Vector Calculus Gradient, Divergence & Curl | BMLabs | BMLabs Mathematics

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Vector Algebra and Calculus Learning Map

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Concepts

Vector Algebra and Calculussubject
SCALARS AND VECTORSchapter
Concept and motivation of vectors and scalarssection
Addition and subtraction of vectorssection
Multiplication and division of a vector by a scalarsection
Division of a segment in a given ratiosection
Linear combination of vectorssection
Collinear and coplanar vectorssection
Rectangular resolutionsection
Centroid or Mean centresection
Centre of masssection
Centroid of areasection
Vector character of physical quantitiessection
Some useful theoremssection
SCALAR AND VECTOR PRODUCTSchapter
Introductionsection
Scalar product of two vectorssection
Orthogonal triad of vectorssection
Distributive lawsection
Scalar product in terms of co-ordinatessection
PRODUCTS OF THREE OR MORE VECTORSchapter
Scalar triple productsection
Volume of a tetrahedronsection
Vector triple productsection
Scalar product of four vectorssection
Vector product of four vectorssection
Reciprocal system of vectorssection
VECTOR EQUATIONS AND APPLICATIONSchapter
Vector equationssection
Solution of some vector equationssection
Vector equation of a straight linesection
Condition of intersection of two straight linessection
Equations of the bisectors of the angles between two straight linessection
Vector equation of a planesection
Equation of a straight line in non-parametric formsection
Shortest distance between two skew linessection
Equation of a plane in the normal formsection
Angle between two planessection
Distance of a point from a planesection
Equation of a plane passing through the intersection of two planessection
Planes bisecting the angles between two planessection
Perpendicular distance of a point from a straight linesection
Vector equation of a spheresection
Equation of a sphere with two given points as the extremities of a diametersection
Equation of the tangent plane on the spheresection
Concurrent forcessection
Lami's theoremsection
Work done by a forcesection
Moment of a force about a pointsection
Velocity at any point of a rotating rigid bodysection
DIFFERENTIATION OF VECTORSchapter
Vector function, limit and continuitysection
Derivative of a vectorsection
Derivatives of sum and productsection
Constant vectorssection
Derivative of triple productssection
Partial derivatives of vectorssection
Application to differential geometrysection
Serret-Frenet formulasection
Curvature and torsionsection
Surfaces, normal and tangent planesection
DIFFERENTIAL OPERATORSchapter
Scalar and vector point functions and fieldssection
Directional derivativesection
Expressions for directional derivativesection
Gradient of a scalar point functionsection
Further discussions on gradientsection
Divergence and curl of a vectorsection
Rules associated with divergence and curlsection
Second order differential operatorssection
Irrotational and solenoidal vectorssection
Vector Integrationchapter
Integration with respect to a scalar variablesection
Standard resultssection
Line integralssection
Tangential line integralsection
Conservative fieldsection
Other line integralssection
Circulationsection
Surface integralssection
Normal surface integralsection
Other surface integralssection
Volume integralssection
Integral Transformschapter
Gradient defined as an integralsection
Divergence of a vector functionsection
Divergence in cartesian co-ordinatessection
Gauss's divergence theoremsection
Green's theoremssection
Curl of a vector functionsection
Curl of a vector in cartesian co-ordinatessection
Stokes' theoremsection
Some deductions from Stokes' theoremsection
Green's theorem in a planesection
Dynamics of a Particlechapter
Velocity and acceleration at an instantsection
Kinematics of a particlesection
Relative motionsection
Moving axessection
Velocity and acceleration referred to a set of moving axessection
Radial and transverse resolutes of velocity and accelerationsection
Some important definitionssection
Kinetics of a particlesection
Motion under gravitysection
Activity of a forcesection
Some important principlessection
Central forcessection
Planetary motionsection
Impulse of a forcesection
Dynamics of a System of Particles and of Rigid Bodychapter
Motion of a system of particlessection
Some important resultssection
Principle of conservation of linear and angular momentumsection
Motion relative to the centre of masssection
Angular velocity vectorsection
Kinematics of a rigid bodysection
Kinetics of a rigid bodysection
Equations of motion of a rigid bodysection
Moving frame of reference in spacesection
Motion relative to the rotating framesection
Euler's equations of motionsection

