Physics equations/00-Mathematics for this course
About the textbook
editThis 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
editRiemannSum
- 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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Left sum
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Right sum
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Middle sum
UnitVectors
- 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:
DotProduct
- is the dot product between two vectors separated in angle by θ.
CrossProductVisual
- 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 .
Wikiversity resources
edit- 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
edit- 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
edit- 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
edit- b:Calculus Seems to be first rate.
- b:Engineering_Tables#Mathematical_Tables
Wikipedia articles
edit- 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
edit- 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 operator.
- w:Vector calculus identities Encyclopedic list.
- w:Surface integral an honest look at a difficult topic
Links outside Wikimedia
edit- 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.