Program
BCSAI — Computer Science & AI
Physics for Computer Science
An applied, in-depth structure of the 30-session course — every module and every numbered session with its objectives, topics, governing equations and key readings. Live demos on the interactive lab are cross-linked where a session has a matching simulation.
This course introduces the basic concepts for understanding the physics behind computer science. It begins with elementary physics of mechanical systems and electromagnetic forces, then moves to the analysis of electric circuits. The main part describes basic models of semiconductors and how they are used to build transistors — the key element to represent formal logic in a computer. The final part is devoted to an emergent computer science, quantum computing, where the basic principles of quantum mechanics are introduced.
The narrative is deliberately cumulative: classical mechanics fixes the language of force, energy and conservation laws; electromagnetism and circuits turn those ideas into voltages and currents; the solid-state block explains why a doped crystal can switch; and the quantum block reopens the foundations to explain both the transistor's deepest physics and the qubit that may succeed it. The through-line is the single question: what physical laws make computation possible?
Professor profile — experimental and computational physicist (solid-state & polymer physics); PhD, Case Western Reserve University. Office hours on request by email.
Learning objectives
Understand the basic laws of any modern electronic and computing technology — namely:
- Understand Newton's laws and the phenomena associated with mechanical forces.
- Understand the main phenomena associated with electromagnetic forces.
- Solve elementary DC circuits.
- Understand basic models of semiconductors.
- Understand the basic structure of transistors, and how they can be used to build logic circuits.
- Understand the basic principles of quantum mechanics.
How the objectives connect. Each objective is the physical foundation of the next:
forces and energy ($\sum\vec F=m\vec a$) generalise to electromagnetic forces ($\vec F=q\vec E+q\vec v\times\vec B$),
which power circuits ($V=IR$), which are realised in semiconductors (the p–n junction), which compose into
transistors and logic gates, whose deepest explanation — and possible successor — is quantum mechanics
($i\hbar\,\partial_t\psi=\hat H\psi$).
Methodology & assessment
IE University's teaching method is collaborative, active and applied. Students build knowledge across a diverse range of activities; the professor leads and guides toward the learning objectives. Total dedication is 150 hours, split across the learning activities below.
Learning activities
Evaluation criteria
Components in detail — deliverable & evaluation
Final exam40%
Deliverable: a comprehensive written exam (sessions 29–30) spanning all five blocks.
Evaluation: graded on correctness of derivations, problem solving and conceptual reasoning.
Gate: a minimum grade of 3.5/10 on this exam is required to pass the course, regardless of the
weighted average.
Intermediate tests30%
Deliverable: the midterm test (session 16, blocks 1–3) and the final test on
electronics and quantum physics (session 28, blocks 4–5). Evaluation: short problems and conceptual
questions; the two tests jointly form the 30% component.
Group work20%
Deliverable: a group project on a physics topic not covered in the theoretical
lectures. Evaluation: assessed on physical correctness, depth and clarity of presentation. GenAI tools
may be used for specific tasks with appropriate acknowledgment.
Class participation10%
Deliverable: ongoing engagement across the 30 sessions. Evaluation: asking and
answering questions in class and completing homework.
Pass, attendance & re-sit rules
- Attendance: the 80% attendance rule applies. Students who do not comply fail both calls (ordinary and extraordinary) for the year and must re-take the course the following year.
- Four calls: each student has four chances to pass a course, distributed over two consecutive academic years (ordinary calls plus June/July re-sits).
- Re-sit (June/July): a comprehensive exam requiring physical presence on campus (Segovia or Madrid); continuous evaluation is not carried over. Minimum passing grade 5, maximum grade 8.0 ("notable").
- Re-takers: students re-enrolled from a previous year must check the assigned professor's syllabus and agree specific criteria; maximum retake grade 10.0.
- Review & appeals: a grade review session follows each call; attending it is a prerequisite for any grade appeal.
- Program rule: failing more than 18 ECTS after the June/July re-sits may lead to being asked to leave the program.
- GenAI policy: permitted for specified tasks with acknowledgment; inappropriate use is academic misconduct and may fail the assignment or course.
Program — 30 sessions, 5 blocks
Every session is delivered live in-person. Numbers match the syllabus. Each session carries its governing equation(s), a key idea, and annotated readings; tags link to the matching interactive demo.
