Calculus: Complete Course

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Woody Lewenstein

20:05:08

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1 - Introduction

1 - Introduction.mp4

01:48

2 - Whats in the Course.mp4

02:19

2 - Introduction to Calculus

3 - What is Calculus.mp4

09:55

4 - Intuitive Limits.mp4

12:44

5 - Terminology.mp4

03:15

6 - The Derivative of a Polynomial at a Point.mp4

15:34

7 - The Derivative of a Polynomial in General.mp4

10:40

8 - The Derivative of xn.mp4

07:40

9 - The Derivative of xn Proof.mp4

05:47

10 - Negative and Fractional Powers.mp4

10:36

3 - Differentiation Key Skills

12 - Finding the Gradient at a Point.mp4

07:47

13 - Tangents.mp4

09:53

14 - Normals.mp4

12:12

15 - Stationary Points.mp4

12:29

16 - Increasing and Decreasing Functions.mp4

10:35

17 - Second Derivatives.mp4

14:34

18 - Optimisation Part 1.mp4

14:48

19 - Optimisation Part 2.mp4

07:24

4 - Integration Key Skills

20 - Reverse Differentiation.mp4

15:03

21 - Families of Functions.mp4

04:22

22 - Finding Functions.mp4

03:56

23 - Integral Notation.mp4

06:09

24 - Integration as Area An Intuitive Approach.mp4

11:49

25 - Integration as Area An Algebraic Proof.mp4

07:50

26 - Areas Under Curves Part 1.mp4

09:11

27 - Areas Under Curves Part 2.mp4

11:32

28 - Areas Under the XAxis.mp4

08:12

29 - Areas Between Functions.mp4

09:47

5 - Applications of Calculus

30 - Motion.mp4

10:08

31 - Probability.mp4

12:06

6 - Calculus with Chains of Polynomials

32 - fxn Spotting a Pattern.mp4

11:22

33 - Differentiating fxn An Algebraic Proof.mp4

10:41

34 - The Chain Rule for fxn.mp4

08:17

35 - Using the Chain Rule for fxn.mp4

14:17

36 - Reverse Chain Rule for fxn.mp4

12:21

37 - Reverse Chain Rule for fxn Definite Integrals.mp4

08:20

7 - Calculus with Exponentials and Logarithms

38 - Introduction to Exponentials.mp4

07:46

39 - Introduction to Logarithms.mp4

15:50

40 - THE Exponential Function.mp4

08:18

41 - Differentiating Exponentials.mp4

07:26

42 - Differentiating Chains of Exponentials Part 1.mp4

06:39

43 - Differentiating Chains of Exponentials Part 2.mp4

06:21

44 - The Natural Log and its Derivative.mp4

11:57

45 - Differentiating Chains of Logarithms.mp4

14:14

46 - Reverse Chain Rule for Exponentials.mp4

10:08

47 - Reverse Chain Rule for Logarithms.mp4

07:19

8 - Calculus with Trigonometric Functions

48 - Radians.mp4

09:22

49 - Small Angle Approximations.mp4

09:42

50 - Differentiating Sinx and Cosx.mp4

11:49

51 - OPTIONAL Proof of the Addition Formulae.mp4

06:14

52 - Differentiating Chains of Sinx and Cosx.mp4

15:09

53 - Reverse Chain Rule for Trig Functions.mp4

10:28

54 - Integrating Powers of Sinx and Cosx.mp4

06:08

9 - Advanced Techniques in Differentiation

55 - The Chain Rule.mp4

20:27

56 - The Product Rule An Intuitive Approach.mp4

08:20

57 - Using the Product Rule.mp4

08:42

58 - Algebraic Proof of the Product Rule.mp4

04:33

59 - The Quotient Rule.mp4

15:32

60 - Derivatives of All Six Trigonometric Functions.mp4

12:57

61 - Implicit Differentiation.mp4

20:27

62 - Stationary and Critical Points.mp4

09:22

10 - Advanced Techniques is Integration

63 - Integrating the Squares of All Trigonometric Functions.mp4

16:36

64 - Integrating Products of Trigonometric Functions.mp4

09:13

65 - Reverse Chain Rule.mp4

09:17

66 - Introduction to Partial Fractions.mp4

15:30

67 - Integrating with Partial Fractions.mp4

12:00

68 - Integration by Parts Part 1.mp4

12:16

69 - Integration by Parts Part 2.mp4

06:01

70 - Integration by Parts Part 3.mp4

07:56

71 - Integration by Substitution Part 1.mp4

08:14

72 - Integration by Substitution Part 2.mp4

05:48

73 - Integration by Substitution Part 3.mp4

06:06

74 - Integration by Substitution Part 4.mp4

11:59

75 - Area of a Circle Proof with Calculus.mp4

06:03

76 - Reduction Formulae Part 1.mp4

15:07

77 - Reduction Formulae Part 2.mp4

09:26

11 - Advanced Applications in Differentiation

78 - Connected Rates of Changes.mp4

08:29

79 - Newtons Method.mp4

13:34

80 - LHopitals Rules Part 1.mp4

14:35

81 - LHopitals Rule Part 2.mp4

12:44

82 - Maclaurin Series Part 1.mp4

13:42

