Courses — Bellaziraptor

AP Physics 2

Algebra-based second-year physics: thermodynamics, electricity and magnetism, optics, and modern physics. Seven units, one lesson each. Units 1, 2 and 3 are written, each with a bench lab and interactive labs you can actually run; the rest are queued.

Units

Unit 1 · 5 labs

Thermodynamics

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

Unit 2 · 5 labs

Electric Force, Field, and Potential

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

Unit 3 · 5 labs

Electric Circuits

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

Unit 4 · Planned

Magnetism & EM Induction

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

Unit 5 · Planned

Geometric Optics

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

Unit 6 · Planned

Waves, Sound & Physical Optics

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

Unit 7 · Planned

Modern Physics

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

Interactive labs

1 · Ideal gas & PV work 1 · Thermal conductivity 1 · Entropy 1 · Heat transfer & calorimetry 1 · Boyle’s law (bench) 2 · Coulomb force & superposition 2 · Field lines & equipotentials 2 · Charged particle between plates 2 · Parallel-plate capacitor 2 · Mapping equipotentials (bench) 3 · Ohm’s law & resistivity 3 · Series vs parallel bulbs 3 · Two-loop circuit solver 3 · RC charging & discharging 3 · Resistivity of a wire (bench)

Check against your syllabus

This unit list follows the 2024 redesign of AP Physics 2, which moved fluids to AP Physics 1 and starts the course with thermodynamics — seven units in all. Some teachers reorder units 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

Each unit is one lesson page. The contents panel on the left gives the study order; the formula sheet sits near the end.
Work the numbered sections in order. Each ends with worked examples — try them before opening the solution.
Do the lab. The exam asks experimental-design questions, and having actually taken the data makes those much easier.
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.

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. e^a+b = e^ae^b is not optional in EE.

Where each unit lands in the EE curriculum

Unit	What 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 `e`^atcos `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` d`t` and energy as ∫`p` d`t`.
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.

Core antiderivative table

These are the ones you should recognize instantly, without deriving. Everything in Unit 1 is machinery for converting an unfamiliar integral into one of these. (Constant of integration omitted throughout.)

Integral	Result	Integral	Result
∫ `x`ⁿ d`x`	`x`ⁿ⁺¹`n`+1, `n` ≠ −1	∫ 1`x` d`x`	ln\|`x`\|
∫ `e`^ax d`x`	1`ae`^ax	∫ `a`^x d`x`	`a`^x / ln `a`
∫ sin `x` d`x`	−cos `x`	∫ cos `x` d`x`	sin `x`
∫ sec² `x` d`x`	tan `x`	∫ csc² `x` d`x`	−cot `x`
∫ sec `x` tan `x` d`x`	sec `x`	∫ csc `x` cot `x` d`x`	−csc `x`
∫ tan `x` d`x`	ln\|sec `x`\|	∫ cot `x` d`x`	ln\|sin `x`\|
∫ sec `x` d`x`	ln\|sec `x` + tan `x`\|	∫ csc `x` d`x`	−ln\|csc `x` + cot `x`\|
∫ d`xa`² + `x`²	1`a` arctan(`xa`)	∫ d`x`√(`a`² − `x`²)	arcsin(`xa`)
∫ sinh `x` d`x`	cosh `x`	∫ cosh `x` d`x`	sinh `x`

The three that get memorized wrong

∫ sec x dx — the answer is a logarithm, not a power of sec. Nobody derives this mid-exam; memorize it.
∫ dx/(a²+x²) has a 1/a out front; ∫ dx/√(a²−x²) does not. Losing that factor is the single most common arithmetic slip in Unit 1.
∫ x⁻¹ dx is the exception to the power rule. Applying xⁿ⁺¹/(n+1) here gives division by zero.

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. Every idea that needs spatial intuition has a 3D lab you can drive, in Interactive Laboratories.

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

1 · Vectors in 3D 1 · Into & out of the page 1 · Vector formula sheet 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

Unit	What it buys you
1 — Vectors & geometry	The cross product is the Lorentz force and the Poynting vector. Cylindrical coordinates are coaxial cables; spherical are point charges and antennas.
2 — Vector functions	Charged-particle trajectories in E and B fields, and the paths every line integral runs along.
3 — Partial derivatives	`E` = −∇`V`. Small-signal models are multivariable linearisation; tolerance analysis is the total differential.
4 — Multiple integrals	Total charge is ∭`ρ` d`V`; stored field energy and the capacitance of real geometries come from triple integrals.
5 — Vector fields & line integrals	Voltage is a line integral of `E`. Path independence is Kirchhoff’s voltage law; Ampère’s law is a circulation.
6 — Surface integrals & theorems	Flux 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.

