By Russell L. Herman
Advent and ReviewWhat Do i have to understand From Calculus?What i want From My Intro Physics Class?Technology and TablesAppendix: Dimensional AnalysisProblemsFree Fall and Harmonic OscillatorsFree FallFirst Order Differential EquationsThe uncomplicated Harmonic OscillatorSecond Order Linear Differential EquationsLRC CircuitsDamped OscillationsForced SystemsCauchy-Euler EquationsNumerical recommendations of ODEsNumerical ApplicationsLinear SystemsProblemsLinear AlgebraFinite Dimensional Vector SpacesLinear TransformationsEigenvalue ProblemsMatrix formula of Planar SystemsApplicationsAppendix: Diagonali. Read more...
summary: creation and ReviewWhat Do i must comprehend From Calculus?What i want From My Intro Physics Class?Technology and TablesAppendix: Dimensional AnalysisProblemsFree Fall and Harmonic OscillatorsFree FallFirst Order Differential EquationsThe basic Harmonic OscillatorSecond Order Linear Differential EquationsLRC CircuitsDamped OscillationsForced SystemsCauchy-Euler EquationsNumerical recommendations of ODEsNumerical ApplicationsLinear SystemsProblemsLinear AlgebraFinite Dimensional Vector SpacesLinear TransformationsEigenvalue ProblemsMatrix formula of Planar SystemsApplicationsAppendix: Diagonali
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Extra info for A Course in Mathematical Methods for Physicists
2 (1 + x ) p = 1 + px + 2 −1/2 The factor γ = 1 − vc2 is important in special relativity. Namely, this is the factor relating differences in time and length measurements by observers moving relative inertial frames. For terrestrial speeds, this gives an appropriate approximation. 38. 113) c. 1− v2 c For v c, the first approximation is found by inserting v/c = 0. Thus, one obtains γ = 1. This is the Newtonian approximation and does not provide enough of an approximation for terrestrial speeds. Thus, we need to expand γ in powers of v/c.
85) We can express this result in the usual form using the logarithmic form of the inverse hyperbolic cosine, cosh−1 x = ln( x + x 2 − 1). The result is sec θ dθ = ln(sec θ + tan θ ). Evaluation of sec3 θ dθ. This example was fairly simple using the transformation sec θ = cosh u. Another common integral that arises often is integrations of sec3 θ. In a typical calculus class, this integral is evaluated using integration by parts. ) In the next example, we will show how hyperbolic function substitution is simpler.
Therefore, this infinite series converges and the sum is 1 S= = 2. 26. ∑∞ k =2 3k In this example we first note that the first term occurs for k = 2. It sometimes helps to write out the terms of the series, ∞ 4 4 4 4 4 = 2 + 3 + 4 + 5 +.... k 3 3 3 3 k =2 3 ∑ introduction and review 25 Looking at the series, we see that a = 49 and r = 13 . Since |r|<1, the geometric series converges. So, the sum of the series is given by S= 4 9 1 3 1− 2 = . 27. ∑∞ n =1 ( 2n − 5n ) Finally, in this case we do not have a geometric series, but we do have the difference of two geometric series.
A Course in Mathematical Methods for Physicists by Russell L. Herman