The Equations of Motion in a Rotating Coordinate System
... simplification to assume that the earth is locally flat and to use a rectangular coordinate system with z pointing vertically upwards. » Holton (§2.3, pp31-35) shows the precise circumstances under which such an approximation is valid. » In general, the use of spherical coordinates merely refines th ...
... simplification to assume that the earth is locally flat and to use a rectangular coordinate system with z pointing vertically upwards. » Holton (§2.3, pp31-35) shows the precise circumstances under which such an approximation is valid. » In general, the use of spherical coordinates merely refines th ...
Word Format
... Our initial definition of a vector turns out to be vague and insufficient for more advanced applications. In advanced physics, mathematical equations and entities including vectors are defined by how they behave when the coordinate system is transformed (changed). Since the transformation properties ...
... Our initial definition of a vector turns out to be vague and insufficient for more advanced applications. In advanced physics, mathematical equations and entities including vectors are defined by how they behave when the coordinate system is transformed (changed). Since the transformation properties ...
Matrix elements for the Morse potential using ladder operators
... Equation (29) was obtained under the implicit assumption of having only positive integer powers in Eqs. (28). If we look at the analytic properties of M as a function of A, however, we immediately notice that M is a meromorphic function. Its analytic continuation is simply obtained by continuing the ...
... Equation (29) was obtained under the implicit assumption of having only positive integer powers in Eqs. (28). If we look at the analytic properties of M as a function of A, however, we immediately notice that M is a meromorphic function. Its analytic continuation is simply obtained by continuing the ...
Fast multiply, nonzero structure
... Applying this matrix requires no arithmetic, but it does require O(n) index lookups and element copies. This is a prototypical example of a sparse matrix – one in which most of the matrix elements are zero – but the sparse structure is completely destroyed when we change the basis. The fifth matrix ...
... Applying this matrix requires no arithmetic, but it does require O(n) index lookups and element copies. This is a prototypical example of a sparse matrix – one in which most of the matrix elements are zero – but the sparse structure is completely destroyed when we change the basis. The fifth matrix ...
Updated Course Outline - Trinity College Dublin
... [ Sydsaeter, ch. 6 & 7 (up to 7.9) ] [ Chiang, ch. 6, 7.1 to 7.3, 8.1, 8.5 (up to p. 199), 9.3 & 9.5 ] 1. Definition and interpretation a. Difference quotient b. Derivative c. Increasing and decreasing functions d. Limits e. Continuity vs differentiability 2. Rules of Differentiation a. Constant fun ...
... [ Sydsaeter, ch. 6 & 7 (up to 7.9) ] [ Chiang, ch. 6, 7.1 to 7.3, 8.1, 8.5 (up to p. 199), 9.3 & 9.5 ] 1. Definition and interpretation a. Difference quotient b. Derivative c. Increasing and decreasing functions d. Limits e. Continuity vs differentiability 2. Rules of Differentiation a. Constant fun ...
Relativistic Quantum Mechanics
... The fact that quantum states of free relativistic particles are fully defined by the Lorentz transformation supplemented by the space-time translation was discovered by Wigner. Here we will follow his idea in a qualitative way just to get the main concept across. First, we note that Lorentz transfor ...
... The fact that quantum states of free relativistic particles are fully defined by the Lorentz transformation supplemented by the space-time translation was discovered by Wigner. Here we will follow his idea in a qualitative way just to get the main concept across. First, we note that Lorentz transfor ...