Coordinate systems and their volume elements

Every integral in this course is written in one of three coordinate systems, and the thing people forget is not the coordinates — it is the stretch factor that goes with them. Memorise this table; Unit 4 derives it, Units 5 and 6 use it constantly.

\(\theta\) is the same angle in cylindrical and spherical — measured in the \(xy\)-plane from the positive \(x\)-axis. \(\phi\) is measured *down from the positive \(z\)-axis*, so the equator is \(\phi = \pi/2\). Physics and EE texts swap the letters \(\theta\) and \(\phi\); check which convention your course uses.
System	Coordinates	Conversion to Cartesian	Volume element \(dV\)	Natural for
Cartesian	\((x, y, z)\)	—	\(dx\,dy\,dz\)	Boxes, planes, anything with flat faces
Cylindrical	\((r, \theta, z)\), \(r \ge 0\)	\(x = r\cos\theta,\; y = r\sin\theta,\; z = z\)	\(r\,dr\,d\theta\,dz\)	Cylinders, cones, paraboloids, coaxial cable, anything symmetric about the \(z\)-axis
Spherical	\((\rho, \theta, \phi)\), \(\rho \ge 0\), \(0 \le \phi \le \pi\)	\(x = \rho\sin\phi\cos\theta,\; y = \rho\sin\phi\sin\theta,\; z = \rho\cos\phi\)	\(\rho^2\sin\phi\,d\rho\,d\theta\,d\phi\)	Spheres, point charges, antenna radiation patterns, anything symmetric about a point

The del operator, four ways

One symbol, \(\nabla = \langle \partial_x, \partial_y, \partial_z\rangle\), and the four things it can do. Units 3, 5 and 6 introduce them one at a time; here they are side by side so you can see the pattern.

Operation	Acts on	Gives	Formula (Cartesian)	Meaning
Gradient \(\nabla f\)	scalar field	vector field	\(\langle f_x, f_y, f_z\rangle\)	Direction and rate of steepest increase. \(\mathbf{E} = -\nabla V\).
Divergence \(\nabla\cdot\mathbf{F}\)	vector field	scalar field	\(\dfrac{\partial F_1}{\partial x} + \dfrac{\partial F_2}{\partial y} + \dfrac{\partial F_3}{\partial z}\)	Net outflow per unit volume — source strength. \(\nabla\cdot\mathbf{E} = \rho/\varepsilon_0\).
Curl \(\nabla\times\mathbf{F}\)	vector field	vector field	\(\begin{vmatrix}\mathbf{i}&\mathbf{j}&\mathbf{k}\\ \partial_x&\partial_y&\partial_z\\ F_1&F_2&F_3\end{vmatrix}\)	Rotation per unit area — how a paddle wheel would spin. \(\nabla\times\mathbf{E} = -\partial_t\mathbf{B}\).
Laplacian \(\nabla^2 f\)	scalar field	scalar field	\(f_{xx} + f_{yy} + f_{zz}\)	Divergence of the gradient. \(\nabla^2 V = -\rho/\varepsilon_0\) (Poisson); \(\nabla^2 V = 0\) in empty space (Laplace).

The two identities that decide everything

\(\nabla\times(\nabla f) = \mathbf{0}\). The curl of a gradient is always zero. So a field with nonzero curl cannot be a gradient — it has no potential, and its line integrals depend on the path. This is why an induced electric field has no voltage function.
\(\nabla\cdot(\nabla\times\mathbf{F}) = 0\). The divergence of a curl is always zero. So a curl field has no sources — which is exactly the statement that magnetic field lines never begin or end.

AP Spanish Language and Culture

Exam preparation built around the four things the AP exam asks you to do: understand authentic print and audio Spanish, write a formal email and a source-based argumentative essay, hold a five-turn conversation, and give a two-minute cultural comparison. Units 2–4 cover every verb tense in Spanish; the task units run on the exam’s own clocks, with text-to-speech audio, a conversation simulator and self-recording built into the page.

Units

Unit 1 · Exam & interpretation

The Exam & Interpretive Communication

Format, scoring, the six themes, and reading and listening strategies for Section I.

Unit 2 · Verb tenses

Indicative Tenses

Presente, pretérito, imperfecto, futuro, condicional, and preterite vs. imperfect.

Unit 3 · Verb tenses

Compound Tenses & Verb Phrases

The perfect tenses, irregular participles, progressives, periphrases, the passive.

