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To actually solve this problem, we work backwards. For simplicity, the current level of capital is denoted as k . V T + 1 ( k ) {\displaystyle V_{T+1}(k)} is already known, so using the Bellman equation once we can calculate V T ( k ) {\displaystyle V_{T}(k)} , and so on until we get to V 0 ( k ) {\displaystyle V_{0}(k)} , which is the value of ...
To solve for the subgame perfect equilibrium, one should continually work backwards from subgame to subgame until the starting point is reached. As this process progresses, the initial extensive form game will become shorter and shorter. The marked path of vectors is the subgame perfect equilibrium. [9]
The natural logarithm of e itself, ln e, is 1, because e 1 = e, while the natural logarithm of 1 is 0, since e 0 = 1. The natural logarithm can be defined for any positive real number a as the area under the curve y = 1/x from 1 to a [4] (with the area being negative when 0 < a < 1). The simplicity of this definition, which is matched in many ...
The multiple valued version of log(z) is a set, but it is easier to write it without braces and using it in formulas follows obvious rules. log(z) is the set of complex numbers v which satisfy e v = z; arg(z) is the set of possible values of the arg function applied to z. When k is any integer:
Solve an equation [14] Also suggested: Look for a pattern [15] Draw a picture [16] Solve a simpler problem [17] Use a model [18] Work backward [19] Use a formula [20] Be creative [21] Applying these rules to devise a plan takes your own skill and judgement. [22] Pólya lays a big emphasis on the teachers' behavior.
The logarithm is denoted "log b x" (pronounced as "the logarithm of x to base b", "the base-b logarithm of x", or most commonly "the log, base b, of x "). An equivalent and more succinct definition is that the function log b is the inverse function to the function x ↦ b x {\displaystyle x\mapsto b^{x}} .
The backward Euler method is an implicit method: the new approximation + appears on both sides of the equation, and thus the method needs to solve an algebraic equation for the unknown +. For non-stiff problems, this can be done with fixed-point iteration:
The backward differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations.They are linear multistep methods that, for a given function and time, approximate the derivative of that function using information from already computed time points, thereby increasing the accuracy of the approximation.