Angewandte Mathematik: Body and Soul
Analysis in mehreren Dimensionen
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We introduce a computational method for designing minimum-drag galvanic anodes for tunnel thrusters, assuming a given maximum anode mold diameter and a given anode weight. The method is illustrated for a tunne...
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In this section we collect the basic models of engineering and science expressed as differential equations. For specification of boundary and initial values we refer to the text.
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In some cases, we can compute a primitive function (or antiderivative or integral) of a given function analytically, that is we can give give a formula for the primitive function in terms of known functions. F...
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We met the equation x 2 = 2 in the context of the Muddy Yard model, trying to determine the length of the diagonal of a square with side length 1.
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We start by giving two basic examples of the use of mathematics for describing practical situations. The first example is a problem in household economy and the second is a problem in surveying, both of which ...
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In this chapter, we shall study the following initial value problem for a second order differential equation: Find a function u(x) defined for x ≥ 0 satisfying
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We now generalize the Bisection algorithm used above to compute the positive root of the equation x2 − 2 = 0, to compute roots of the equation
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It would make no sense to overload the student with all kinds of little things that might be of occasional use. Instead, it is important that students become familiar with ways to think mathematically, recogni...
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In this chapter, we recall how natural numbers and integers may be constructively defined, and how to prove the basic rules of computation we learn in school. The purpose is to give a quick example of developi...
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We’re making the right decisions to bring the solution to an end. (George W. Bush)
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Yesterday was my 21st birthday, at that age Newton and Pascal had already acquired many claims to immortality. (Fourier 1789, age 21)
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It is not generally possible to find an explicit formula for a primitive function of a given arbitrary function in terms of known elementary functions, by which we mean the polynomials, rational functions, root f...
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We showed above that we can solve the equation x 2=a for any positive rational number a using the Bisection algorithm.