non-book problem
... 4. Show that if L1 and L2 are linear operators, then L1 + L2 is a linear operator. 5. Show by induction on n that if an operator L is linear, then for all n ≥ 1, all constants c1 , c2 , . . . , cn , and all functions f1 , f2 , . . . fn , L[c1 f1 + c2 f2 + . . . + cn fn ] = c1 L[f1 ] + c2 L[f2 ] + . ...
... 4. Show that if L1 and L2 are linear operators, then L1 + L2 is a linear operator. 5. Show by induction on n that if an operator L is linear, then for all n ≥ 1, all constants c1 , c2 , . . . , cn , and all functions f1 , f2 , . . . fn , L[c1 f1 + c2 f2 + . . . + cn fn ] = c1 L[f1 ] + c2 L[f2 ] + . ...
CHUNG-ANG UNIVERSITY Solutions to Problem Set #1 Answers to
... Once we are done finding the solution, it is highly recommended that you substitute your solution into each equation to verify that you have the right answer. You may also verify your answer using MATLAB as follows, >> rref([1 -3 4 7 ; 0 1 2 2 ; 0 0 1 5]) ans = ...
... Once we are done finding the solution, it is highly recommended that you substitute your solution into each equation to verify that you have the right answer. You may also verify your answer using MATLAB as follows, >> rref([1 -3 4 7 ; 0 1 2 2 ; 0 0 1 5]) ans = ...
Task - Illustrative Mathematics
... d. Every day the amount of water in the pool decreases by the same amount, one liter, so it decreases in a linear fashion. e. Every 124 minutes the amount of the drug gets multiplied by 1/2, so this quantity ...
... d. Every day the amount of water in the pool decreases by the same amount, one liter, so it decreases in a linear fashion. e. Every 124 minutes the amount of the drug gets multiplied by 1/2, so this quantity ...
Mathematical optimization
In mathematics, computer science and operations research, mathematical optimization (alternatively, optimization or mathematical programming) is the selection of a best element (with regard to some criteria) from some set of available alternatives.In the simplest case, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, optimization includes finding ""best available"" values of some objective function given a defined domain (or a set of constraints), including a variety of different types of objective functions and different types of domains.