Calculus: Complete Course

سرفصل های دوره

From Beginner to Expert - Calculus Made Easy, Fun and Beautiful

1 - Introduction

1 - Introduction

2 - Whats in the Course

2 - Introduction to Calculus

3 - What is Calculus

4 - Intuitive Limits

5 - Terminology

6 - The Derivative of a Polynomial at a Point

7 - The Derivative of a Polynomial in General

8 - The Derivative of xn

9 - The Derivative of xn Proof

10 - Negative and Fractional Powers

3 - Differentiation Key Skills

12 - Finding the Gradient at a Point

13 - Tangents

14 - Normals

15 - Stationary Points

16 - Increasing and Decreasing Functions

17 - Second Derivatives

18 - Optimisation Part 1

19 - Optimisation Part 2

4 - Integration Key Skills

20 - Reverse Differentiation

21 - Families of Functions

22 - Finding Functions

23 - Integral Notation

24 - Integration as Area An Intuitive Approach

25 - Integration as Area An Algebraic Proof

26 - Areas Under Curves Part 1

27 - Areas Under Curves Part 2

28 - Areas Under the XAxis

29 - Areas Between Functions

5 - Applications of Calculus

30 - Motion

31 - Probability

6 - Calculus with Chains of Polynomials

32 - fxn Spotting a Pattern

33 - Differentiating fxn An Algebraic Proof

34 - The Chain Rule for fxn

35 - Using the Chain Rule for fxn

36 - Reverse Chain Rule for fxn

37 - Reverse Chain Rule for fxn Definite Integrals

7 - Calculus with Exponentials and Logarithms

38 - Introduction to Exponentials

39 - Introduction to Logarithms

40 - THE Exponential Function

41 - Differentiating Exponentials

42 - Differentiating Chains of Exponentials Part 1

43 - Differentiating Chains of Exponentials Part 2

44 - The Natural Log and its Derivative

45 - Differentiating Chains of Logarithms

46 - Reverse Chain Rule for Exponentials

47 - Reverse Chain Rule for Logarithms

8 - Calculus with Trigonometric Functions

48 - Radians

49 - Small Angle Approximations

50 - Differentiating Sinx and Cosx

51 - OPTIONAL Proof of the Addition Formulae

52 - Differentiating Chains of Sinx and Cosx

53 - Reverse Chain Rule for Trig Functions

54 - Integrating Powers of Sinx and Cosx

9 - Advanced Techniques in Differentiation

55 - The Chain Rule

56 - The Product Rule An Intuitive Approach

57 - Using the Product Rule

58 - Algebraic Proof of the Product Rule

59 - The Quotient Rule

60 - Derivatives of All Six Trigonometric Functions

61 - Implicit Differentiation

62 - Stationary and Critical Points

10 - Advanced Techniques is Integration

63 - Integrating the Squares of All Trigonometric Functions

64 - Integrating Products of Trigonometric Functions

65 - Reverse Chain Rule

66 - Introduction to Partial Fractions

67 - Integrating with Partial Fractions

68 - Integration by Parts Part 1

69 - Integration by Parts Part 2

70 - Integration by Parts Part 3

71 - Integration by Substitution Part 1

72 - Integration by Substitution Part 2

73 - Integration by Substitution Part 3

74 - Integration by Substitution Part 4

75 - Area of a Circle Proof with Calculus

76 - Reduction Formulae Part 1

77 - Reduction Formulae Part 2

11 - Advanced Applications in Differentiation

78 - Connected Rates of Changes

79 - Newtons Method

80 - LHopitals Rules Part 1

81 - LHopitals Rule Part 2

82 - Maclaurin Series Part 1

83 - Maclaurin Series Part 2

84 - The Leibnitz Formula

85 - Taylor Series

12 - Advanced Applications in Integration

86 - Volumes of Revolution Around the XAxis Part 1

87 - Volumes of Revolution Around the XAxis Part 2

88 - Volumes of Revolution Around the YAxis

89 - Surface Areas of Revolution Part 1

90 - Surface Areas of Revolution Part 2

91 - Arc Lengths

13 - Alternative Coordinate Systems

92 - Parametric Equations Introduction

93 - Converting Parametric Equations into Cartesian Equations

94 - Differentiating Parametric Equations

95 - Integrating Parametric Equations

96 - Volumes of Revolution with Parametric Equations

97 - Surface Areas and Arc Lengths of Parametric Equations

98 - Polar Coordinates Introduction

99 - Converting Between Polar and Cartesian Form

100 - Differentiating Polar Curves

101 - How to Integrate Polar Curves

102 - Integrating Polar Curves

14 - First Order Differential Equations

103 - What is a Differential Equation

104 - Separating Variables Part 1

105 - Separating Variables Part 2

106 - Separating Variables Modelling Part 1

107 - Separating Variables Modelling Part 2

108 - Integrating Factors

15 - Second Order Differential Equations

109 - Homogeneous Second Order Differential Equations Part 1

110 - Homogeneous Second Order Differential Equations Part 2

111 - Homogeneous Second Order Differential Equations Part 3

112 - NonHomogeneous Second Order Differential Equations

113 - Boundary Conditions

114 - Coupled Differential Equations Part 1

115 - Coupled Differential Equations Part 2

116 - Reducible Differential Equations Part 1

117 - Reducible Differential Equations Part 2

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