Page 1 Basic Concept of Differential and Integral Calculus CPT Section D Quantitative Aptitude Chapter 9 Dr. Atul Kumar Srivastava Page 2 Basic Concept of Differential and Integral Calculus CPT Section D Quantitative Aptitude Chapter 9 Dr. Atul Kumar Srivastava Learning Objectives Understand the use of this Branch of mathematics in various branches of science and Humanities Understand the basics of differentiation and integration Know how to compute derivative of a function by the first principal, derivative of a function by the use of various formulae and higher order differentiation Make familiar with various techniques of integration Understand the concept of definite integrals of functions and its properties. 2 Page 3 Basic Concept of Differential and Integral Calculus CPT Section D Quantitative Aptitude Chapter 9 Dr. Atul Kumar Srivastava Learning Objectives Understand the use of this Branch of mathematics in various branches of science and Humanities Understand the basics of differentiation and integration Know how to compute derivative of a function by the first principal, derivative of a function by the use of various formulae and higher order differentiation Make familiar with various techniques of integration Understand the concept of definite integrals of functions and its properties. 2 Differential calculusOutlines What is Differential Calculus – An Introduction Derivative or Deferential Coefficient (First Principal Definition) Basic Formulas Laws for Differentiation (Algebra of Derivative of Functions) Derivative of A Function of Function (Chain Rule) .Derivative of Implicit Function .Derivative of Function In Parametric Form 3 Page 4 Basic Concept of Differential and Integral Calculus CPT Section D Quantitative Aptitude Chapter 9 Dr. Atul Kumar Srivastava Learning Objectives Understand the use of this Branch of mathematics in various branches of science and Humanities Understand the basics of differentiation and integration Know how to compute derivative of a function by the first principal, derivative of a function by the use of various formulae and higher order differentiation Make familiar with various techniques of integration Understand the concept of definite integrals of functions and its properties. 2 Differential calculusOutlines What is Differential Calculus – An Introduction Derivative or Deferential Coefficient (First Principal Definition) Basic Formulas Laws for Differentiation (Algebra of Derivative of Functions) Derivative of A Function of Function (Chain Rule) .Derivative of Implicit Function .Derivative of Function In Parametric Form 3 What is differential calculus – an introduction One of the most fundamental operations in calculus is that of differentiation. In the study of mathematics, there are many problems containing two quantities such that the value of one quantity depends upon the other. A variation in the value of any ones produces a variation in the value of the other. For example the area of a square depends upon it's side. The area of circle and volume of sphere depend upon their radius etc. Differential calculus is the Branch of Mathematics which studies changes To express the rate of change of any function we introduce concept of derivative. The concept involves a very small change in the dependent variable with reference to a very small change in the independent variable 4 Page 5 Basic Concept of Differential and Integral Calculus CPT Section D Quantitative Aptitude Chapter 9 Dr. Atul Kumar Srivastava Learning Objectives Understand the use of this Branch of mathematics in various branches of science and Humanities Understand the basics of differentiation and integration Know how to compute derivative of a function by the first principal, derivative of a function by the use of various formulae and higher order differentiation Make familiar with various techniques of integration Understand the concept of definite integrals of functions and its properties. 2 Differential calculusOutlines What is Differential Calculus – An Introduction Derivative or Deferential Coefficient (First Principal Definition) Basic Formulas Laws for Differentiation (Algebra of Derivative of Functions) Derivative of A Function of Function (Chain Rule) .Derivative of Implicit Function .Derivative of Function In Parametric Form 3 What is differential calculus – an introduction One of the most fundamental operations in calculus is that of differentiation. In the study of mathematics, there are many problems containing two quantities such that the value of one quantity depends upon the other. A variation in the value of any ones produces a variation in the value of the other. For example the area of a square depends upon it's side. The area of circle and volume of sphere depend upon their radius etc. Differential calculus is the Branch of Mathematics which studies changes To express the rate of change of any function we introduce concept of derivative. The concept involves a very small change in the dependent variable with reference to a very small change in the independent variable 4 Continued y=f(x) • x  Independent variable • y  Dependent Variable Thus differentiation is a process of finding the derivative of a continuous function. It is defined as the limiting value of the ratio of the change in the function corresponding to small change in the independent variable as the later tends to zero. 5Read More
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