# Math Homework Help Experts

## Professional Mathematics Help

Mathematics is the oldest academic discipline of the world and a foundation of natural sciences, social sciences, engineering and technology including physics, chemistry, medicines, statistics. It is concerned with the study of structure, quantity, space and their changes

The term “mathematics” is originated from the Greek word mathema means study, learning or mathematical study. Initially it was developed to count the quantities and measuring the space and time but later it was developed by Greek mathematicians and its first appearance can be found in Greek mathematicians work including Euclid’s element in 600 BC, China in 300 BC, India in AD 100 and in Muslim countries in AD 800, which was developed and classified by modern mathematicians in various branches of mathematics. Mathematics is classified in two major categories Pure mathematics and Applied mathematics

### Pure Mathematics

Pure mathematics deals with the quantity, structure, space and their changes and works as the base for complex mathematics. Pure mathematics is based on general elements of mathematics and includes numbers (natural number and integers), sets, operations or relations between sets, groups, fields, geometry, calculus, Functions, chaos theory, space. Pure mathematics has its own sub-branches such as continuity, limits, Calculus (differentiation and integration), Real analysis, Algebra, Discrete mathematics, Complex analysis, Functional analysis, Abstract algebra, Geometry (projective and inversive geometry), topology, Number theory.

### Applied Mathematics

Applied mathematics is concerned with the use of abstract mathematical tools to solve the problems of natural and social sciences and engineering. It encircles a vast area of the field and plays an important role to help the researchers to find out the solution of complex mathematical questions. Main streams of applied mathematics are Actuarial science (along with probability, statistics and economic theory), Management science, Numerical analysis, Operations research, scientific computing or computer science (uses logic, algebra, and combinations) and Statistics (including probability and decision theory). Applied mathematics is frequently used in physics, chemistry, biology, medicines, engineering, computer science, medicines, economics and mathematical physics.

## Differential Geometry Homework Help

Differential geometry is a discipline of mathematics which is used to study the geometric problems by suing the techniques of differential and integral calculus including linear and multi-linear algebra. Although geometry is an old branch of mathematics but differential geometry is a new concept in comparison of it and has been developed in eighteenth and nineteenth century which reached to its peak in twentieth century with the help of other disciplines of mathematics. It is similar to differential topology and covers overall topics of 3D geometry including plane, spaces and curves. Major branches of differential geometry are: Riemannian geometry: studies the Riemannian manifolds, and smooth manifolds with Riemannian metric. Pseudo-Riemannian geometry: is used to generalize the Riemannian geometry in the case of metric tensor does not need positive-definite. It’s a special case of Lorentzian manifold is the base of Einstein’s general relativity theory of geometry. Finsler geometry: It is used to study the objects by using Finsler manifold (a differential manifold with a Finsler metric) Symplectic geometry: It is the study of symplectic manifold by using symplectic manifolds. Complex differential geometry: It is also known as Complex and Kahler geometry and studies the complex manifold with the help of complex structure. CR geometry is used to study the intrinsic geometry of boundaries of domains in a complex manifold. Differential topology: is another discipline of differential geometry which studies the global geometric invariants without a symplectic or metric form. Mostly it is used to study in astronomy to measure the space (sky) and to describe the space-time, positions of satellites, astronomical objects such as planets, asteroids, etc. Applications of differential geometry: Differential geometry is extensively used in various branches of engineering, physics, economics, geometric modeling, computer-aided geometric design, probability, statistics, information technology, structural geology, image processing and economics.