Relationships

Vector Algebra and Calculus --contains--> SCALARS AND VECTORS
SCALARS AND VECTORS --contains--> Concept and motivation of vectors and scalars
SCALARS AND VECTORS --contains--> Addition and subtraction of vectors
SCALARS AND VECTORS --contains--> Multiplication and division of a vector by a scalar
SCALARS AND VECTORS --contains--> Division of a segment in a given ratio
SCALARS AND VECTORS --contains--> Linear combination of vectors
SCALARS AND VECTORS --contains--> Collinear and coplanar vectors
SCALARS AND VECTORS --contains--> Rectangular resolution
SCALARS AND VECTORS --contains--> Centroid or Mean centre
SCALARS AND VECTORS --contains--> Centre of mass
SCALARS AND VECTORS --contains--> Centroid of area
SCALARS AND VECTORS --contains--> Vector character of physical quantities
SCALARS AND VECTORS --contains--> Some useful theorems
Vector Algebra and Calculus --contains--> SCALAR AND VECTOR PRODUCTS
SCALAR AND VECTOR PRODUCTS --contains--> Introduction
SCALAR AND VECTOR PRODUCTS --contains--> Scalar product of two vectors
SCALAR AND VECTOR PRODUCTS --contains--> Orthogonal triad of vectors
SCALAR AND VECTOR PRODUCTS --contains--> Distributive law
SCALAR AND VECTOR PRODUCTS --contains--> Scalar product in terms of co-ordinates
Vector Algebra and Calculus --contains--> PRODUCTS OF THREE OR MORE VECTORS
PRODUCTS OF THREE OR MORE VECTORS --contains--> Scalar triple product
PRODUCTS OF THREE OR MORE VECTORS --contains--> Volume of a tetrahedron
PRODUCTS OF THREE OR MORE VECTORS --contains--> Vector triple product
PRODUCTS OF THREE OR MORE VECTORS --contains--> Scalar product of four vectors
PRODUCTS OF THREE OR MORE VECTORS --contains--> Vector product of four vectors
PRODUCTS OF THREE OR MORE VECTORS --contains--> Reciprocal system of vectors
Vector Algebra and Calculus --contains--> VECTOR EQUATIONS AND APPLICATIONS
VECTOR EQUATIONS AND APPLICATIONS --contains--> Vector equations
VECTOR EQUATIONS AND APPLICATIONS --contains--> Solution of some vector equations
VECTOR EQUATIONS AND APPLICATIONS --contains--> Vector equation of a straight line
VECTOR EQUATIONS AND APPLICATIONS --contains--> Condition of intersection of two straight lines
VECTOR EQUATIONS AND APPLICATIONS --contains--> Equations of the bisectors of the angles between two straight lines
VECTOR EQUATIONS AND APPLICATIONS --contains--> Vector equation of a plane
VECTOR EQUATIONS AND APPLICATIONS --contains--> Equation of a straight line in non-parametric form
VECTOR EQUATIONS AND APPLICATIONS --contains--> Shortest distance between two skew lines
VECTOR EQUATIONS AND APPLICATIONS --contains--> Equation of a plane in the normal form
VECTOR EQUATIONS AND APPLICATIONS --contains--> Angle between two planes
VECTOR EQUATIONS AND APPLICATIONS --contains--> Distance of a point from a plane
VECTOR EQUATIONS AND APPLICATIONS --contains--> Equation of a plane passing through the intersection of two planes
VECTOR EQUATIONS AND APPLICATIONS --contains--> Planes bisecting the angles between two planes
VECTOR EQUATIONS AND APPLICATIONS --contains--> Perpendicular distance of a point from a straight line
VECTOR EQUATIONS AND APPLICATIONS --contains--> Vector equation of a sphere
VECTOR EQUATIONS AND APPLICATIONS --contains--> Equation of a sphere with two given points as the extremities of a diameter
VECTOR EQUATIONS AND APPLICATIONS --contains--> Equation of the tangent plane on the sphere
VECTOR EQUATIONS AND APPLICATIONS --contains--> Concurrent forces
VECTOR EQUATIONS AND APPLICATIONS --contains--> Lami's theorem
VECTOR EQUATIONS AND APPLICATIONS --contains--> Work done by a force
VECTOR EQUATIONS AND APPLICATIONS --contains--> Moment of a force about a point
VECTOR EQUATIONS AND APPLICATIONS --contains--> Velocity at any point of a rotating rigid body
Vector Algebra and Calculus --contains--> DIFFERENTIATION OF VECTORS
DIFFERENTIATION OF VECTORS --contains--> Vector function, limit and continuity
DIFFERENTIATION OF VECTORS --contains--> Derivative of a vector
DIFFERENTIATION OF VECTORS --contains--> Derivatives of sum and product
DIFFERENTIATION OF VECTORS --contains--> Constant vectors
DIFFERENTIATION OF VECTORS --contains--> Derivative of triple products
DIFFERENTIATION OF VECTORS --contains--> Partial derivatives of vectors
DIFFERENTIATION OF VECTORS --contains--> Application to differential geometry
DIFFERENTIATION OF VECTORS --contains--> Serret-Frenet formula
DIFFERENTIATION OF VECTORS --contains--> Curvature and torsion
DIFFERENTIATION OF VECTORS --contains--> Surfaces, normal and tangent plane
Vector Algebra and Calculus --contains--> DIFFERENTIAL OPERATORS