Block 1
Foundations & classical mechanics
sessions 1–5Elementary physics: what physics is, units and modeling, then Newton's laws and mechanical energy — the groundwork for everything that follows.
Learning outcomes — by the end of Block 1 you can
- express any quantity in SI base units and check equations by dimensional analysis;
- draw a correct free-body diagram and apply $\sum\vec F=m\vec a$ to find acceleration;
- use the work–energy theorem and conservation of energy to solve motion problems without integrating forces.
1
Overview of the course
Live · introductionOrient to the course and establish a shared language of physical units.
- Overview of the course — the arc from mechanics to quantum computing and how each block builds on the last.
- Introduction to physical units — SI base units and dimensional consistency as a sanity check on every result.
$[\text{any quantity}]=\mathrm{m}^a\,\mathrm{kg}^b\,\mathrm{s}^c\,\mathrm{A}^d$dimensional form
Key idea. A formula can only be right if both sides share the same dimensions — dimensional analysis catches most algebra errors for free.
2
Basic concepts in Physics and Science
Live · lectureFrame physics as the modeling of reality and connect it to computer science.
- What is Physics? — describing nature with quantitative, testable models.
- Matter, space and time — the primitive quantities physics builds on.
- Forces — interactions that change a body's state of motion.
- Equations of movement — kinematics linking position, velocity and acceleration.
- Doing science — hypothesis, measurement, falsification.
- Measurements and units — uncertainty and significant figures.
- Modeling reality — choosing the simplest model that captures the phenomenon.
- Physics and computer science — simulation, numerical methods and hardware as applied physics.
$x(t)=x_0+v_0 t+\tfrac12 a t^2$uniform-acceleration kinematics
Worked example. A body starting at rest with $a=2\,\mathrm{m/s^2}$ travels $x=\tfrac12 a t^2=9\,\mathrm{m}$ in $t=3\,\mathrm{s}$ — a model abstracted to a single equation.
3
Newton's laws
Live · lectureUnderstand Newton's three laws and analyze forces with free-body diagrams.
- Forces — pushes/pulls measured in newtons.
- Newton's First law — inertia: with no net force, velocity is constant.
- Newton's Second law — net force sets acceleration.
- Newton's Third law — action–reaction pairs are equal and opposite.
- Free body diagrams — isolate one body and draw every force on it.
- Equilibrium — $\sum\vec F=0$ for bodies at rest or constant velocity.
$\sum \vec F = m\vec a$Newton's 2nd law
$\vec F_{AB}=-\vec F_{BA}$Newton's 3rd law
Worked example. A $2\,\mathrm{kg}$ block pushed with $12\,\mathrm{N}$ against $4\,\mathrm{N}$ of friction feels $F_{net}=8\,\mathrm{N}$, so $a=F_{net}/m=4\,\mathrm{m/s^2}$.
Serway ch. 4–5 — particle dynamics and applications of Newton's laws, with friction and incline worked examples mirroring the demo.
4
Mechanical energy
Live · lectureRelate work and power to kinetic and potential energy and apply conservation.
- Work — energy transferred by a force along a displacement.
- Power — rate of doing work.
- Work-energy theorem — net work equals the change in kinetic energy.
- Kinetic energy — energy of motion, $\tfrac12 mv^2$.
- Potential energy — stored energy of configuration, e.g. $mgh$.
- Conservation of mechanical energy — KE+PE constant without dissipation.
- Conservation of energy — the universal bookkeeping law including heat.
$W=\int \vec F\cdot d\vec r,\quad P=\dfrac{dW}{dt}$work & power
$W_{net}=\Delta K=\tfrac12 mv_f^2-\tfrac12 mv_i^2$work–energy theorem
$E=\tfrac12 mv^2+mgh=\text{const}$conservation of mechanical energy
Worked example. A mass dropped from $h=5\,\mathrm{m}$ converts $mgh$ into $\tfrac12 mv^2$, landing at $v=\sqrt{2gh}\approx 9.9\,\mathrm{m/s}$ — no force integration needed.
Serway ch. 7–8 — work, kinetic energy and the conservation of energy, including spring potential energy used by the SHM demo.
5
Workshop on mechanical systems
Live · workshopApply Newton's laws and energy conservation to solve mechanical-system problems.
- Hands-on problem solving — forces, motion and energy on inclines, pulleys and springs.
