Titlebook: Mathematics for Physicists and Engineers; Fundamentals and Int Klaus Weltner,Sebastian John,Jean Grosjean Textbook 20142nd edition Springer

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Exponential, Logarithmic and Hyperbolic Functions,Consider the multiplication of a number by itself, for example .×.×.. A simple way of expressing this is to write ... If we multiplied a by itself . times we would write ... We would say a to the power .;. is known as an . or ..

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Integral Calculus,In Chap. 5 we started from a graph of a function which could be differentiated and obtained its slope or gradient.

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Taylor Series and Power Series,In Chap. 5 we showed that the sum of a geometric series is given by . This formula holds true for .. We will now consider this result from a different point of view. The left-hand side of the equation is an infinite series in powers of ., while the right-hand side is a simple function of .. Figure 8.1 shows the graph of this function.

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Complex Numbers,The square of positive as well as negative real numbers is always a positive real number. For example, 32 = (−3). = 9. The root of a positive number is therefore a positive or negative number.We nowintroduce a newtype of numberwhose square always gives a negative real number: they are called ..

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Transformation of Coordinates; Matrices,One important aspect in the solution of physical and engineering problems is the choice of coordinate systems. The right choice may considerably reduce the degree of difficulty and the length of the necessary computations.

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