Physics equations/00-Mathematics for this course

About the textbook edit

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.

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 (Δx_j→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 ${\hat {z}}\times {\hat {x}}={\hat {y}}$ .

Vectors Has most of what you need to get started and a bit of what you do not need.
Topic:Trigonometry Concise.
Trigonometry Parallel Wikiversity effort
- Trigonometry/Polar Relevant to this course

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.

b:Subject:Physics an impressive list is growing. If a book is listed as "featured" it is probably good. If it is not classified as "complete" it probably very incomplete.
b:Physics Study Guide a featured book
b:FHSST_Physics a featured high school textbook

w:Linear_equation#Algebraic_equations misplaced but interesting list of pages.
- w:Elementary_algebra Fun to skim if you already know the subject.
w:List_of_trigonometric_identities a really long list
w:Euclidean vector
- w:Dot product
- w:Cross product
- w:Vector algebra relations Encyclopedic but useful and convenient.
- w:Vector_(mathematics_and_physics) A wide assortment of entities are called "vectors".
w:Riemann sum. Everybody needs to know something about the Riemann sum.

w:Differentiation rules Long and complete list of rules associated with first semester calculus.
w:Vector calculus Advanced. Everything you need in a calculus-based first year physics course.
w:Del_in_cylindrical_and_spherical_coordinates Long list of essential identities regarding the ${\vec {\nabla }}$ operator.
w:Vector calculus identities Encyclopedic list.
w:Surface integral an honest look at a difficult topic

oregonstate BridgeBook a wiki focusing on the undergraduate physics major.
UC Davis physwiki Not much material but the wikis are first rate. Part of a suite that includes other subjects.
openstax Physics Commercial quality (and massive) algebra/trig based textbook, nominally the one used for this course. This book can be accessed as a wiki and edited; the only reason for doing so would be to re-write it as a calculus based text.