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Differential Calculus FormulasDifferential Calculus Formulas "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20060331 14:46:06
Re: Differential Calculus Formulas"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #3 20060401 14:41:58
Re: Differential Calculus Formulassolving procedure p(t) could any function without y, constant is ok. Linear means no y, y^{2} or yy', etc. So virtually there are only y and y' multiplied by function of t or constant, function of t, and constant are allowed in the 1st Order Linear DE. And the DEs satisfying this condition can be easily transformed into the standard form above through division. Last edited by George,Y (20070522 14:22:02) X'(yXβ)=0 #4 20060409 01:24:54
Re: Differential Calculus FormulasDerivatives of some Elelmentary functions If u and v are functions of x, and c is a constant, provided v≠0 Character is who you are when no one is looking. #5 20060409 01:38:37
Re: Differential Calculus FormulasChain rule Inverse Function Character is who you are when no one is looking. #6 20060409 01:48:07
Re: Differential Calculus FormulasInverse Trignometric Functions Character is who you are when no one is looking. #7 20060422 15:34:59
Re: Differential Calculus Formulasnth derivative Leibnitz theorem If u and v are functions of x and n is a positive integer, then Character is who you are when no one is looking. #8 20060506 19:49:38
Re: Differential Calculus FormulasHyperbolic functions Inverse Hyperbolic functions Character is who you are when no one is looking. #9 20060506 21:50:10
Re: Differential Calculus FormulasDerivatives of functions of the form (x² ± a²) Character is who you are when no one is looking. #10 20060517 00:02:47
Re: Differential Calculus FormulasTangents and Normals If dy/dx=0 at a point P, then the slope of the tangent at P is zero, therefore, the tangent is parallel to the xaxis. If dy/dx = infinity at a point P, then the slope of the tangent at P is infinity, therefore, the tangent is parallel to the yaxis. Equations of tangent and normal at a point: Slope of the tangent at point P (x1, y1) on the curve y=f(x) is the value of dy/dx at (x1,y1). Let dy/dx=m at (x1,y1). Then the equation of the tangent at (x1,y1) is Normal at point P is perpendicular to the tangent at P and passes through P(x1,y1). Therefore, Equation of the normal at P(x1,y1) is Angle between two curves The angle between two curves is the angle between the tangents to the curves at the point of intersection. Let be the equations of two curves C1 and C2 intersecting at P. Then, the slope of tangent at P to the first curve is given by at P. Similarly, the slope of the tangent to the second curve is given by at P. Then, the angle between the curves is given by or If m1=m2, then the curves touch each other at P. If m1m2=1, then the curves cut each other orthogonally at P. Character is who you are when no one is looking. #11 20060806 16:32:28
Re: Differential Calculus FormulasDerivative of a Parametric Function L'Hôpital's Rule For differentiable functions f(x) and g(x), This is useful for determining limits which give indeterminate forms such as 0/0, ∞/∞, 0^{0}, 1^{∞}, 0 × ∞, ∞  ∞, and ∞^{0}. Local Extrema (Maxima and Minima) The point a on a curve f(x) is a local maximum if f'(a) = 0 and f''(a) < 0. The point a on a curve f(x) is a local minimum if f'(a) = 0 and f''(a) > 0. #12 20060807 20:00:43
Re: Differential Calculus FormulasThe Laplace Transform The Laplace transform is a linear operator, and thus The inverse Laplace transform is also a linear operator: Solution of a Linear Differential Equation of Constant Coefficients using a Laplace Transform Consider the linear differential equation Taking the Laplace transform of both sides, and noting that we may write the differential equation as or, collecting coefficients, Now, given that we have the initial conditions at x = 0, we can proceed to solve for L[y], and once we have an equation for L[y], we may simplify it (often by means of partial fractions) and then find the inverse Laplace transform, and thus find y. If initial conditions are given at some x_{0} ≠ 0, let u = x  x_{0} and solve the differential equation in terms of u, then substitute the value of x back in when the solution is finished. List of Selected Laplace Transforms Note: Taking the inverse Laplace transform of these equations will give an expression for the inverse Laplace transform of a function F(s). Feel free to request any other Laplace transforms/inverse Laplace transforms. I have about 150 other transforms for a wide variety of cases, but they seem too obscure for posting. Example problems may be posted on request to aid in clarity. Last edited by Zhylliolom (20060807 20:03:52) #13 20081231 06:10:19
Re: Differential Calculus Formulasi am very obseded by those functions[integral,derivative,trigonometry,etc... even if i have some difficulties in some of them] and calculus even if i have difficulties understanding some of them(i am only 12 years old).I also loved quadratic equations when i was younger. #14 20100521 02:27:26
Re: Differential Calculus Formulasdifferentional equation problems y'=x^x how to solve? and y'=(arctgx)^x how to solve? #15 20100521 07:22:16
Re: Differential Calculus FormulasHi wailinaung; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #16 20100922 01:19:32
Re: Differential Calculus Formulas
:(thank u ganesh 