Differential Calculus From Scratch

Differentiation, Limits, Application of derivatives

What you'll learn

Understand basic concepts of limits and evaluate trigonometric limits, limits at infinity. check the existence of limit of a function.

Verify the continuity of a function at a point and in an interval.

Perform differentiation from first principles

Evaluate the derivative of functions, product of functions, quotient of two functions and function of a function.

Perform differentiation of implicit functions, logarithmic functions and infinite series.

Perform differentiation of parametric functions and derivative of one function w.r.t. another function

Evaluate derivatives of higher order.

Solve the problems based on application of derivatives

Understand and verify Rolle’s and Lagrange’s mean value theorems

Find the equations of tangents and normals to a curve at a point using differentiation.

Verify whether a function is increasing or decreasing

Find the points of local maxima and minima using first derivative test, second derivative test and applications of the concept of maxima and minima

Requirements

Basic algebra and Trigonometry of grade 10

Description

This course has been designed for class 11 and 12 students. All the concepts of differentiation are explained along with solved examples. Lots of problems are solved to make the students confident to solve the problems. Questions of all levels of difficulties are solved. Efforts have been made to make the complex concepts simple and easy for students. Concepts of differentiation not only form a major portion of mathematics but also have applications in physics The following topics are covered in this course:1. Limits: Basic concepts, trigonometric limits, limits at infinity, existence of limit of a function.2. Continuity: Continuity at a point, Continuous functions3. Differentiability: Right hand derivative and left hand derivative, differentiability of a function.4. Differentiation: Differentiation from first principles, derivative of functions, derivative of the product of functions. Derivative of quotient of two functions, derivative of a function of a function. Differentiation of implicit functions, differentiation of logarithmic functions, differentiation of infinite series. Differentiation of parametric functions, derivative of one function w.r.t. another function, derivatives of higher order.5. Application of derivatives6. Rolle’s and Lagrange’s theorems7. Tangents and normals.8. Monotonic functions: Increasing and decreasing functions9. Local maxima and local minima: first derivative test, second derivative test, applications of the concept of local maxima and minimaCourse Title: Differential calculus from scratch(For grade 11 and 12)Prerequisite: Basic Algebra and trigonometry of grade 10Duration of course : 23hr 15 min

Overview

Section 1: Introduction

Lecture 1 Introduction

Section 2: Limits

Lecture 2 Introduction-1

Lecture 3 Evaluation of limits of a function

Lecture 4 Evaluation of limit of rational function

Lecture 5 Solved Examples-1

Lecture 6 Solved Examples-2

Lecture 7 Basic theorems of limits

Lecture 8 Important Expansions

Lecture 9 Solved examples-3

Lecture 10 Solved examples-4

Lecture 11 Theorem and its proof

Lecture 12 Questions based on theorem

Lecture 13 Limit of Trigonometric functions

Lecture 14 Solved examples-5

Lecture 15 Solved examples-6

Lecture 16 Solved examples-7

Lecture 17 Solved examples-8

Lecture 18 Solved examples-9

Lecture 19 Solved examples-10

Lecture 20 Some important trigonometric formulas

Lecture 21 Solved examples-11

Lecture 22 Solved examples-12

Lecture 23 Solved examples-13

Lecture 24 Limits at infinity

Lecture 25 Solved examples-14

Lecture 26 Some important formulas

Lecture 27 Solved examples-15

Lecture 28 Existence of limit

Lecture 29 Solved examples-16

Lecture 30 Solved examples-17

Section 3: CONTINUITY

Lecture 31 Introduction

Lecture 32 Solved examples-18

Lecture 33 Solved examples-19

Lecture 34 Solved examples:20

Lecture 35 Continuity of a function in an open interval

Lecture 36 Solved examples-21

Section 4: Differentaibility

Lecture 37 Introduction

Lecture 38 Checking the differentiability of the function

Lecture 39 Solved examples-22

Lecture 40 Solved examples-23

Lecture 41 Solved examples-24

Lecture 42 Solved examples-25

Lecture 43 Solved examples-26

Section 5: Differentiation

Lecture 44 Differentiation from first principles

Lecture 45 Solved examples-27

Lecture 46 Solved examples-28

Lecture 47 Solved examples-29

Lecture 48 Solved examples-30

Lecture 49 Derivatives of common functions

Lecture 50 Derivatives of sinx and cosx from first principles

Lecture 51 Derivate of tanx from first principles of derivatives

Lecture 52 Derivative of cotx from first of principles of derivatives

Lecture 53 Derivative of secx and cosecx from first principles of derivatives

Lecture 54 Differentiation of functions

Lecture 55 Solved examples-31

Lecture 56 Derivative of product of functions

Lecture 57 Solved examples-32

Lecture 58 Solved examples-33

Lecture 59 Solved examples-34

Lecture 60 Solved examples-35

Lecture 61 Quotient rule

Lecture 62 Solved example-36

Lecture 63 Solved examples-37

Lecture 64 Solved examples-38

Lecture 65 Derivative of a function of a function

Lecture 66 Solved examples-39

Lecture 67 Solved examples-40

Lecture 68 Solved examples-41

Lecture 69 Solved examples-42

Lecture 70 Solved examples-43

Lecture 71 Solved examples-44

Lecture 72 Solved examples-45

Lecture 73 Solved examples-46

Lecture 74 Derivatives of inverse trigonometric functions

Lecture 75 Solved examples-47

Lecture 76 Solved examples-48

Lecture 77 Solved examples-49

Lecture 78 Solved examples-50

Lecture 79 Important trigonometric formulas

Lecture 80 Solved examples-51

Lecture 81 Solved examples-52

Lecture 82 Solved examples-53

Lecture 83 Solved examples-54

Lecture 84 Solved examples-55

Lecture 85 Solved examples-56

Lecture 86 Solved examples-57

Lecture 87 Solved examples-58

Lecture 88 Differentiation of implicit functions

Lecture 89 Solved examples-59

Lecture 90 Solved examples-60

Lecture 91 Solved examples-61

Lecture 92 Solved examples-62

Lecture 93 Differentiation of Logarithmic Functions

Lecture 94 Solved example-63

Lecture 95 Solved example-64

Lecture 96 Solved example-65

Lecture 97 Solved example-66

Lecture 98 Differentiation of infinite series

Lecture 99 Differentiation of Parametric Functions

Lecture 100 Solved examples-67

Lecture 101 Solved examples-68

Lecture 102 Solved examples-69

Lecture 103 Solved examples-70

Lecture 104 Derivative of one function w.r.t. another function

Section 6: Derivatives of higher order

Lecture 105 Introduction

Lecture 106 Solved examples -72

Lecture 107 Solved examples-73

Lecture 108 Solved examples-74

Section 7: Applications of derivatives

Lecture 109 Solved examples-75

Lecture 110 Solved examples-76

Lecture 111 Solved examples-77

Lecture 112 Solved examples-78

Lecture 113 Solved examples-79

Lecture 114 Solved examples-80

Lecture 115 Solved examples-81

Lecture 116 Solved examples-82

Lecture 117 Solved examples-83

Lecture 118 Solved examples-84

Lecture 119 Solved examples-85

Lecture 120 Solved examples-86

Section 8: Rolle's Theorem

Lecture 121 Rolle's theorem

Lecture 122 Solved examples- 87

Lecture 123 Solved examples - 88

Lecture 124 Solved examples-89

Lecture 125 Solved examples-90

Section 9: Lagrange's Mean Value Theorem

Lecture 126 Lagrange's Mean Value Theorem

Lecture 127 Solved examples-91

Lecture 128 Solved examples-92

Lecture 129 Solved examples-93

Lecture 130 Solved examples-94

Lecture 131 Solved examples-95

Section 10: Tangents and Normals

Lecture 132 Tangents and Normals

Lecture 133 Solved examples-96

Lecture 134 Solved examples-97

Lecture 135 Solved examples-98

Lecture 136 Solved examples-99

Lecture 137 Solved examples-100

Lecture 138 Solved examples-101

Lecture 139 Solved examples-102

Section 11: Increasing and decreasing functions

Lecture 140 Increasing and decreasing functions

Lecture 141 Checking whether the function is increasing or decreasing in an interval

Lecture 142 Solved examples-103

Lecture 143 Solved examples-104

Lecture 144 Solved examples-105

Section 12: Local maxima and local minima

Lecture 145 Local maxima and minima and first derivative test

Lecture 146 Solved examples-105

Lecture 147 Solved examples-106

Lecture 148 Find points of local maxima and minima with first derivative test

Lecture 149 Solved examples-107

Lecture 150 Solved examples-108

Lecture 151 Solved examples-109

Lecture 152 Solved examples-110

Lecture 153 Solved examples-111

Lecture 154 Solved examples-112

Lecture 155 Solved examples-113

Lecture 156 Solved examples-114

Grade 11 and Grade 12 students