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Dimensions & Units
Electrical Fundamentals
Introduction
Double subscript notation
Common Terms
Circuit elements
Voltage sources
Resistors
Capacitors
Inductors
Kirchhoff Laws
Introduction to Waves
Definitions in AC Theory
Phasor Representation
Impedance & Admittance
Power and Power factor
Power systems
3-Phased System
Fluid Mechanics
Statics
Introduction to Fluid Mechanics
Properties of Fluids
Hydrostatic Pressure
Pressure
Pressure Measurements
Pressure Head
Hydrostatic Thrust
Buoyancy
Equilibrium of Submerged Bodies
Relative Equilibrium
Forced Vortex Motion
Dynamics
Introduction to Fluid Dynamics
Conservation Laws
Mathematics
Algebra
Vectors
Introduction to Vectors
Vector Equation of Straight Lines
Vector Equation of Planes
Skew Lines
Matrices
Introduction to Matrices
Matrix Multiplication
Transpose
Determinant
Adjoint
Inverse
Elementary Transformations
Echelon Form
System of Linear Equations
Rank
Solutions of Homogenous Systems
Solution of Non-homogenous Systems
Eigenvalues & Eigenvectors
Orthogonal & Orthonormal Vectors
Trace
Diagonalization
Cayley-Hamilton Theorem
Matrix Norms
Complex Numbers
Real Analysis
Introduction to Real Analysis
Set theory
Set of Numbers
Continued Fraction Expansion
Field Axioms
Completeness Axiom
Order Axioms
Relations
Functions
Composition
Countability
Limits
Continuity
Continuity Theorems
Differentiability
Extreme Values
Other Theorems
Higher Order Derivatives
Taylor's Theorem
Sequences
Series
ODE
Introduction to Differential Equations
Solving First Order ODE
Higher Order ODE
Solving Second Order ODE
Wronskian
Variation of parameters
Riemann Integration
Introduction
Riemann Integral
Partition
Riemann Sum
Refinements
Upper & Lower integral
Riemann Integrable
Cauchy Criterion
Theorems on Integrability
Properties of Integrals
Mechanics
Statics
Introduction to Statics
Derived Formulas for Common Shapes
Parallel Axis Theorem
Perpendicular Axis Theorem
Transformation Law
Principal Axes
Beams
Principle of Superposition
Structural Elements
Trusses
Analysis of Trusses
Beam Analogy (Approximate) method
Indeterminate Trusses
Dynamics
Introduction to Dynamics
2D kinematics of a rigid body
Mechanisms
Four-bar Linkage
Epicyclic Gears
Mobility of Mechanisms
Inversions of a mechanism
Programming Fundamentals
Interning
Practice Resources
One's & Two's Complement
Floating-point representation
Properties of Materials
Basics
Introduction to Properties of Materials
Metals
Ceramics
Polymers
Composites
Crystal Structure
Space Lattice
Summary of the 4
Miller Indices
Allotropy
Defects in Crystals
Functional Materials
Mechanical Properties
Introduction
Tensile Test
Definitions
Flexural Test
Charpy Impact Test
Electrical Properties
Introduction
Energy Band Theory
Semiconductivity
Dielectric behavior
Piezoelectricity
Conductive Polymers
Nanotechnology
Introduction
Graphene
Carbon Nanotubes
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Refinements
is called a refinement of
if
and
are partitions of
and
.
When
is a refinement of
: