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Sequences and Series - Michigan State University

2 2. Sequences and Series A topological way to say lima n = ais the following: Given any -neighborhood V (a) of a, there exists a place in the sequence after which all of the terms are in V (a): Easy Fact: lim(c) = cfor all constant sequences (c): Quanti ers. The de nition of lima n = aquanti es the closeness of a n to aby an arbi-

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Introduction Differential equations describe exchanges of matter, energy, information or any other quantities, often as they vary in time and/or space. Their thorough ana-lytical treatment forms the basis of fundamental the-ories in mathematics and physics, and they are in-

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Introduction to differential calculus - University of Sydney

1 Introduction In day to day life we are often interested in the extent to which a change in one quantity affects a change in another related quantity. This is called a rate of change. For example, if you own a motor car you might be interested in how much a change in the amount of fuel used affects how far you have travelled.

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