$a=\dfrac{\sum F}{m},\quad \omega=\sqrt{k/m}$dynamics & SHM toolkit
Key idea. Choose force methods when you need instantaneous acceleration, energy methods when you only need start/end speeds — picking the right tool is half the problem.
Block 2
Electromagnetism
sessions 6–11Electric charge, fields and potential; capacitance and dielectrics; current, magnetic forces and electromagnetic induction — the main phenomena of electromagnetic forces.
Learning outcomes — by the end of Block 2 you can
- compute the field and potential of point charges and relate work to potential energy;
- find the capacitance, field and stored energy of a capacitor, with and without a dielectric;
- apply the Lorentz force and Faraday's law to charges, currents and changing flux.
6
Electric force and voltage
Live · lectureUnderstand the electrostatic field and relate electric work to potential energy.
- Electric charge — quantised, conserved property of matter.
- Electric force — Coulomb's inverse-square attraction/repulsion.
- Electrostatic field — force per unit test charge.
- Electric potential — potential energy per unit charge (volts).
- Electric work — work moving charge through a potential difference.
- Electric Potential energy — stored energy of a charge configuration.
$F=\dfrac{1}{4\pi\varepsilon_0}\dfrac{q_1 q_2}{r^2}$Coulomb's law
$\vec E=\dfrac{\vec F}{q},\quad V=\dfrac{U}{q}$field & potential
Key idea. The field $\vec E$ is the geometry of force; the potential $V$ is its energy bookkeeping — and $\vec E=-\nabla V$ ties them together.
Serway ch. 22–25 — electric fields, Gauss's law, potential and potential energy underpinning the E-field demo.
7
Capacitance
Live · lectureUnderstand polarization, dielectrics and how capacitors store charge and energy.
- Polarization — alignment of bound charge in a field.
- Electric dipole — equal-and-opposite charge pair, the building block of dielectrics.
- Dielectrics — insulators that raise capacitance by factor $\kappa$.
- Capacitors — devices that store charge and energy in a field.
$Q=CV,\quad C=\dfrac{\kappa\varepsilon_0 A}{d}$capacitance
$U=\tfrac12 CV^2$stored energy
Worked example. Inserting a dielectric with $\kappa=4$ quadruples $C$, so at fixed $V$ it stores four times the charge and energy — the basis of DRAM cells.
Young & Freedman ch. 24 — capacitance, dielectrics and energy storage matching the capacitor demo's $C$, $E$ and $U$ readouts.
8
Workshop on electric forces and capacitance
Live · workshopSolve problems on electrostatic fields, potential and capacitor networks.
- Applied problems — superposing fields, potential differences and series/parallel capacitor networks.
$C_\parallel=\textstyle\sum C_i,\quad \tfrac1{C_s}=\textstyle\sum\tfrac1{C_i}$capacitor networks
Key idea. Capacitors combine oppositely to resistors: capacitances add in parallel, reciprocals add in series.
9
Current and magnetic forces
Live · lectureConnect electric current and Ohm's law to magnetic fields, forces and materials.
- Electric current — rate of charge flow, $I=dQ/dt$.
- Ohm's law — current proportional to voltage across a resistor.
- Electromotive force — energy per charge supplied by a source.
- Magnetic force — the velocity-dependent Lorentz force.
- Magnetic field — produced by moving charge / current.
- Magnetic flux — field threading a surface.
- Magnetic dipole — current loop as a magnet.
- Magnetic materials — dia-, para- and ferromagnetism.
$\vec F=q\vec v\times\vec B,\quad r=\dfrac{mv}{|q|B}$Lorentz force & gyroradius
$V=IR,\quad I=\dfrac{dQ}{dt}$Ohm's law & current
Key idea. The magnetic force does no work — it is always $\perp$ to $\vec v$ — so it bends paths into circles without changing speed.
Serway ch. 27–30 — current, resistance, magnetic fields and sources of magnetism behind the Lorentz-force and Ohm demos.
10
Induction
Live · lectureUnderstand electromagnetic induction via Faraday's and Lenz's laws and inductance.
- Faraday's law — a changing flux induces an EMF.
- Lenz's law — the induced current opposes the change.
- Alternators — rotating loops turning motion into AC.
- Self-inductance — a coil opposing changes in its own current.
- Inductors — energy-storing magnetic components.
