An introduction to databases. Logistics Intro Data Models Database Design Phases Bad Design ER Model Drawing ER Diagrams SQL (Structed Query Language) SQL Schema SQL Query Anatomy SELECT and FROM WHERE AS keyword String Operations LIKE ORDER BY Set Operations UNION INTERSECT EXPECT Null Values Aggregation GROUP BY HAVING Nested Subqueries Subquery tests for WHERE Subquery test for FROM DELETE, INSERT, UPDATE DELETE INSERT UPDATE JOINS Natural/Inner Joins Outer Joins Views Integrity Constraints Authorization Privileges Roles Object-relational Databases Complex Types User Defined Types Inheritance Textual Data Big Data Streaming Data Physical Storage Types Interfaces Magnetic Disks Flash RAID RAID Levels Indexing Ordered Indices B+ Tree Hash Indices Transactions Scheduling Query Processing Parsing Optimization Evaluation Relational Algebra Building Execution graph Query Cost Relational Algebra Implementations Selection Sorting Joins Duplicate elimination Projection Set Operations Implementation Outer Join Aggregations Evaluating Expressions Pipelining Logistics Course link...

An introduction to solid state physics. Logistics Heat Capacity of Solids Einstein Model of Heat Capacity of Solids Debye Model of Heat Capacity of Solids Electrical Properties (Drude Model) Constant E&M Force Thermal Conductivity Sommerfield Model Fermi-Dirac Statistics Sommerfield Model (cont.) LCAO (Linear Combination of Atomic Orbitals)/ Tight Binding Theory Chemistry Review Shell Theory Ionic Bonds Covalent Bonds LCAO Basics Vibrations 2 Types of Springs Crystal Structure Reciprocal Space Logistics Location: 307 Pupin Time: 2:40-3:55 PM Tuesdays and Thursdays Textbook: The Oxford Solid State Basics Grading Scheme 30% problem sets (5 in total....

An introduction to plasma physics. Logistics Grading Scheme MHD Equillibrium Consequences of MHD Equillibrium Theta Pinch Z Pinch Screw Pinch Toroidal Geometry Definitions Forces Grad Shafranov Equation Stream Functions Grad Shafranov Derivation Sketch Aspect Ratio Expansion Logistics Location: Mudd 825 Time: 1:10-2:40 Book: MHD Stability of Tokamaks by Zohm Grading Scheme Projects: 60% Homework: 40% MHD Equillibrium Suprisingly useful since particles in plasma undergo gyration, which enhances number of collisions and causes discrete particle to behave more fluid-like Setting time derivatives in MHD equations to zero This is a good assumption, since deviations from this result in motion with timescales on the order of microseconds (called the Alfven time $\tau_{A}$) Hence, if you are physically observe the plasma, good chance it is in EQ $\vec{v} = 0$ is the magneto-static limit (or that $v« v_{a}$) where $v_{a}$ is the Alfven speed (which in turn is defined as size of detector divided by $\tau_{a}$) In space, the magneto-static approximation is normally not valid Define the plasma beta as $\beta = \frac{p}{\frac{B^{2}}{2\mu}}$ or the thermal energy divided by the magnetic field energy Equation of state $P = n_{e}T_{e}+n_{i}T_{i}$ Momentum equation: $\rho(\frac{\partial}{\partial t}\vec{v}+\vec{v}\nabla\cdot \vec{v}) = \vec{J}\times B =\nabla P$ Maxwell’s equations $\nabla \times \vec{B} = \mu_{0}\vec{J}$ $\nabla \cdot B = 0$ $v \times B +E =0 \rightarrow E = 0$ $\frac{\partial }{\partial t} B = -\nabla \times E \rightarrow \frac{\partial }{\partial t} B =0$ Continuity $\frac{\partial}{\partial t}\rho + \nabla \cdot v = 0$ 0=0 Energy $\frac{\partial}{\partial t}P+\vec{v}\cdot\nabla p -c_{s}^{2}(\frac{\partial}{\partial t}\rho + \vec{v}\cdot \nabla \rho) = 0$ To Summarize, for MHD equilibrium, we have that...