## Trigonometry Homework Help

Trigonometry is a discipline of pure and applied mathematics which is used to study triangles and relationships between their sides and angles. Trigonometry describes these relationships and their applicability with the help of trigonometric functions to measure the objects in a space. The word Trigonometry is originated from the Greek Trigonon (triangle) a metron (measure). It is a part of middle and secondary school education and it taught as either a separate course or a pre-calculus curriculum. Earlier trigonometry was developed by Hipparchus, who is known as “the father of trigonometry” as he prepared the first trigonometric table. Later his work was extended by ancient Greeks mathematicians, likewise modern sine function of trigonometry was defined in by an Indian mathematician and astronomer Aryabhatt in his book Surya Siddhanta in 5th century. In medieval time, Trigonometry was enriched by Persian and Islamic mathematicians and it was used to solve the problems in spherical geometry. Now it is an essential in various branches of science and technology including astronomy, navigation, and engineering. Basically trigonometry is based on three angles and three lines of a triangle, which are calculated with the help of known angles or sides by using its six function including Sine, Cosine, Tangent, Cosine, Cosec Sine and their reciprocals cosecant (or cosec), secant (sec) and cotangent (cot) sine respectively. All the functions are calculated with the help of trigonometric tables. Applications of trigonometry: trigonometric is a necessity for various branches of engineering and science and helps to locating positions of celestial objects in the given space. Its applications are widely used in astronomy, geography, satellite navigation, electronics, probability theory, statistics, medical imaging (as CAT scan and ultrasound), biology, chemistry, pharmacy, seismology, meteorology, oceanography, geodesy, civil engineering, architecture, economics, electrical engineering, computer graphics, cartography and crystallography.

## Calculus Homework Help Experts

Calculus is a discipline of applied mathematics and is concerned with limits, functions, derivatives, integrals and infinite series. Calculus has two major branches –  differential calculus and integral calculus. Calculus is the study of change and is used to solve complex equations of mathematics. It is a part of mathematical analysis and is used extensively in science, engineering and economics with the help of its functions and operations. Roots of calculus can be found in ancient Equation Moscow papyrus (1820 BC) without many details. Likewise Greek mathematician Eudoxus invented the method of exhaustion to calculate the areas and volumes and Archimedes developed this idea by inventing heuristics which was the method of integral calculus. Later Calculus was developed by Europeans mathematics and Isaac Newton used it in his laws of motions and gravitation. In modern time various mathematicians discovered new theorems to solve the complex equations of mathematics like analytical functions, higher derivatives, Taylor series and analytical functions.

Gottfried Wilhelm Leibniz, Isaac Newton and Maria Gaetana Agnesi, Cauchy, Riemann, Weierstrass, Lebesgue and Laurent Schwartz are some major mathematician’s name who helped calculus by their work. Now it is taught as either a separate or a part of mathematics papers. Both branches of calculus cover different scopes of mathematical calculation such as differential calculus is used to do computation of velocity, acceleration and slope of a curve while the integral calculus is used to find area, volume, arc length, work, pressure and center of mass. Likewise in more complex and advanced applications we use power series and Fourier series. Calculus is an undivided part of engineering including other disciplines of science such as physical sciences, actuarial science, computer science, statistics, economics, business, medicines, demography and such on. It provides tool for typical difficulties of mathematics related to division by zero or infinite and helps to calculate the exact value of a function or variable.

## Differential Calculus Homework Help Experts

Differential calculus is one of the two traditional sub-disciplines of the calculus which is used to study the rates of changes in the quantities. It studies the derivatives of a function and its relations, in which the chosen input value describes the rate of changes of the function. This process of finding a derivative of a function is known as differentiation and differential calculus is used to calculate the differentiation. As well as integral calculus, differential calculus is based on fundamental theorem of calculus is the reverse process of integral calculus. Differential calculus is an ancient mathematics and its concept can be find in work of Euclid (300 BCE) and Archimedes (287 BCE), likewise it was developed in India by Aryabhatta (476-550) who used infinitesimals to study the accurate motion of the moon. It was also enriched by Persian mathematician Sharaf al-Din-al-Tosi (1135-1213) who discovered the derivatives of cubic polynomials and other mathematicians. In modern time Isaac Newton and Gottfried Leibniz worked in differential calculus and used it in general mathematics to find the solution of complex problems. Fundamental theorems of differential calculus are based on function and its derivatives and it is used to describe the differential equations. It is a must have tool of science and engineering subjects such as physics, chemistry, geology, pharmacy, astronomy, etc. Main topics of differential calculus are Calculus with polynomials, Chain rule, Constant factor rule in differentiation, Derivative, Derivative (examples), Derivative of a constant, Differential (calculus), Differential equation, Differential operator, Extreme value theorem, First derivative test, Implicit differentiation, Inverse functions and differentiation, Leibniz’s notation for differentiation, Leibniz’s rule, L’HÃ´pital’s rule, Linearity of differentiation, Logarithmic derivative, Maxima and minima, Mean value theorem, Newton’s method, Newton’s notation for differentiation, Notations , Product rule, Quotient rule, Regiomontanus’ angle maximization problem, Related rates, Second derivative test, Simplest rules, Stationary point, Sum rule in differentiation, Taylor’s theorem.

