Calculus in a Real and Complex World |
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Page 338
... initial value problems — with the initial conditions : g ( 0 ) = 0.25 , g ( 0 ) = 0.5 , and g ( 0 ) = 1.50 . Notice that the tangents to these curves match the slope field . By looking at slope fields like Figure III.23 one can tell a ...
... initial value problems — with the initial conditions : g ( 0 ) = 0.25 , g ( 0 ) = 0.5 , and g ( 0 ) = 1.50 . Notice that the tangents to these curves match the slope field . By looking at slope fields like Figure III.23 one can tell a ...
Page 765
Frank Wattenberg. and the values of the constants C1 , C2 , C3 , and c4 are determined by the initial conditions . The longterm behavior of a solution depends on the sign of λ = −b / 2 = ( a11 + α22 ) / 2 . 1. If < 0 then lim x ( t ) ...
Frank Wattenberg. and the values of the constants C1 , C2 , C3 , and c4 are determined by the initial conditions . The longterm behavior of a solution depends on the sign of λ = −b / 2 = ( a11 + α22 ) / 2 . 1. If < 0 then lim x ( t ) ...
Page 776
... initial conditions into second order initial conditions by x ' ( 0 ) y ' ( 0 ) = a11x ( 0 ) + α12y ( 0 ) = a21x ( 0 ) + α22y ( 0 ) . This gives us two separate initial value problems — one for x ( t ) and the other for y ( t ) —that can ...
... initial conditions into second order initial conditions by x ' ( 0 ) y ' ( 0 ) = a11x ( 0 ) + α12y ( 0 ) = a21x ( 0 ) + α22y ( 0 ) . This gives us two separate initial value problems — one for x ( t ) and the other for y ( t ) —that can ...
Contents
Approximation Limits and Derivatives | 1 |
6 The Natural Logarithm | 6 |
Newtons Method | 10 |
Copyright | |
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angle answer antiderivative approximation attracting Bisection Method Byties calculations cheese chord complex numbers compute conjecture Consider constant converges critical points curve definite integral denote described differential equation direction field dynamical system Pn+1 energy equilibrium point equilibrium point 0,0 estimate Euler's Method exact example Exercises Exercise f(Pn feet Find the derivative formula function f(x global minimum Hence initial conditions initial value problem interval L'Hôpital's Rule light ray lim h→0 lim Pn limit linear dynamical system logistic models longterm behavior look Mathematica negative Newton's Method notation Notice object P₁ particular population multiplier positive power series Proof radius real number rectangle region Riemann sum sequence shown in Figure shows Sketch a graph slope field solution solve species Suppose tangent Taylor Series Theorem trajectory variable velocity x-axis y-axis zero