

Units

Unit 1 · 3 labs

Vectors & the Geometry of Space

3D coordinates, dot and cross products, lines, planes, quadric surfaces, cylindrical and spherical coordinates.

 Unit 2 · 1 lab

Vector Functions & Motion

Space curves, arc length, the TNB frame, curvature, tangential and normal acceleration, charged particles in fields.

 Unit 3 · 2 labs

Partial Derivatives

Contour maps, partials, tangent planes, chain rule, the gradient, directional derivatives, extrema, Lagrange multipliers.

 Unit 4 · 3 labs

Multiple Integrals

Double and triple integrals, order of integration, polar, cylindrical and spherical, Jacobians, mass and moments.

 Unit 5 · 2 labs

Vector Fields & Line Integrals

Work and circulation, conservative fields and potentials, Green’s theorem, divergence and curl.

 Unit 6 · 2 labs

Surface Integrals, Stokes & Gauss

Parametric surfaces, flux, Stokes’ theorem, the divergence theorem, and all four Maxwell equations in both forms.

Practice exams

Exam 1

Vectors & geometry

10 questions · 90 min

 Exam 2

Vector functions

10 questions · 90 min

 Exam 3

Partial derivatives

10 questions · 90 min

 Exam 4

Multiple integrals

10 questions · 90 min

 Exam 5

Vector fields & line integrals

10 questions · 90 min

 Exam 6

Surface integrals & theorems

10 questions · 90 min

Interactive labs inside the lessons

1 · Plane explorer 1 · Quadric surface viewer 1 · Locate a point three ways 2 · Space curve & moving frame 3 · Surface, contours & gradient 3 · Critical points & the second-derivative test 4 · Riemann boxes under a surface 4 · Region explorer: strips & limits 4 · The volume element, edge by edge 5 · Work along a path 5 · Divergence & curl probe 6 · Flux through a surface 6 · Stokes checker

What you need coming in

  • Calculus II — integration techniques above all. Multiple integrals are single integrals nested; the inner one still has to be done.
  • The chain rule, fluently. Unit 3 generalises it and Unit 5 depends on it.
  • Polar coordinates. Cylindrical is polar with a z bolted on; spherical is the 3D version.
  • Basic vectors — components, magnitude, dot product. Unit 1 rebuilds them, but the 3D vectors lab is the fastest refresher.

Where each unit lands in the EE curriculum

UnitWhat it buys you
1 — Vectors & geometryThe cross product is the Lorentz force and the Poynting vector. Cylindrical coordinates are coaxial cables; spherical are point charges and antennas.
2 — Vector functionsCharged-particle trajectories in E and B fields, and the paths every line integral runs along.
3 — Partial derivativesE = −∇V. Small-signal models are multivariable linearisation; tolerance analysis is the total differential.
4 — Multiple integralsTotal charge is ∭ρ dV; stored field energy and the capacitance of real geometries come from triple integrals.
5 — Vector fields & line integralsVoltage is a line integral of E. Path independence is Kirchhoff’s voltage law; Ampère’s law is a circulation.
6 — Surface integrals & theoremsFlux is Gauss’s law. The divergence and Stokes theorems convert all four Maxwell equations to differential form.
How to work through it

Read the unit page and play with every lab — drag the view, move the sliders, break the presets. Then close the page and do the practice exam cold, timed. Send every miss back to the section it came from; each question maps to exactly one section.

Open the standalone course page, with the coordinate-system and del-operator tables →