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Please do not use this template. Instead go to Physics equations/Equations or a subpage and transclude from there.

Sample Superstructure[edit]

Sample Substructure[edit]


  • Foo

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used for alternative versions of the same equation

Geometry and algebra[edit]


  • is the circumference of circle;   is its area.
  • is the surface area of a sphere;   is its volume.

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Theta in radians minimalistic.svg
  • defines angle (in radians), where s is arclength and r is radius.

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  • (where A is the angle shown)

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  • and defines the arcsine function as the inverse of the sine. Similarly, is called the arctangent, or the inverse tangent, and is called arccosine, or the inverse cosine and so forth. In general, and for any function and its inverse. Complexities occur whenever the inverse is not a true function; for example, since , the inverse is multi-valued:

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First year calculus[edit]

  • ,     and the derivative is in the limit that
  • is the chain rule.
  • ,      ,     ,     ,     
  • expresses the fundamental theorem of calculus.

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Riemann sum convergence.png
  • is the Riemann sum representation of the integral of f(x) from x=a to x=b. It is the area under the curve, with contributions from f(x)<0 being negative (if a>b). The sum equals the integral in the limit that the widths of all the intervals vanish (Δxj→0).

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  • is the Riemann sum representation of the integral of f(x) from x=a to x=b.

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  • The fundamental theorem of calculus allows us to construct integrals from known derivatives:

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Vector algebra[edit]


Polar to cartesian.svg
  • and are the x and y components of a displacement from the origin to some point. The inverse transformations are:
  • , and
  • , which is multi-valued and therefore not a true function.
  •   and     are called the x and y components of vector A, respectively.
  • is called the magnitude,norm (or sometimes absolute value) of vector A.
  • Omission of the arrow indicates that the quantity is the scalar magnitude of that vector. Another notation that distinguishes between a vector and a scalar is boldface font: A is a vector and A A  is the scalar magnitude.

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Vectors A+B=C.png
  • and have geometric interpretation as vector addition and subtraction as shown in the figure. Vector addition and subtraction can also be defined through the components. For example, the following two statements are equivalent:
  • AND

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  • is the cross product of and . The cross product, is directed perpendicular to and by the right hand rule.
  • wehre is the angle between vectors and .
  • is also the magnitude of the of the parallelogram defined by the vectors and .
  • if and are either parallel or antiparallel.
  • The unit vectors obey , , and .

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  • is the dot product between two vectors separated in angle by θ.

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  • A unit vector is any vector with unit magnitude equal to one. For any nonzero vector, is a unit vector. An important set of unit vectors is the orthonormal basis associated with Cartesian coordinates:
  • The basis vectors are also written as , so that any vector may be written . Even more elegance is achieved by labeling the directions with integers:

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Removed templates[edit]



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