Unit 4 · Verb tenses

The Subjunctive & the Imperative

Every subjunctive tense and trigger, sequence of tenses, si-clauses, commands.

Unit 5 · Language practice

Grammar & Vocabulary in Context

Ser/estar, por/para, pronouns, connectors, register, accents, theme vocabulary.

Unit 6 · Essay practice

Email Reply & Argumentative Essay

Tasks 1 and 2 with sources, citation, model answers and timed writing.

Unit 7 · Conversation

Interpersonal Speaking

Task 3: the 20-second formula, phrases for every turn, a simulator that talks back.

Unit 8 · Cultural analysis

The Cultural Comparison

Task 4: products, practices, perspectives, and a cultural knowledge bank by theme.

Practice exams

Exam 1

Interpretación

Print & audio · multiple choice

Exam 2

Indicativo

Simple tenses

Exam 3

Compuestos y perífrasis

Perfect tenses · passive

Exam 4

Subjuntivo e imperativo

Triggers · si-clauses

Exam 5

Lengua

Grammar in context

Exam 6

Correo y ensayo

Tasks 1 & 2, timed

Exam 7

Conversación

Three simulations

Exam 8

Comparación cultural

Four presentations

Full exam

Simulacro completo

~2 h 45 min

Reference

Verb tables · every tense, 91 verbs Cheat sheets · all the exceptions

The exam at a glance

Section	What you do	Time	Weight
I · Multiple choice	65 questions on print, combined and audio sources	~1 h 35 min	50%
II · Task 1	Email reply	15 min	12.5%
II · Task 2	Argumentative essay from three sources	~55 min	12.5%
II · Task 3	Conversation, five 20-second turns	~5 min	12.5%
II · Task 4	Cultural comparison, 4 min prep + 2 min talk	~6 min	12.5%

How to work through it

Read each unit with the tools on — play the audio, run the drills, start the timers, record yourself. Then take the practice exam cold and timed, and score the speaking and writing against the rubric honestly. Keep a list of the mistakes you repeat; by spring that list is your review sheet.

Every verb tense, and where it is taught

Spanish has three moods and, counting the compound forms, eighteen tenses plus the imperative. You need to produce the first fifteen rows and recognise the rest. The verb tables conjugate all of them for 91 verbs.

Plus the non-finite forms — infinitive *hablar*, gerund *hablando*, participle *hablado* — and the progressive (*estar hablando*) in every tense, all in Unit 3.
Mood	Tense	English	Example (hablar)	Unit
Indicativo	Presente	Present	hablo	2
Indicativo	Pretérito	Preterite	hablé	2
Indicativo	Imperfecto	Imperfect	hablaba	2
Indicativo	Futuro	Future	hablaré	2
Indicativo	Condicional	Conditional	hablaría	2
Indicativo	Pretérito perfecto	Present perfect	he hablado	3
Indicativo	Pluscuamperfecto	Past perfect	había hablado	3
Indicativo	Futuro perfecto	Future perfect	habré hablado	3
Indicativo	Condicional perfecto	Conditional perfect	habría hablado	3
Subjuntivo	Presente	Present subjunctive	(que) hable	4
Subjuntivo	Imperfecto (-ra / -se)	Imperfect subjunctive	hablara / hablase	4
Subjuntivo	Pretérito perfecto	Present perfect subjunctive	haya hablado	4
Subjuntivo	Pluscuamperfecto	Past perfect subjunctive	hubiera / hubiese hablado	4
Imperativo	Afirmativo	Affirmative commands	habla, hable, hablemos, hablad, hablen	4
Imperativo	Negativo	Negative commands	no hables, no hable, no hablemos…	4
Indicativo	Pretérito anterior	Preterite perfect (literary — recognise)	hube hablado	3
Subjuntivo	Futuro	Future subjunctive (archaic — recognise)	hablare	4
Subjuntivo	Futuro perfecto	Future perfect subjunctive (archaic — recognise)	hubiere hablado	4

The six themes

Every source, prompt and conversation on the exam is drawn from one of six themes. You will not be told which one, and the cultural comparison can land on any of them — so Unit 5 gives you vocabulary for each and Unit 8 gives you ready-made cultural examples for each.

