# Physics equations/00-Mathematics for this course

This resources uses, openstax Physics, an open source textbook available for free at http://cnx.org/content/col11406/1.7) Most sections of the Physics equations have a link to the appropriate chapter.

This section is an exception, since openstax Physics has no such review.

### Equations found on Physeq templates

RiemannSum
• $\int _{a}^{b}f(x)\mathrm {d} x\approx \sum f(x_{j})\Delta x_{j}$ 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).
UnitVectors
• A unit vector is any vector with unit magnitude equal to one. For any nonzero vector, ${\hat {V}}={\vec {V}}/V$ is a unit vector. An important set of unit vectors is the orthonormal basis associated with Cartesian coordinates:
• $\mathbf {\hat {i}} \cdot \mathbf {\hat {i}} =\mathbf {\hat {j}} \cdot \mathbf {\hat {j}} =\mathbf {\hat {k}} \cdot \mathbf {\hat {k}} =1$ • $\mathbf {\hat {j}} \cdot \mathbf {\hat {k}} =\mathbf {\hat {k}} \cdot \mathbf {\hat {i}} =\mathbf {\hat {j}} \cdot \mathbf {\hat {k}} =0$ • The basis vectors $(\mathbf {\hat {i}} ,\mathbf {\hat {j}} ,\mathbf {\hat {k}} )$ are also written as $({\hat {x}},{\hat {y}},{\hat {z}})$ , so that any vector may be written ${\vec {A}}=A_{x}{\hat {x}}+A_{y}{\hat {y}}+A_{z}{\hat {z}}$ . Even more elegance is achieved by labeling the directions with integers: ${\vec {A}}=A_{1}{\hat {e_{1}}}+A_{2}{\hat {e_{2}}}+A_{3}{\hat {e_{3}}}$ $=\Sigma A_{j}{\hat {e_{j}}}\,.$ DotProduct
• ${\vec {A}}\cdot {\vec {B}}=AB\cos \theta =A_{x}B_{x}+A_{y}B_{y}+A_{z}B_{z}\,$ is the dot product between two vectors separated in angle by θ.
CrossProductVisual
• ${\vec {A}}\times {\vec {B}}={\vec {C}}$ is the cross product of ${\vec {A}}$ and ${\vec {B}}$ . The cross product, ${\vec {C}}$ is directed perpendicular to ${\vec {A}}$ and ${\vec {B}}$ by the right hand rule.
• $|{\vec {A}}\times {\vec {B}}|=C=|AB\sin \theta |$ wehre $\theta$ is the angle between vectors ${\vec {A}}$ and ${\vec {B}}$ .
• $|{\vec {A}}\times {\vec {B}}|=C$ is also the magnitude of the of the parallelogram defined by the vectors ${\vec {A}}$ and ${\vec {B}}$ .
• ${\vec {A}}\times {\vec {B}}=0$ if ${\vec {A}}$ and ${\vec {B}}$ are either parallel or antiparallel.
• The unit vectors obey ${\hat {x}}\times {\hat {y}}={\hat {z}}$ , ${\hat {y}}\times {\hat {z}}={\hat {x}}$ , and ${\hat {z}}\times {\hat {x}}={\hat {y}}$ .

## Wikiversity resources

### CALCULUS-based Wikiversity resources

• Vector calculus Vector derivatives. Gradient, div, and stokes theorems.
• Coordinate systems Designed to facilitate a simple understanding of line, surface and volume integrals.
• Coulomb's Law Introduces the Coulomb integral using a line charge. It then extends this result to a plane charge using a double integral.