Logistics Conventions Newtonian Gravity The Two Body Problem Kepler’s Second Law Kepler’s Third Law From Kepler To Newton The Equivalence Principle Gravitational Redshift Light falls Differential Geometry Definitions/Basics Crash Course Example 2-Sphere Special Relativity Minkowski Spacetime Diagrams Metric Useful Tricks 4-Vectors 4-velocity Dual Vectors 4-momentum Inverse Metric Variational Approach Moving to GR Christoffel Symbols We haven’t done GR yet. Let’s do that Qausi-Stationary Curved or not Curved Tensors General Covariance Useful facts Scalar Field Transformation Vector Field Transformation Dual Vector Transformation Stress-Energy Tensor $T^{\mu\nu}$ Dust Covariant Derivatives Properties of Covariant Derivatives Tidal Forces of Curvature Newtonian GR version Directional Covariant Derivative Reimannian tensor Reimannian Tensor properties Parallel Transport Stress Energy Tensor Conservation EM Force Law Einstein’s Equation What the Heck is $\kappa$?...

Creating Bootable USB BIOS Tinkering Setting up Ubuntu Logging In Connecting to the Internet Cronjobs (Auto-Reconnect) Shell Script Adding to Crontab SSH Auto-Update Hardening SSH Enabling password-less Authentication Fail2ban Graphics Over SSH Power External Storage Website Setup Apache2 UFW Github CLI Static IP Port Forwarding Cloudflared Cloudflared DDNS Cronjobs (Website) Automatically pulling from Github Permissions and Configurations Conclusion Previously, I managed to set up this website on a Raspberry Pi SBC clone....

Ohm’s Law Drude Model Flux Maxwell’s Equations Mutual Inductance Self Inductance Energy in Fields Maxwell’s Equation in Matter Electric Magnetic Boundary Conditions Continuity Equations Charge Energy Momentum Angular Momentum Waves Basic Waves Polarization EM Waves Reflection and Transmission Absorption and Dispersion Absorption Dispersion Wave Guides Potentials Gauge Freedom Coulomb Gauge Lorenz gauge Leinard-Weichart Potentials Radiation Dipoles Point Charges Ohm’s Law $\vec{J} = \sigma (\vec{E}+v\times \vec{B}) \approx \sigma \vec{E}$ $J$ is the current density $\sigma$ is the conductivity $\vec{E}$ is the electric field Microscopic description typically, the velocities are so slow that we can drop the magnetic field term $\vec{I} = \int \vec{J}\cdot \vec{dA}$...

Grading Breakdown Heat Equation Steady state solutions Time Dependent Solution Seperation of Variables Laplace Equation Polar Coordinates Mean Value Property Maximum Principle Fourier Series Convergence Term by Term Differentiation Solving Inhomogeneous Equations Wave Equation Strum Liouville Theory SL properties Green’s Identity Minimization Principle Parseval’s Identity Bessel’s Identity Multi-Dimensional PDEs Green’s Identity (Higher Dimensions) Polar Coordinates Bessel’s equation Fourier Transforms Green’s Functions Heat Equation Case Study Dirac Delta Green’s Function via Differential Equation Nonhomogeneous BCs Green’s Function via Eigenvalue Expansion Fredholm Alternative Grading Breakdown HW: 40% Assigned on Monday weekly....

Basic CLI commands Vim Cheatsheet Standard Library Functions Compiling and Linking Gcc Header Files Lecture 2 Make Git Lecture 3 Data Types in C Sizeof() Computer Representation of Numbers Signed versus Unsigned Operator Gotchas Precedence Left shift Short Circuit Pre and Post Increment Undefined Behavior Expressions vs Statements Storage Classes Automatic Variables (Local) Static Variables Memory Address Space Stack Data Pointers Void Pointers Faux Pass by Reference NULL pointers Pointer Errata Dangling Pointers Arrays Pointer Arithmetic GUT of Pointers and Arrays Heap Heap Safety Strings String Literals argv Constant Pointers Function Pointers Parsing Function Pointers Structs Unions Typdef Libraries IO Standard I/O Stdout Stdin Stderr Redirection Pipes Files Blocking and Reading Buffering File Seeking Formatted IO Inspecting binary files Endianness Network byte order Forks Reaping Children exec() UNIX Users and Groups Shell Scripts TCP/IP netcat File Descriptors Sockets API Connect Bind, Listen, Accept Send and Receive HTTP/1....

Class Information Review Aside: Single Photon Generation Harmonic Oscillator Principles of Quantum Mechanics Commutators Identical Particles Two Particle Systems Bosons and Fermions Exchange Forces Solids Free Electron Gas Band Structure Bloch’s Theorem Dirac Comb Conservation Laws Translations Translated Operators Translational Symmetry Discrete Translational Symmetry Continuous Translational Symmetries Parity Parity Selection Rules Rotational Symmetry Object Classifications Degeneracy Wigner-Eckart Theorem Time Translation Heisenberg Picture Time-Independent Peturbation Theory Degenerate Peturbation Theory Fine Structure of Hydrogen Spin-Orbit Coupling (fine structure) Variational Principle Quantum Dynamics Two Level System Electromagnetic Radiation Peturbations Einstein Coefficients Fermi’s Golden Rule Class Information Grade Breakdown: HW 20%, Midterm 35%, Final 45% Midterm October 19th Book: Griffith’s Quantum Mechanics 3rd Edition Review Matter and light can both act as either particles or waves Double Slit experiment Can describe non-relativistic particles by Schrodinger’s Equation $i\hbar \frac{\partial}{\partial t}\Psi = -\frac{\hbar^2}{2m}\nabla^2 \Psi +V(r) \Psi(r,t)$ Can transform to positional representation via Fourier Transform Physical interpretation: $|\Psi(x,t)|^2$ tells you the probability that the particle is located at a certain position at a certain time (or has a certain momentum at a certain time) You can calculate the expectation value of an observable Q: $ <Q> = \int \Psi^{*} \hat{Q} \Psi dx $ Specific operators include: $\hat{x} = x$ $\hat{p} = -i\hbar \frac{\partial}{\partial x}$ Derived as follows: $ <p> = m \frac{\partial}{\partial t} <x> = m\frac{ \partial}{\partial t} \int x |\Phi|^2 dx$ Use Schrodinger Equation to convert time partial to space partial, then integrate by parts to get: $ <p> = -i\hbar \int \Psi^{*}\frac{\partial}{\partial x} \Psi dx$ All other operators can be written as a function of x and p Fundamental commutation rule: $[x,p] = xp-px = i\hbar$ Aside: Single Photon Generation Pass a photon through a nonlinear medium where the polarization goes as a power of the electric field This nonlinearity causes parametric down conversion, which is the process where a photon of higher energy gets converted to two photons of lower energies $\hbar\omega_{1} = \hbar\omega_{2}+\hbar\omega_{3}$ Most of the photons pass through the crystal, but a few undergo this process Hence, if you detect a photon of $\hbar\omega_{3}$, you will be gaurenteed to detect a photon of energy $\hbar\omega_{2}$ You know that an event has happened, but you don’t know exactly when an event will occur (probabilistic) Extremely difficult to scale up Harmonic Oscillator $\hat{a} = \frac{1}{\sqrt{2m\hbar \omega}}(m\omega \hat{x}+i\hat{p})$ $\hat{a^{+}} = \frac{1}{\sqrt{2m\hbar \omega}}(m\omega \hat{x}-i\hat{p})$ $[\hat{a},\hat{a^{+}}] = 1$ $\hat{H} = \hbar \omega (\hat{a^{+}}\hat{a}+\frac{1}{2})$ $[\hat{a^{+}},\hat{H}] = -\hbar\omega \hat{a^{+}}$ $[\hat{a},\hat{H}] = \hbar\omega \hat{a}$ Successively applying $\hat{a^{+}}$ and $\hat{a}$ to to eigenfunctions of $\hat{H}$ also yields eigenfunctions with energies raised/lowered by $\hbar \omega$....