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Solving mathematics is not like walking in the park; even the scholars face hurdles. However, you can't skip the same as mathematics is an integral part of science, engineering and physics. Mathematics can be categorized into two parts such as fundamental mathematics & advanced mathematics. Let’s enlighten you with the advanced topics in mathematics.

### Polynomial Function

A polynomial function is a function such as quadratic, quartic or even cubic featuring only non-negative integer power of x. A polynomial of degree n is a function of f(x) = anXn + an-1Xn-1 +…. a2x2 + a1x+a0

Where a’s are the real numbers and also known as coefficients of polynomials.

The turning point of polynomial functions is an essential feature: a point of a function where the graph of the functions differs from sloping downward to upwards. So the gradients also alter from negative to positive or even from positive to negative. The quadratic function has one turning point, whereas a cubic can have two turning points.

### Derivatives & Antiderivatives

Derivatives in mathematics are the rate change of a function w.r.t a variable. These are the fundamentals to solve complex problems related to differential equations and calculus. Derivative of a function can be understood as the slope of the graph of a function or even the slope of a tangent line at a specific point.

Antiderivatives are the opposite of derivatives, which is a function that follows a reverse derivative function. A function can have many derivatives, but altogether they form an arbitrary constant. Antiderivatives are the key part of indefinite integrals.

### Calculus & Analysis

Calculus is one of the most crucial scientific achievements that revolutionized physical problems into regular calculations. The primary aspect of calculus is exploring the instant rate of change of a variable quantity. It deals with calculating areas, and volumes by considering different tools.

The analysis is another crucial branch of mathematics that supports the theory of calculus to offer a logical foundation. The analysis also introduces the key aspects of differentiation and integration.

### Differential Equations

A differential equation is an equation that features one or more functions w.r.t to its derivatives, where the derivative of the function defines the rate of change of a specific function at a specific point. The differential equation is instrumental in the fields of physics, biology and engineering. It is defined as dy/dx = f(x)

Here x and y are dependent and independent variables respectively.

There are two integral approaches to finding the right answer for the differential equations, such as separation of variables and integration factors

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