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Core - Physics

    Chapter 2

    Vectors and Scalars

    2.1 : Introduction to Scalars01:21

    2.1 : Introduction to Scalars

    Many familiar physical quantities can be specified completely by giving a single number and the appropriate unit. For example, "a class period lasts ...

    14.3K views
    2.2 : Introduction to Vectors01:21

    2.2 : Introduction to Vectors

    To define some physical quantities, there is a need to specify both magnitude as well as direction. For example, when the U.S. Coast Guard dispatches a ...

    13.9K views
    2.3 : Vector Components in the Cartesian Coordinate System01:29

    2.3 : Vector Components in the Cartesian Coordinate System

    Vectors are usually described in terms of their components in a coordinate system. Even in everyday life, we naturally invoke the concept of orthogonal ...

    19.3K views
    2.4 : Polar and Cylindrical Coordinates01:22

    2.4 : Polar and Cylindrical Coordinates

    The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on ...

    14.4K views
    2.5 : Spherical Coordinates01:23

    2.5 : Spherical Coordinates

    Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe ...

    10.0K views
    2.6 : Vector Algebra: Graphical Method01:10

    2.6 : Vector Algebra: Graphical Method

    Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the ...

    12.0K views
    2.7 : Vector Algebra: Method of Components01:08

    2.7 : Vector Algebra: Method of Components

    It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like ...

    13.8K views
    2.8 : Scalar Product (Dot Product)01:11

    2.8 : Scalar Product (Dot Product)

    The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a ...

    8.2K views
    2.9 : Vector Product (Cross Product)01:17

    2.9 : Vector Product (Cross Product)

    Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of ...

    9.4K views
    2.10 : Scalar and Vector Triple Products01:06

    2.10 : Scalar and Vector Triple Products

    Two vectors can be multiplied using a scalar product or a vector product. The resultant of a scalar product is scalar, while with vector products, the ...

    2.3K views
    2.11 : Gradient and Del Operator01:14

    2.11 : Gradient and Del Operator

    In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The ...

    2.5K views
    2.12 : Divergence and Curl01:15

    2.12 : Divergence and Curl

    The divergence of a vector field at a point is the net outward flow of the flux out of a small volume through a closed surface enclosing the volume, as ...

    1.7K views
    2.13 : Second Derivatives and Laplace Operator01:22

    2.13 : Second Derivatives and Laplace Operator

    The first order operators using the del operator include the gradient, divergence and curl. Certain combinations of first order operators on a scalar or ...

    1.2K views
    2.14 : Line, Surface, and Volume Integrals01:15

    2.14 : Line, Surface, and Volume Integrals

    A line integral for a vector field is defined as the integral of the dot product of a vector function with an infinitesimal displacement vector along a ...

    2.3K views
    2.15 : Divergence and Stokes' Theorems01:06

    2.15 : Divergence and Stokes' Theorems

    The divergence and Stokes' theorems are a variation of Green's theorem in a higher dimension. They are also a generalization of the fundamental ...

    1.5K views
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