DIFFERENTIAL OPERATORS --contains--> Scalar and vector point functions and fields
DIFFERENTIAL OPERATORS --contains--> Directional derivative
DIFFERENTIAL OPERATORS --contains--> Expressions for directional derivative
DIFFERENTIAL OPERATORS --contains--> Gradient of a scalar point function
DIFFERENTIAL OPERATORS --contains--> Further discussions on gradient
DIFFERENTIAL OPERATORS --contains--> Divergence and curl of a vector
DIFFERENTIAL OPERATORS --contains--> Rules associated with divergence and curl
DIFFERENTIAL OPERATORS --contains--> Second order differential operators
DIFFERENTIAL OPERATORS --contains--> Irrotational and solenoidal vectors
Vector Algebra and Calculus --contains--> Vector Integration
Vector Integration --contains--> Integration with respect to a scalar variable
Vector Integration --contains--> Standard results
Vector Integration --contains--> Line integrals
Vector Integration --contains--> Tangential line integral
Vector Integration --contains--> Conservative field
Vector Integration --contains--> Other line integrals
Vector Integration --contains--> Circulation
Vector Integration --contains--> Surface integrals
Vector Integration --contains--> Normal surface integral
Vector Integration --contains--> Other surface integrals
Vector Integration --contains--> Volume integrals
Vector Algebra and Calculus --contains--> Integral Transforms
Integral Transforms --contains--> Gradient defined as an integral
Integral Transforms --contains--> Divergence of a vector function
Integral Transforms --contains--> Divergence in cartesian co-ordinates
Integral Transforms --contains--> Gauss's divergence theorem
Integral Transforms --contains--> Green's theorems
Integral Transforms --contains--> Curl of a vector function
Integral Transforms --contains--> Curl of a vector in cartesian co-ordinates
Integral Transforms --contains--> Stokes' theorem
Integral Transforms --contains--> Some deductions from Stokes' theorem
Integral Transforms --contains--> Green's theorem in a plane
Vector Algebra and Calculus --contains--> Dynamics of a Particle
Dynamics of a Particle --contains--> Velocity and acceleration at an instant
Dynamics of a Particle --contains--> Kinematics of a particle
Dynamics of a Particle --contains--> Relative motion
Dynamics of a Particle --contains--> Moving axes
Dynamics of a Particle --contains--> Velocity and acceleration referred to a set of moving axes
Dynamics of a Particle --contains--> Radial and transverse resolutes of velocity and acceleration
Dynamics of a Particle --contains--> Some important definitions
Dynamics of a Particle --contains--> Kinetics of a particle
Dynamics of a Particle --contains--> Motion under gravity
Dynamics of a Particle --contains--> Activity of a force
Dynamics of a Particle --contains--> Some important principles
Dynamics of a Particle --contains--> Central forces
Dynamics of a Particle --contains--> Planetary motion
Dynamics of a Particle --contains--> Impulse of a force
Vector Algebra and Calculus --contains--> Dynamics of a System of Particles and of Rigid Body
Dynamics of a System of Particles and of Rigid Body --contains--> Motion of a system of particles
Dynamics of a System of Particles and of Rigid Body --contains--> Some important results
Dynamics of a System of Particles and of Rigid Body --contains--> Principle of conservation of linear and angular momentum
Dynamics of a System of Particles and of Rigid Body --contains--> Motion relative to the centre of mass
Dynamics of a System of Particles and of Rigid Body --contains--> Angular velocity vector
Dynamics of a System of Particles and of Rigid Body --contains--> Kinematics of a rigid body
Dynamics of a System of Particles and of Rigid Body --contains--> Kinetics of a rigid body
Dynamics of a System of Particles and of Rigid Body --contains--> Equations of motion of a rigid body
Dynamics of a System of Particles and of Rigid Body --contains--> Moving frame of reference in space
Dynamics of a System of Particles and of Rigid Body --contains--> Motion relative to the rotating frame
Dynamics of a System of Particles and of Rigid Body --contains--> Euler's equations of motion

Vector Algebra and Calculus

Learning structure

Vector Algebra and Calculus Learning Map

Concepts

Relationships

Chapters

SCALARS AND VECTORS

SCALAR AND VECTOR PRODUCTS

PRODUCTS OF THREE OR MORE VECTORS

VECTOR EQUATIONS AND APPLICATIONS

DIFFERENTIATION OF VECTORS

DIFFERENTIAL OPERATORS

Vector Integration

Integral Transforms

Dynamics of a Particle

Dynamics of a System of Particles and of Rigid Body

Curated pathways

Metric Spaces

Introduction To Discrete Mathematics