Differential Equations
Lessons
- First Order ODEsClassification · Linear 1st Order · Separable · Exact · Integ Factors · Practice
- Second Order ODEsHomogeneous · Wronskian · Undetermined · Var of Params · Reduction [Optional] · Practice
- Mechanical VibrationsModeling · Free Undamped · Free Damped · Forced Undamped · Forced Damped · Practice Problems
- Laplace Transform BasicsDefinition · Computing · Inverse LT · Properties · Solving IVPs
- Laplace Transforms: AdvancedReview IVPs · Heaviside · Piecewise IVPs · Convolution · Dirac Delta · Practice
- Fourier Series & PDEsOrthogonality · Waves · PDEs · Convergence · Complex FS · Practice
- Fourier TransformConvergence · Complex FS · FS to FT · Definition · Computing · Properties · Practice
Data Structures and Algorithms
Lessons
- Algorithm Analysis Concept ReferenceMotivation · Problem Solving · Big-O · Growth Rates · Reverse-Engineering
- ADTs and Linear StructuresAbstract Data Types · Linked Lists · Stacks and Queues · Applications · Practice Problems
- Trees and Binary Search TreesTree Fundamentals · Tree Traversals · BST Operations · BST Analysis · Practice
- Self-Balancing TreesAVL Trees · AVL Rotations · Red-Black Trees · RB Insertion · Practice
- Heaps, Priority Queues and Hash TablesHeaps & PQ · Heap Operations · Hash Tables · Collision Resolution · Practice
- Sorting AlgorithmsElementary Sorts · Merge Sort · Quicksort · Lower Bounds, Heap, Radix · Practice Problems
- Graph Algorithms and Design ParadigmsGraph Fundamentals · BFS & DFS · Dijkstra · MST · Design Paradigms
Principles of Electronic Materials
Lessons
- Quantum Mechanics I: Waves and the Schrodinger EquationWave-Particle Duality · Wave Equation · QM Formalism · Schrodinger Eq. · Infinite Potential Well
- Quantum Mechanics II: Confinement, Tunneling, and AtomsFinite Potential Well · Quantum Tunneling · Uncertainty Principle · Hydrogen Atom · Atoms & Periodic Table
- Bonding, Crystal Structures, and DefectsInteratomic Forces · Bond Types · Crystal Structures · Miller Indices · Crystal Defects
- Band Theory and Electronic PropertiesBand Formation · Band Diagrams · Semiconductors · Effective Mass · Density of States · Fermi-Dirac
- Metallic Conduction and Optical PropertiesFree Electron Model · Drude Model · Metal Contacts · Seebeck Effect · EM Waves in Media · Dispersion and Fresnel
- Dielectric Materials and PiezoelectricityPolarization · Polarization Mechanisms · Frequency Dependence · Gauss's Law and Capacitors · Piezoelectricity
- Photonics: Lasers, Waveguides, and Semiconductor DevicesLaser Fundamentals · Semiconductor Lasers · Quantum Dot Lasers · Silicon Photonics · Optical Modulators · Photodetectors · Photonic Integration
Circuits
Lessons
- DiodesBasics · PN Junction · Models · Small Signal · Rectifiers · Clip & Clamp
- FiltersPassive · Time Domain · H(s) · Bode · Active · 2nd Order
- MOSFETsBasics · I-V Curves · CLM & Body · SS Model · CS Amp · CG, SF · Cascode · CMOS Inverter · Logic Gates
- Operational AmplifiersAmplifiers · Ideal Opamp · Inverting · Non-Inverting · Sum & Diff · CMRR & InAmp
Numerical Methods NEW
Lessons
- Errors and Computer ArithmeticAccuracy · IEEE 754 · FP Arithmetic · Cancellation · Conditioning
- Mathematical ToolsWeighted Avg · Fixed Point · Taylor Series · Interpolation · Gauss. Elim. · Iterative · Bracketing
- Approximation MethodsHorner's Rule · Interpolation · Least Squares · LS Applications · Advanced LS · Fourier · Comparison
- Root FindingQuadratic · Newton's · Bisection · Secant / IQI · Advanced · Iterative Solvers · Newton nD
- ODE Initial-Value ProblemsEuler · RK Methods · RK4 Step Size · Adaptive · Systems · Stability
- BVPs and PDEsShooting · Finite Diff · Neumann BCs · Heat Eq · Wave Eq · Laplace
- OptimizationStep-by-Step · Newton Extrema · Golden Ratio · SPI / Brent · Newton nD · Gradient Descent · Hooke-Jeeves / LP · Bezier Curves
Digital Computers NEW
Lessons
- Foundations and Computer OrganizationIntro · Numbers · Comp Org · Data Types
- RISC-V Assembly ProgrammingISA Basics · Data Transfer · Branches · Logic & Shift · Procedures
- Instruction Encoding and Assembly ToolsR/I Formats · S/B Formats · U/J Formats · Encoding Examples · CALL Pipeline
- Input/Output SystemsI/O Basics · Polling · Interrupts · Trap Handling · Comparison
- Single-Cycle ProcessorDatapath I · Datapath II · Control · Inst Traces · Critical Path · Summary
- Performance and PipeliningMetrics · Pipeline Basics · Timing · Data Hazards · Control Hazards · Forwarding
- Memory HierarchyMemory Gap · Direct-Mapped · Set-Associative · Write Policies · Cache Perf · Virtual Mem · TLB