Physics equations/00-Mathematics for this course

About the textbook

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.

See also Calculus review and Fundamental theorem of calculus

Equations found on Physeq templates

RiemannSum

$\int_a^bf(x)\mathrm{d}x\approx\sum f(x_j)\Delta x_j$ 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).

Left sum
Right sum
Middle sum

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

$\vec{A} \cdot \vec{B} = AB\cos\theta = A_xB_x + A_yB_y + A_zB_z\,$ is the dot product between two vectors separated in angle by θ.

CrossProductVisual

right-hand rule

$\vec A \times\vec B = \vec C$ 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

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

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.

Wikibooks

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

CALCULUS-based Wikibooks

b:Calculus Seems to be first rate.
b:Engineering_Tables#Mathematical_Tables

Wikipedia articles

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.

CALCULUS-based Wikipedia articles

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

Links outside Wikimedia

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.

This article is issued from Wikiversity - version of the Wednesday, February 24, 2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.