## Number Theory Homework Help Experts

“Mathematics is the queen of the sciences and number theory is the queen of mathematics.”  – Gauss Number Theory is a discipline of pure mathematics concerned with the properties of numbers especially integers and their problem. Number theory is a vast filed subdivided into several branches. Elementary number theory is also known as arithmetic or the higher arithmetic. In elementary number theory, we study the integers without use of complex mathematical techniques such as questions of divisibility, using Euclidean algorithm in computation of greatest common divisors, investigation of perfect numbers and congruence, integer factorizations into prime numbers, etc. Number theory has its root in ancient Roman and Indian civilization. It was used by Greeks to finding integer solutions to linear indeterminate equation, while it was extensively studied by Indian scholars and Aryabhatt arranged its theorem in a systematic order in his book named Aryabhatiya. In modern time it was redeveloped by Legendre and Gauss and they also started its uses to solve the question regarding integers. Number theory is divided in sub fields based on the questions and their solution methods. Its main divisions are Elementary number theory, Analytic number theory, Algebraic number theory, Geometry of numbers, Combinatorial number theory, Computational number theory, Arithmetic algebraic geometry, Arithmetic topology, Arithmetic dynamics, Applied number theory, Modular forms (also known as complex analytic functions), Prime number theory, Public-key cryptography, Residue number system. Number theory covers various topics of every field and is a wide subject who has become an essential need of the science and is used broadly almost in every field of the science and technology as well as our daily life subject like economics, engineering, computer programming etc.

## Complex Analysis Homework Help

Complex analysis (also known as the theory of functions of a complex variable) is one of the most useful branches of pure mathematics which is used to investigate the functions of complex numbers. It is a fundamental requirement of advanced mathematics and various disciplines of sciences including applied mathematics, algebra, number theory, physics, electrical and electronics engineering, etc. Complex analysis is concerned with analytic functions of complex variables or meromorphic functions and is used widely to solve two dimensional problems in mathematics and physics. It is a new branch of mathematics than others and has its roots in earlier 19th century. Euler, Gauss, Riemann, Cauchy, Weierstrass and several other prominent scholars have developed complex analysis with their efforts and made it useful and beneficial for other disciplines of mathematics and sciences. Complex analysis is a vast subject and has its own theorems and functions to solve the equation including Holomorphic function, Antiholomorphic function, Cauchy-Riemann equations, Conformal mapping, Power series, Radius of convergence, Laurent series, Meromorphic function, Entire function, Pole (complex analysis), Zero (complex analysis), Residue (complex analysis), singularity (Isolated, removable and essential), Branch point, Principal branch, Weierstrass-Casorati theorem, Landau’s constants, Holomorphic functions are analytic, Schwarzian derivative, Analytic capacity, Disk algebra, Bieberbach conjecture, Borel-CarathÃ©odory theorem, Hadamard three-circle theorem, Hardy theorem, progressive function and Corona theorem, Nevanlinna theory, Picard’s theorem, Paley-Wiener theorem, Value distribution theory of holomorphic functions, Contour integrals, Line integral, Cauchy integral theorem, Cauchy’s integral formula, Residue theorem, Liouville’s theorem (complex analysis), Examples of contour integration, Fundamental theorem of algebra, Simply connected, Winding number, Morera’s theorem, Mellin transform, Kramers – Kronig relation, Analytic continuation, Antiderivative (complex analysis), BÃ´cher’s theorem, CarathÃ©odory’s theorem (conformal mapping), Cayley transform, Complex differential equation, Harmonic conjugate, Hilbert’s inequality, Method of steepest descent, Mittag-Leffler’s theorem, Montel’s theorem, Periodic points of complex quadratic mappings, Pick matrix, Riemann mapping theorem, Riemann sphere, Riemann surface, Riemann-Roch theorem, Runge approximation theorem, Schwarz lemma and Weierstrass factorization theorem.