$\varepsilon=-\dfrac{d\Phi_B}{dt}$Faraday–Lenz law
$\varepsilon_L=-L\dfrac{dI}{dt},\quad U=\tfrac12 LI^2$inductance & energy
Key idea. The minus sign (Lenz) is energy conservation in disguise: the induced current always fights the change that created it.
Young & Freedman ch. 29–30 — electromagnetic induction, Faraday's and Lenz's laws, and inductance.
11
Workshop on magnetism and induction
Live · workshopSolve problems on magnetic forces, flux and induced electromotive force.
- Applied problems — gyroradius, flux through moving loops and induced EMF.
$\Phi_B=\int \vec B\cdot d\vec A$magnetic flux
Key idea. Most induction problems reduce to computing $\Phi_B$ and differentiating it in time.
Block 3
Electric circuits
sessions 12–16Direct-current circuit analysis — components, Kirchhoff's rules and systematic methods — applied right up to a simple circuit for a machine-learning model, then review and the midterm.
Learning outcomes — by the end of Block 3 you can
- identify passive/active components and reduce series–parallel resistor networks;
- apply Kirchhoff's current and voltage laws to solve multi-loop DC circuits;
- compute power dissipation and analyse the transient response of an RC circuit.
12
Direct current circuits
Live · lectureAnalyze DC circuits systematically using components, power and Kirchhoff's rules.
- Circuits — closed conducting paths for charge.
- Passive components — resistors, capacitors, inductors.
- Active components — sources and amplifying devices.
- Electrical measuring devices — ammeters and voltmeters.
- Kirchhoff's rules — node (current) and loop (voltage) laws.
- Transient and steady state — time-dependent vs. settled behaviour.
- Electric power — energy dissipation rate, $P=VI$.
- Systematic circuit analysis — node/mesh methods.
$\textstyle\sum_{\text{node}} I=0,\quad \sum_{\text{loop}} V=0$Kirchhoff's rules
$P=VI=I^2R=\dfrac{V^2}{R}$electric power
$V_C(t)=V_0\!\left(1-e^{-t/RC}\right)$RC transient
Worked example. $9\,\mathrm{V}$ across $R_1=100\,\Omega$ and $R_2=220\,\Omega$ in series gives $I=9/320\approx 28\,\mathrm{mA}$ and $P=VI\approx 0.25\,\mathrm{W}$.
Serway ch. 28 — direct-current circuits, Kirchhoff's rules and RC transients matching both circuit demos.
13
Workshop on DC circuits: circuit analysis
Live · workshopPractice systematic analysis of series and parallel DC circuits.
- Hands-on circuit analysis — reducing networks and solving for branch currents.
$R_s=\textstyle\sum R_i,\quad \tfrac1{R_p}=\textstyle\sum\tfrac1{R_i}$series/parallel resistors
Key idea. Collapse the network to one equivalent resistor, find the total current, then back-substitute to recover each branch.
14
Workshop on DC circuits: a simple circuit for a simple machine learning model
Live · workshopBuild a DC circuit that realizes a simple machine-learning model — physics meets CS.
- Circuit realization of an ML model — resistors as weights, summing node as a neuron, threshold as activation.
$y=\Theta\!\left(\textstyle\sum_i w_i x_i - b\right)$perceptron as a circuit
Key idea. A weighted sum is just Kirchhoff's current law at a node; conductances $1/R_i$ play the role of the weights $w_i$ — analog computation made physical.
15
Q&A review session
Live · reviewConsolidate mechanics, electromagnetism and circuits ahead of the midterm.
- Open question & answer review — clearing doubts across blocks 1–3.
Key idea. Bring worked problems where the method, not just the answer, is unclear — the highest-leverage use of review time.
16
Midterm test
Live · assessmentGraded intermediate test covering blocks 1–3 (mechanics, electromagnetism, circuits).
- Scope — Newton's laws, energy, fields, capacitance, magnetism, induction, DC circuits.
- Weighting — counts toward the 30% intermediate-tests component.
Block 4
Semiconductors, transistors & digital logic
sessions 17–23From the physics of solids and doping to p–n junctions, diodes and bipolar transistors — and how transistors build the logic gates at the heart of every computer.