Tema	Theme	Typical contexts
Las familias y las comunidades	Families and communities	Family structure, traditions and values, education communities, citizenship, social networks
La ciencia y la tecnología	Science and technology	Access to technology, health and medicine, innovation, energy, the ethics of science
La belleza y la estética	Beauty and aesthetics	Architecture, visual and performing arts, literature, ideals of beauty, fashion
La vida contemporánea	Contemporary life	Education and careers, entertainment, travel and tourism, holidays, lifestyles, relationships
Los desafíos mundiales	Global challenges	Environmental, economic, political and social issues; health; population and demographics
Las identidades personales y públicas	Personal and public identities	Language and identity, heroes and historical figures, nationalism, beliefs, alienation and assimilation

What each free-response task is really graded on

Email: did you answer every question, in usted, with a proper greeting and closing, and ask something back? Missing one of those caps the score no matter how good the Spanish is.
Essay: a clear thesis, and all three sources cited and used as evidence — not summarised. The audio source is the one people drop.
Conversation: a full answer to each turn, every time. Twenty seconds of on-topic Spanish beats five perfect words and fifteen seconds of silence.
Cultural comparison: a real comparison — both communities, similarities or differences, and the perspective behind the practice. Description alone tops out around a 3.

A study plan to May

Starting in late September leaves about thirty weeks. Run two tracks at once: one unit of structured study, and a daily fifteen minutes of real Spanish (a news clip, a podcast segment, an article) that keeps Section I stamina growing.

When	Structured study	Every week, alongside
Weeks 1–2	Unit 1 — learn the exam; take Exam 1 cold as a baseline.	15 min/day of listening or reading
Weeks 3–10	Units 2, 3 and 4 — two to three weeks each; drills until 90%+ accuracy.	One email reply (15 min)
Weeks 11–13	Unit 5 — grammar in context and theme vocabulary.	One email + one conversation
Weeks 14–18	Unit 6 — one full timed essay per week.	Conversation + cultural comparison
Weeks 19–23	Unit 7 and Unit 8 — record yourself, score with the rubric.	One essay every other week
Weeks 24–28	Mixed review: retake Exams 1–8, one per week; re-study whatever scores lowest.	All four tasks weekly
Last 2 weeks	The simulacro in one sitting; then the verb cheat sheets and your own error list.	Light daily listening; sleep

How to work through this

Read a unit page with the tools switched on — press play on the audio, run the drills, start the timers, record yourself. Then close it and take the practice exam cold, timed, no notes. Score the free-response answers against the rubric honestly (listening to your own recording is uncomfortable, and it is the single most useful thing on this site). Keep a running list of the mistakes you repeat; by spring that list is your review sheet.

About the audio

Listening sources are read aloud by your browser’s built-in Spanish text-to-speech voice, so nothing is downloaded and every transcript is on the page. Synthetic voices are clearer and more even than real speakers — use them to learn the format, and use real Spanish media every day to get used to natural speed and accents. Recording works in any current browser once you allow the microphone; recordings never leave your device.

Physics II: Electricity & Magnetism for Electrical Engineers

Calculus-based electricity and magnetism, written for someone meeting it at university for the first time and heading into electrical engineering. Nine units take you from a single charge to the electromagnetic wave: fields, Gauss’s law, potential, capacitors, circuits, magnetic forces and sources, induction, and AC circuits with Maxwell’s equations. Every unit starts from intuition and pictures, points at where the idea shows up in EE, and comes with a lab you can drive and a timed practice exam.

Units

Unit 1 · 1 lab

Electric Charge & Electric Fields

Coulomb’s law as vectors, superposition, field lines, rods, rings and disks, dipoles.

Unit 2 · 1 lab

Gauss’s Law

Electric flux, choosing Gaussian surfaces, spheres, lines and sheets, conductors in equilibrium.

Unit 3 · 1 lab

Electric Potential

Potential energy, voltage as a line integral, continuous distributions, \(\mathbf{E} = -\nabla V\), equipotentials.

Unit 4 · 1 lab

Capacitance & Dielectrics

Parallel-plate, coaxial and spherical capacitors, series and parallel, stored energy, dielectrics.

Unit 5 · 1 lab

Current, Resistance & DC Circuits

Current density, resistivity, EMF, Kirchhoff’s rules, meters, and RC transients solved properly.

Unit 6 · 1 lab

Magnetic Fields & Forces

\(q\mathbf{v}\times\mathbf{B}\), circular and helical motion, Hall effect, forces and torques on currents, motors.

Unit 7 · 1 lab

Sources of Magnetic Field

Biot–Savart, wires, loops and arcs, forces between wires, Ampère’s law, solenoids and toroids.

Unit 8 · 1 lab

Induction & Inductance

Faraday and Lenz, motional EMF, generators, inductors, RL and LC circuits, transformers.

Unit 9 · 1 lab

AC Circuits & Electromagnetic Waves

Phasors, impedance, resonance, AC power, Maxwell’s equations and the waves they predict.

