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Sahithyan's S1
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Dimensions & Units
Electrical Fundamentals
Basics
Introduction
Generation of Electricity
Common Terms
Circuit elements
Resistors
Capacitors
Inductors
Kirchhoff Laws
Waves
AC Theory
Phasor Representation
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Power and Power factor
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Fluid Mechanics
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Properties of Fluids
Hydrostatic Pressure
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Hydrostatic Thrust
Buoyancy
Stability of a Body
Relative Equilibrium
Forced Vortex Motion
Dynamics
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Classification of Fluid Flow
Conservation Laws
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Section Formula
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Matrices
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Matrix Multiplication
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Elementary Transformations
Echelon Form
System of Linear Equations
Rank
Solutions of Homogenous Systems
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Eigenvalues & Eigenvectors
Orthogonal
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Trace
Diagonalization
Cayley-Hamilton Theorem
Matrix Norms
Complex Analysis
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Roots of Unity
Complex Functions
Limits
Continuity
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Real Analysis
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Set theory
Set of Numbers
Continued Fraction Expansion
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Riemann Zeta Function
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Solving First Order ODE
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Variation of parameters
Riemann Integration
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Partition
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Upper & Lower integral
Riemann Integrable
Cauchy Criterion
Theorems on Integrability
Properties of Integrals
Sequential Characterization of Integrability
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Fundamental Theorem of Calculus
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2D kinematics of a rigid body
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A book
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Structure of Atoms
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Energy Band Theory
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Conductive Polymers
Nanotechnology
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Graphene
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Degradation
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Degradation of Metals
Forms of Corrosion
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Degradation of Polymers
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Sahithyan's S1 — Mathematics
Countability
A set
is countable
iff
, where
is a one-one function.
Examples
Countable: Any finite set,
Uncountable:
, Any open/closed intervals in
.
Transitive property
Say
.