Learning outcomes — by the end of Block 4 you can
- explain conduction via energy bands, holes and doping in semiconductors;
- read a diode I–V curve and analyse rectifier circuits with the Shockley equation;
- describe BJT operation and build logic gates and truth tables from transistors.
17
Semiconductors
Live · lectureUnderstand band structure, doping and conduction in semiconductors.
- Condensed matter — solids and liquids with strong interactions.
- Crystalline solid — periodic atomic lattice.
- Bonding in solids — covalent, ionic, metallic bonds.
- Energy bands — allowed energy ranges with a gap $E_g$.
- Semiconductors — small-gap materials, conductivity between metals and insulators.
- Holes — missing electrons acting as positive carriers.
- Impurities and doping — n-type (donors) and p-type (acceptors).
- Electric field on semiconductors — drift of carriers.
- Inhomogeneous semiconductors — junctions between doped regions.
$n\propto e^{-E_g/2k_BT}$thermal carrier density
Key idea. A semiconductor is an insulator with a gap small enough ($\sim1\,\mathrm{eV}$ for Si) that heat and doping populate the conduction band — controllable conductivity is what makes devices possible.
Young & Freedman ch. 42 — molecules and condensed matter: bonding, energy bands and semiconductors.
18
Diodes
Live · lectureUnderstand the p–n junction, its I–V curve and diode-based circuits.
- P-N junction: structure — adjoining p- and n-type regions.
- P-N junction in equilibrium — depletion region and built-in potential.
- Polarized P-N junction — forward vs. reverse bias.
- Characteristic curve I-V — exponential turn-on.
- LEDs — radiative recombination emitting photons.
- Circuits with diodes — rectifiers and clippers.
$I=I_S\!\left(e^{V/(nV_T)}-1\right)$Shockley diode equation
Key idea. The junction conducts one way: forward bias lowers the barrier so current rises exponentially, reverse bias all but blocks it — a one-way valve for charge.
Serway ch. 43 — semiconductor devices: the p–n junction, diodes and LEDs feeding the diode I–V demo.
19
Workshop on diodes
Live · workshopAnalyze rectifier and clipping circuits built from diodes.
- Hands-on diode circuits — half/full-wave rectifiers and clipping with the ideal-diode model.
$V_{out}\approx V_{in}-V_\gamma\ (\text{on}),\quad 0\ (\text{off})$ideal-diode model
Key idea. Assume a state (on/off), solve, then check the assumption is consistent — the standard method for diode circuits.
20
Bipolar transistors
Live · lectureUnderstand BJT structure, biasing and modeling for circuit analysis.
- Transistors — three-terminal devices controlling current.
- BJT transistor — npn/pnp sandwiches of doped silicon.
- Basic functioning — small base current controls large collector current.
- Polarization of the transistor — biasing into active/cutoff/saturation.
- Modeling the transistor — small-signal and large-signal models.
- Circuit analysis with transistors — amplifiers and switches.
$I_C=\beta I_B,\quad I_E=I_C+I_B$BJT current gain
Key idea. A tiny base current commands a much larger collector current ($\beta\sim100$) — amplification, and the basis of using a transistor as a switch.
Sedra & Smith (suppl.) — bipolar junction transistors, biasing and small-signal models for circuit analysis.
21
Workshop on circuits with BJT
Live · workshopAnalyze and bias amplifier and switching circuits using BJTs.
- Hands-on BJT circuits — setting the operating point and computing gain.
$g_m=\dfrac{I_C}{V_T},\quad A_v=-g_m R_C$transconductance & gain
Key idea. Bias the transistor to a stable Q-point first; only then does the small-signal gain analysis apply.
22
Logic gates
Live · lectureSee how transistors implement digital logic, truth tables and logic families.
- Digital circuits — two-level (0/1) signalling.
- Logic gates — AND, OR, NOT, NAND, NOR, XOR.
- Truth tables — full input→output specification.
- Logic families — TTL, CMOS and their trade-offs.
$Y=\overline{A\cdot B}\ \ (\text{NAND}),\quad Y=A\oplus B\ \ (\text{XOR})$Boolean logic
Key idea. NAND is functionally complete — every Boolean function, and thus every computer, can be built from NAND gates alone.
23
Workshop on logic gates
Live · workshopBuild and verify logic functions from gates and truth tables.
- Hands-on logic-gate construction — realising functions and checking them against truth tables.
$Y=A\oplus B=\overline{A}B+A\overline{B}$XOR from basic gates
Key idea. Any truth table maps directly to a sum-of-products expression, which then maps to a gate-level circuit.
Block 5
Quantum physics & quantum computing
sessions 24–30The origins of quantum theory through to qubits and quantum logic — an emergent computer science — closing with review and the final assessments.
Learning outcomes — by the end of Block 5 you can
- explain the experiments (blackbody, photoelectric) that forced the quantum hypothesis;
- relate photon energy and the work function and apply $E_k=hf-\phi$;
- describe a qubit, superposition and basic quantum gates, and contrast them with classical bits.
24
Quantum Physics I: Origins and Concepts
Live · lectureUnderstand the crisis of classical physics that gave rise to quantum mechanics.
- Historical crisis of classical physics — phenomena classical theory could not explain.
- Ultraviolet catastrophe & blackbody radiation — Planck's quantised energy resolves it.
- Photoelectric effect & Planck's hypothesis — light as quanta of energy $hf$.
- Bohr model of the atom — quantised orbits and spectral lines.
- Wave-particle duality — matter and light are both wave and particle.
$E=hf,\quad E_k=hf-\phi$photon energy & photoelectric effect
$\lambda=\dfrac{h}{p}$de Broglie wavelength
Worked example. Below the threshold frequency $f_0=\phi/h$ no electrons are ejected no matter how bright the light — energy comes in indivisible quanta, not in proportion to intensity.
Young & Freedman ch. 38–39 — photons, the photoelectric effect and the particle nature of light; the wave nature of particles.
25
Quantum Physics II: Quantum Computing
Live · lectureUnderstand qubits, superposition and entanglement, and basic quantum logic.
- Superposition and entanglement — states as combinations; correlated multi-qubit states.
- Quantum states and measurement — probabilistic collapse on measurement.
- Qubits vs. classical bits — a continuum of states vs. just 0/1.
- Basic quantum logic gates — X, H, Z, S as unitary operations.
- Quantum computing — exploiting superposition for parallelism.
- Real-world applications: cryptography — Shor's algorithm and quantum key distribution.
$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle,\ \ |\alpha|^2+|\beta|^2=1$qubit state
$i\hbar\dfrac{\partial}{\partial t}|\psi\rangle=\hat H|\psi\rangle$Schrödinger equation
Key idea. Measurement returns $0$ with probability $|\alpha|^2$ and collapses the superposition — quantum algorithms must extract answers before that collapse destroys the parallelism.
Young & Freedman ch. 40 (suppl.) — quantum mechanics, wavefunctions and measurement underpinning the qubit demo.
26
Workshop on Quantum Physics
Live · workshopWork through qubit-state and quantum-gate problems hands-on.
- Hands-on exercises — applying gates to qubit states and computing measurement probabilities.
$H=\tfrac{1}{\sqrt2}\begin{psmallmatrix}1&1\\1&-1\end{psmallmatrix},\ \ X=\begin{psmallmatrix}0&1\\1&0\end{psmallmatrix}$Hadamard & NOT gates
Key idea. A gate is just a unitary matrix acting on the state vector; $H|0\rangle$ creates an equal superposition, the entry point to quantum parallelism.
27
Q&A review session
Live · reviewConsolidate electronics and quantum physics before the final assessments.
- Open question & answer review — clearing doubts across blocks 4–5.
Key idea. Connect the blocks: the same band physics that makes a transistor switch is the quantum mechanics that makes a qubit possible.
28
Final test on electronics and quantum physics
Live · assessmentGraded intermediate test covering blocks 4–5 (semiconductors, transistors, logic, quantum).
- Scope — bands & doping, diodes, BJTs, logic gates, photoelectric effect, qubits.
- Weighting — counts toward the 30% intermediate-tests component.
29·30
Final exam
Live · assessmentComprehensive final exam spanning all five blocks — 40% of the grade, minimum 3.5 required to pass.
- Span — delivered across sessions 29–30.
- Coverage — comprehensive across mechanics, EM, circuits, electronics and quantum.
- Gate — a minimum of 3.5/10 on this exam is required to pass the course.
Key concepts & key equations
A compact reference of the core terms and governing equations that recur across the five blocks.
Mechanics
Newton's second law $\sum\vec F=m\vec a$
Net force on a body equals mass times acceleration — the central equation of dynamics.