Practice exams

Exam 1

Charges & fields

10 questions · 90 min

Exam 2

Gauss’s law

10 questions · 90 min

Exam 3

Electric potential

10 questions · 90 min

Exam 4

Capacitance

10 questions · 90 min

Exam 5

DC circuits

10 questions · 90 min

Exam 6

Magnetic forces

10 questions · 90 min

Exam 7

Magnetic sources

10 questions · 90 min

Exam 8

Induction

10 questions · 90 min

Exam 9

AC & EM waves

10 questions · 90 min

Interactive labs

1 · Fields of continuous charge 2 · Gauss’s law: flux through any surface 3 · The potential landscape 4 · Dielectrics & energy density 5 · RC circuit on an oscilloscope 6 · Charged particles in magnetic fields 7 · Magnetic fields of currents 8 · Faraday’s law: generators & moving magnets 9 · Series RLC: resonance & phasors

What you need coming in

Calculus I and the start of Calculus II — derivatives, integrals, and setting up an integral by chopping something into small pieces. That last skill carries Units 1, 3 and 7.
Vectors — components, magnitude, dot and cross products. Every force and field here is a vector; the 3D vectors lab is a fast refresher.
Physics I mechanics — Newton’s second law, circular motion, work and energy. Charges in fields are just particles with a new force on them.
No E&M background needed. Unit 1 starts from what charge is.

Where each unit lands in the EE curriculum

Unit	What it buys you
1 — Fields	Every device is charges pushing charges. Fields are how you reason about it without tracking each one — from ESD to the inside of a transistor.
2 — Gauss’s law	Shielding and conductors. Why the inside of a metal box is quiet, and the first of the four Maxwell equations.
3 — Potential	Voltage, defined properly. Every node voltage in every circuit is this quantity.
4 — Capacitance	Every capacitor on every board, plus coax cables, MOSFET gates and DRAM cells.
5 — DC circuits	Circuit analysis — Kirchhoff’s rules and RC time constants are the core of Circuits I.
6 — Magnetic forces	Motors, speakers, Hall-effect current sensors and the physics of every CRT and mass spectrometer.
7 — Magnetic sources	Inductors and electromagnets — and why parallel traces carrying current push on each other.
8 — Induction	Generators, transformers, wireless charging and every inductor’s refusal to change its current suddenly.
9 — AC & EM waves	The power grid, filters, tuned radios and antennas — Circuits II, Signals and Electromagnetics all start here.

How to work through it

Read each unit in order and stop at every figure until it makes sense — E&M is a subject you have to see. Drive the unit’s lab until the readouts stop surprising you. Then close everything and take the practice exam cold and timed; the scoring table at the end tells you which sections to go back to.

Current Courses

AP Physics 2

Units

Thermodynamics

Electric Force, Field, and Potential

Electric Circuits

Magnetism & EM Induction

Geometric Optics

Waves, Sound & Physical Optics

Modern Physics

Interactive labs

How to use these notes

Calculus II for Engineers

Units

Techniques of Integration

Applications of Integration

Sequences & Infinite Series

Power Series & Taylor Expansions

Parametric, Polar & Complex

Intro to Differential Equations

Practice exams

Integration techniques

Applications

Sequences & series

Power & Taylor series

Parametric, polar, complex

Differential equations

What you need coming in

Where each unit lands in the EE curriculum

Core antiderivative table

Calculus III for Engineers

Units

Vectors & the Geometry of Space

Vector Functions & Motion

Partial Derivatives

Multiple Integrals

Vector Fields & Line Integrals

Surface Integrals, Stokes & Gauss

Practice exams

Vectors & geometry

Vector functions

Partial derivatives

Multiple integrals

Vector fields & line integrals

Surface integrals & theorems

Interactive labs

What you need coming in

Where each unit lands in the EE curriculum

Coordinate systems and their volume elements

The del operator, four ways

AP Spanish Language and Culture

Units

The Exam & Interpretive Communication

Indicative Tenses

Compound Tenses & Verb Phrases

The Subjunctive & the Imperative

Grammar & Vocabulary in Context

Email Reply & Argumentative Essay

Interpersonal Speaking

The Cultural Comparison

Practice exams

Interpretación

Indicativo

Compuestos y perífrasis

Subjuntivo e imperativo

Lengua

Correo y ensayo

Conversación

Comparación cultural

Simulacro completo

Reference

The exam at a glance

Every verb tense, and where it is taught

The six themes

A study plan to May

Physics II: Electricity & Magnetism for Electrical Engineers

Units

Electric Charge & Electric Fields

Gauss’s Law

Electric Potential