Transcription of Mathematical Methods of Engineering Analysis
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Mathematical Methods of Engineering Analysis
Mathematical Methods of Engineering AnalysisErhan C inlarRobert J. VanderbeiFebruary 2, 2000 ContentsSets and Functions11 Sets ..1 Subsets ..2 Set Operations ..2 Disjoint Sets ..3 Products of Sets ..32 Functions and Sequences ..4 Injections, Surjections, Bijections ..4 Sequences ..53 Countability ..64On the Real Line ..8 Positive and Negative ..9 Increasing, Decreasing ..9 Bounds ..9 Supremum and Infimum ..9 Limits ..10 Convergence of Sequences ..115 Series ..14 Ratio Test, Root Test ..16 Power Series ..17 Absolute Convergence ..18 Rearrangements ..19 Metric Spaces236 Euclidean Spaces ..23 Inner Product and Norm ..23 Euclidean Distance ..247 Metric Spaces ..25 Usage ..26 Distances from Points to Sets and from Sets to Sets ..26 Balls ..268 Open and Closed Sets ..29 Closed Sets ..30 Interior, Closure, and Boundary ..30iOpen Subsets of the Real Line.
2 SETS AND FUNCTIONS Subsets A set A is said to be a subset of a set B if every element of A is an element of B. We write A ⊂ B or B ⊃ A to indicate it and use expressions like A is contained in B,
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