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In solving mathematical equations, particularly linear simultaneous equations, differential equations and integral equations, the terminology homogeneous is often used for equations with some linear operator L on the LHS and 0 on the RHS. In contrast, an equation with a non-zero RHS is called inhomogeneous or non-homogeneous, as exemplified by ...
For curves on surfaces, a curve is 2-sided if and only if it preserves orientation, and 1-sided if and only if it reverses orientation: a tubular neighborhood is then a Möbius strip. This can be determined from the class of the curve in the fundamental group of the surface and the orientation character on the fundamental group, which ...
The unique pair of values a, b satisfying the first two equations is (a, b) = (1, 1); since these values also satisfy the third equation, there do in fact exist a, b such that a times the original first equation plus b times the original second equation equals the original third equation; we conclude that the third equation is linearly ...
The Key Stage 1, 2 and 3 along with GCSE section covers a range of subjects. In Key Stage 1 , 17 subjects are available, including Art and Design , Computing , Design and Technology , English , Geography , History , Maths , Music , Physical Education , PSHE , Citizenship , Religious Education , Science , and Modern Foreign Languages . [ 5 ]
The boundary homomorphism is given by ∂D = 2C 1 and ∂C 1 = ∂C 2 = 0, yielding the homology groups of the Klein bottle K to be H 0 (K, Z) = Z, H 1 (K, Z) = Z×(Z/2Z) and H n (K, Z) = 0 for n > 1. There is a 2-1 covering map from the torus to the Klein bottle, because two copies of the fundamental region of the Klein bottle, one being ...
has no real number solution since no real number squared equals −1. Sometimes a quadratic equation has a root of multiplicity 2, such as: (+) = For this equation, −1 is a root of multiplicity 2. This means −1 appears twice, since the equation can be rewritten in factored form as