Work–energy theorem $W_{net}=\Delta K$
The net work done on a body equals its change in kinetic energy.
Mechanical energy $E=\tfrac12 mv^2+U$
Kinetic plus potential energy; conserved when only conservative forces act.
Simple harmonic motion $\omega=\sqrt{k/m}$
Oscillation of a mass on a spring; period $T=2\pi/\omega$.
Electromagnetism
Coulomb's law $F=\tfrac{kq_1q_2}{r^2}$
Inverse-square electrostatic force between point charges.
Electric field / potential $\vec E=-\nabla V$
Force per charge; potential is energy per charge in volts.
Capacitance $C=\tfrac{\kappa\varepsilon_0 A}{d}$
Charge stored per volt; energy $U=\tfrac12 CV^2$.
Lorentz force $\vec F=q\vec v\times\vec B$
Velocity-dependent magnetic force; bends paths into circles.
Faraday–Lenz law $\varepsilon=-\tfrac{d\Phi_B}{dt}$
A changing magnetic flux induces an opposing EMF.
Circuits
Ohm's law $V=IR$
Voltage across a resistor is proportional to the current through it.
Kirchhoff's rules $\sum I=0,\ \sum V=0$
Charge and energy conservation at nodes and around loops.
Electric power $P=VI=I^2R$
Rate of energy dissipation in a circuit element.
RC time constant $\tau=RC$
Sets how fast a capacitor charges/discharges; ~full after $5\tau$.
Semiconductors & logic
Energy gap $E_g$
Forbidden energy band; small ($\sim1\,\mathrm{eV}$) for semiconductors.
Doping
Adding donors (n-type) or acceptors (p-type) to control conductivity.
Shockley equation $I=I_S(e^{V/nV_T}\!-\!1)$
Diode I–V curve; conducts strongly only under forward bias.
BJT current gain $I_C=\beta I_B$
Small base current controls a large collector current.
Functional completeness
NAND (or NOR) alone can build any Boolean function.
Quantum
Planck–Einstein relation $E=hf$
Energy of a photon is proportional to its frequency.
Photoelectric equation $E_k=hf-\phi$
Ejected-electron energy; no emission below $f_0=\phi/h$.
de Broglie wavelength $\lambda=h/p$
Wavelength associated with a particle of momentum $p$.
Schrödinger equation $i\hbar\,\partial_t\psi=\hat H\psi$
Governs the time evolution of a quantum state.
Qubit $\alpha|0\rangle+\beta|1\rangle$
Two-level quantum system; measured as 0 with probability $|\alpha|^2$.
Bibliography
Core and supporting texts, annotated with the sessions each one supports.
Compulsory
Raymond A. Serway & John W. Jewett (2015). Physics for Scientists and Engineers. Cengage Learning. ISBN 9781305401969
Calculus-based core text spanning mechanics through modern physics. Sessions 3–4 (ch. 4–5, 7–8), 6 (ch. 22–25), 9 (ch. 27–30), 12 (ch. 28), 18 (ch. 43).
Young, H.D., Freedman, R.A. & Ford, A.L. (2020). Sears and Zemansky's University Physics with Modern Physics. Pearson. ISBN 9780135216118
Companion core text; strong on EM, condensed matter and quantum. Sessions 3–4 (ch. 4–5), 7 (ch. 24), 10 (ch. 29–30), 17 (ch. 42), 24 (ch. 38–39), 25 (ch. 40).
Recommended
Moebs, Ling & Sanny. University Physics: Vol. I. OpenStax. ISBN 9781947172203 · openstax.org
Free, open mechanics & thermodynamics text. Supports Block 1 (sessions 1–5).
Moebs, Ling & Sanny. University Physics: Vol. II. OpenStax. ISBN 9781947172210 · openstax.org
Open electromagnetism & circuits text. Supports Blocks 2–3 (sessions 6–16).
Moebs, Ling & Sanny. University Physics: Vol. III. OpenStax. ISBN 9781947172227 · openstax.org
Open optics & modern-physics text. Supports Blocks 4–5 (sessions 17–30).
Supplementary
Sedra, A.S. & Smith, K.C. Microelectronic Circuits. Oxford University Press.
Standard device-and-circuits reference. Supports sessions 20–21 (bipolar transistors and BJT circuits).