1. INTRODUTION. In advance analysis, the notion of 'Compact set' is of paramount importance. In $ \mathbb{R} $, Heine-Borel theorem provides a very simple characterization of compact sets. The definition and techniques used in connection with compactness of sets in $ \mathbb{R} $ are extremely...
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Fourier Series
1. INTRODUCTION The study of a special type of series whose terms are trigonometric functions of a variable was started in the 18th century when J.B.J. Fourier (1768-1830) was successful in his attempt to prove that an arbitrary function given in the interval $[-\pi,\pi]$ can be expressed under...
All The Logarithm Rules You Know and Don’t Know About
The logarithm function is one of the most known and used functions in mathematics and other fields like physics, finance, chemistry, ...etc. this article is logarithmic heaven where you can learn many things about logarithmic functions and where you can find a large list of logarithm rules,...
Riemann Integral
The story of integration started with I. Newton, when in the late 1660 he invented the method of inverse tangents to find areas under curves. In 1680, G. Leibnitz discovered the process of finding tangent line to find area. Thus, they had discovered the integration, being a process of summation,...
Lebesgue Outer Measure
The Riemann integral of a bounded function over a closed, bounded interval is defined using approximations of the function that are associated with partitions of its domain into finite collections of subintervals. The generalization of the Riemann integral to the Lebesgue integral will be achieved...
Permutations & Combinations Made Easy!
Combinatorics This lesson covers the topics of combinatorics (combinations, permutations with and without repetitions, circular and constrained permutations). It will equip you with all the necessary theoretical knowledge on the topic, and show how it is applied in standardized test problems....
Continuity – Calculus
Welcome again to another article!!! This time with a new article in Calculus, and the topic of our journey this time is Continuity; so, after introducing the concept of limits of a function, their properties, and the different operations on limits alongside presenting the indeterminate forms that...
Probability theory – Conditional Probability
Hello again!!! It is time to continue our journey in the field of probability theory; So, after introducing probability theory, the different types of probability and its axioms, and after presenting the basic terminology and how to evaluate the probability of an event in the simplest cases in the...