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... a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific ...
... a. 1. How is solving an equation, related to the current topic, similar to solving equations in topics covered in previous units? 2. Compare (find a similarity and/or difference) the current mathematical concept to previously learned topics. Give specific mathematical examples? 3. Choose a specific ...
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... j s (-1)n if £ is odd but (-7) if /r is even. In particular, if k = 2, the sequence of Fibonacci numbers with even subscripts, { 0, 1, 3, 8, 21, •••} , gives a solution to un+iun„i - u2 = -1. Another solution \$un= n, since (n + Din - 1) - n2 = -1 for all n. Is there a sequence {un} of positive term ...
... j s (-1)n if £ is odd but (-7) if /r is even. In particular, if k = 2, the sequence of Fibonacci numbers with even subscripts, { 0, 1, 3, 8, 21, •••} , gives a solution to un+iun„i - u2 = -1. Another solution \$un= n, since (n + Din - 1) - n2 = -1 for all n. Is there a sequence {un} of positive term ...
Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.