Vector Analysis: An Introduction to Vector-methods and Their Various Applications to Physics and MathematicsJ. Wiley & Sons, 1911 - 262 من الصفحات |
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
a₁ acceleration angular velocity axis called Cartesian circuit closed surface components considered const constant vector coördinates curl F curvature curve defined definition density differential direction div F divergence theorem dt dt electrical ellipsoid equal equation of motion expression F₁ F₂ fluid flux formulæ Gauss's Theorem grad Green's Theorem hence hodograph inertia Laplace's Equation line integral magnetic magnitude mass moving space multiplied normal notation obtain operator origin osculating plane parallel particle path perpendicular plane Poisson's Equation potential principal axes quantity r₁ radius vector represented result rigid body rotation scalar function scalar point-function scalar product solid angle sphere surface integral tangent Taylor's Theorem tion unit vectors V₁ vanishes variable vector function vector product volume w₂ write written zero Απ φω дх მე მი მყ
مقاطع مشهورة
الصفحة 22 - A person travelling eastward at the rate of 4 miles per hour, finds that the wind seems to blow directly from the north; on doubling his speed it appears to come from the north-east; find the direction of the wind and its velocity.
الصفحة 44 - The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its four Dem.— Let ABCD be the a.
الصفحة viii - Poinsot has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligible propositions supersede equations".
الصفحة 24 - ... intersection of corresponding sides lie on a line, then the lines joining the corresponding vertices pass through a common point and conversely. 5. Given a quadrilateral in space. Find the middle point of the line which joins the middle points of the diagonals. Find the middle point of the line which joins the middle points of two opposite sides. Show that these two points are the same and coincide with the center of gravity of a system of equal masses placed at the vertices of the quadrilateral....
الصفحة 44 - The squares of the sides of any quadrilateral exceed the squares of the diagonals by four times the square of the line which joins the middle points of the diagonals.
الصفحة 44 - P meet in a point and are directed along the diagonals of the three faces of a cube meeting at the point. Determine the magnitude of their resultant.
الصفحة 113 - A through a closed surface S is equal to the volume integral of the divergence of the vector field over the region enclosed by S.
الصفحة 46 - The triangle formed by joining the middle point of one of the nonparallel sides of a trapezoid to the extremities of the opposite side, is equivalent to one-half the trapezoid.
الصفحة iii - Vector analysis; an introduction to vector-methods and their various applications to physics and mathematics. Ed.2. 1911. Wiley. "Bibliography,
الصفحة 27 - I is the center of its inscribed circle. Show that the resultant of the vectors a • AD, b • BD, c • CD is (a + b + c) ID, where a, b, c are the lengths of the sides of the triangle. 10. ABCD, A'B'C'D' are two parallelograms in the same plane.