What is Calculus
Calculus is a branch of mathematics which deals with continuous changes. In this article, we will discuss what advanced calculus is along with the concepts involved in introductory calculus.
Definition of the Calculus
Calculus, a branch of Mathematics developed by Newton and Leibniz, deals with studying the rate of change. Calculus Maths is generally used in Mathematical models in order to obtain optimal solutions. It helps us in understanding the differences between the values which are related by a function. Calculus Math mainly focused on crucial topics such as differentiation, integration, limits, functions, etc.
Calculus Mathematics is broadly classified into two main different such as:
- Differential Calculus
- Integral Calculus
Both the differential as well as integral calculus deals with impact on the function of the slight change in the independent variables as it always leads to zero. Both differential as well as integral calculus serves as a foundation for the higher branch of Mathematics known as “Analysis.” Calculus Mathematics plays a crucial role in modern Physics as well as in Science and technology.
Basic Calculus
Basic Calculus is the study of the differentiation and integration. Both concepts have been based on the idea of limits and functions. Some concepts, like continuity, exponents, are the root of advanced calculus.
Basic calculus explains the two different calculus types called “Differential Calculus” and “Integral Calculus.” Differential Calculus helps find the rate of change of a quantity, whereas integral calculus helps find the quantity when rate of change is known.
Calculus Topics
These topics also come under the CBSE Class 11 applied maths Calculus.
- Limits and Continuity
- Differential Calculus
- Differentiation and Integration
- Limits
- Derivatives
- Integral Calculus
- Continuity and Discontinuity
- Derivative of a function Integration
- Continuity and Differentiability
- Quotient Rule
- Methods of Integration
- Mean value Theorem
- Chain Rule
- Definite Integral
- Second Derivative Test
- Anti- Derivative Formula
- Indefinite Integral
- Application of Integration
- Integration by parts
- Derivative of Inverse Trigonometric Function
- Vector Calculus
- Cauchy Riemann Equations
- Integration Factor
- Partial Differential Equation
- Exact Differential Equation Riemann Integral
- Application of Derivatives
- L Hospital Rule
- Simpson’s Rule
- Trapezoidal Rule
- Line Integral
- Surface Integral
Differential Calculus Basics
Differential Calculus is concerned with the finding the rate of change of a function concerning the other variable. In order to get the optimal solution, derivatives are used to find the maximum and minimum values of any function.
Differential calculus comes from the study of the limit of the quotient. It deals with the variables such as the x and y, functions f(x), and the corresponding changes in variables x and y. The symbol dy and dx are known as differentials.
The process of finding the derivatives is known as differentiation. The derivative of the function is denoted by dy/dx or f’(x). It means that the function is the derivative of the y concerning the variable x. Let us discuss some of the essential topics covered in the basic differential calculus.
CBSE Class 11 applied maths Calculus syllabus
- Introducing functions
- Domain and Range of a function
- Types of functions such as the (Polynomial function; Rational function; Composite function; Logarithm function; Exponential function; Modulus function; Greatest Integer function, Signum function)
- Graphical representation of functions
- Concept of limit and continuity of a function
- Instantaneous rates of change
- Differentiation is a process of finding derivative
- Derivatives of algebraic functions using the Chain rule
- Tangent line and equations of tangents
This is the complete basic description of the Calculus, and the CBSE Class 11 applied maths Calculus syllabus.
You can also check CBSE Class 11 Applied Maths Coordinate Geometry
