+1 (315) 557-6473 

We offer the best Modern analysis assignment help service at an affordable price.

Are you wondering where you can get the best modern analysis assignment help? Well, worry no more because we offer high-quality and timely solutions that will guarantee you the best grades. We have the right team of experts who work day and night to ensure that all assignments are delivered on time. By opting to get modern analysis homework help from us, you can be sure that you will get original work. Therefore, if you have been struggling with your assignments, hire us today and enjoy the best services.

The exhaustive list of topics in Modern Analysis in which we provide Help with Homework Assignment and Help with Project is as follows:

  • Sets: Sets of numbers, set operations, family of subsets, constructing
  • new sets from old ones, De Morgan’s laws.
  • Maps: Surjection, injection, invertible maps, direct and inverse images
  • and their relations, inverse of a map, composition of maps, restriction
  • of a map.
  • Finite and infinite sets, countable and uncountable sets, Results related
  • to countable sets.
  • Countability of rational numbers.
  • Absolute value of a real number, epsilon neibourhood of a point,
  • supremum and infimum and properties. Completeness property of the
  • real numbers. Archimedean property, Density of rational numbers.
  • Nested intervals property, uncountability of reals..
  • Sequences, convergence, examples.
  • Conditions of convergence, monotone sequence, examples.
  • Tests of convergence of sequences of real numbers.
  • Subsequences, Bolzano-Weierstrass theorem, Cauchy’s criterion.
  • Infinite series, tests of convergence.
  • Definition and examples of metric spaces.
  • Open ball, neighborhood of a point, open set, closed set, and their
  • properties.
  • Interior, exterior and their properties.
  • Closure of a set and their properties.
  • Limit point of a subset and limit of a sequence in a metric space,
  • Boundary of a set and properties.
  • Equivalence of metric spaces. Product spaces.
  • Continuity of a map between two metric spaces and examples.
  • Various characterizations continuous maps.
  • Cauchy sequence, Complete metric spaces. Example of complete and
  • incomplete metric spaces.
  • Completeness of the space of real numbers.
  • Compactness, examples. Continuous image of a compact space.
  • Heine-Borel theorem.
  • Separation. Connectedness, connected subsets of the real metric space.
  • Properties of connected spaces. Examples. characterization of
  • connectedness. Intermediate value theorem.
  • Differentiable functions, higher derivatives, Leibnitz Rule.
  • Rolle’s theorem, Mean value theorems.
  • L’ Hospital rule. Examples.
  • Taylor’s formula and Taylor series.
  • Monotone functions, maxima and minima.
  • Riemann Integral, example of functions which are not Riemann
  • integrable.
  • Criterion of Riemann integrability, Properties of Riemann integral.
  • Fundamental theorems of integral calculus.
  • Integration by parts.
  • Trapezoidal rule and Simpsion’s rules of approximation of a Riemann
  • integrals.
  • Improper integrals.
  • Sequence and Series of functions, uniform convergence of functions.
  • Weierstrass M-test.
  • Power Series, radius of convergence.
  • Properties of functions represented by real power series.
  • Fourier Series.
  • More on Fourier Series.