83 - Maclaurin Series Part 2.mp4

15:09

84 - The Leibnitz Formula.mp4

03:35

85 - Taylor Series.mp4

13:17

12 - Advanced Applications in Integration

86 - Volumes of Revolution Around the XAxis Part 1.mp4

11:29

87 - Volumes of Revolution Around the XAxis Part 2.mp4

14:22

88 - Volumes of Revolution Around the YAxis.mp4

04:31

89 - Surface Areas of Revolution Part 1.mp4

10:43

90 - Surface Areas of Revolution Part 2.mp4

08:52

91 - Arc Lengths.mp4

09:00

13 - Alternative Coordinate Systems

92 - Parametric Equations Introduction.mp4

07:01

93 - Converting Parametric Equations into Cartesian Equations.mp4

08:07

94 - Differentiating Parametric Equations.mp4

13:04

95 - Integrating Parametric Equations.mp4

12:45

96 - Volumes of Revolution with Parametric Equations.mp4

09:06

97 - Surface Areas and Arc Lengths of Parametric Equations.mp4

12:07

98 - Polar Coordinates Introduction.mp4

08:20

99 - Converting Between Polar and Cartesian Form.mp4

10:34

100 - Differentiating Polar Curves.mp4

14:39

101 - How to Integrate Polar Curves.mp4

10:14

102 - Integrating Polar Curves.mp4

13:38

14 - First Order Differential Equations

103 - What is a Differential Equation.mp4

04:01

104 - Separating Variables Part 1.mp4

14:55

105 - Separating Variables Part 2.mp4

08:25

106 - Separating Variables Modelling Part 1.mp4

10:27

107 - Separating Variables Modelling Part 2.mp4

10:00

108 - Integrating Factors.mp4

15:29

15 - Second Order Differential Equations

109 - Homogeneous Second Order Differential Equations Part 1.mp4

13:02

110 - Homogeneous Second Order Differential Equations Part 2.mp4

11:11

111 - Homogeneous Second Order Differential Equations Part 3.mp4

07:18

112 - NonHomogeneous Second Order Differential Equations.mp4

17:37

113 - Boundary Conditions.mp4

10:25

114 - Coupled Differential Equations Part 1.mp4

13:28

115 - Coupled Differential Equations Part 2.mp4

14:59

116 - Reducible Differential Equations Part 1.mp4

09:03

117 - Reducible Differential Equations Part 2.mp4

09:06

Description

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

What You'll Learn?

Differentiation
Integration
Differential Equations
Optimization
Chain Rule, Product Rule, Quotient Rule
Limits
Maclaurin and Taylor Series

Who is this for?

Data scientists

People studying calculus

Engineers

Financial analysts

Anyone looking to expand their knowledge of mathematics

What You Need to Know?

A good basic foundation in algebra.

Knowledge of trigonometry useful but not essential

Knowledge of exponentials and logarithms useful but not essential

More details

Description
This is course designed to take you from beginner to expert in calculus. It is designed to be fun, hands on and full of examples and explanations. It is suitable for anyone who wants to learn calculus in a rigorous yet intuitive and enjoyable way.

The concepts covered in the course lie at the heart of other disciples, like machine learning, data science, engineering, physics, financial analysis and more.

Videos packed with worked examples and explanations so you never get lost, and many of the topics covered are implemented in Geogebra, a free graphing software package.

Key concepts taught in the course are:
Differentiation Key Skills: learn what it is, and how to use it to find gradients, maximum and minimum points, and solve optimisation problems.
Integration Key Skills: learn what it is, and how to use it to find areas under and between curves.
Methods in Differentiation: The Chain Rule, Product Rule, Quotient Rule and more.
Methods in Integration: Integration by substitution, by parts, and many more advanced techniques.
Applications of Differentiation: L'Hopital's rule, Newton's method, Maclaurin and Taylor series.
Applications in Integration: Volumes of revolution, surface areas and arc lengths.
Alternative Coordinate Systems: parametric equations and polar curves.
1st Order Differential Equations: learn a range of techniques, including separation of variables and integrating factors.
2nd Order Differential Equations: learn how to solve homogeneous and non-homogeneous differential equations as well as coupled and reducible differential equations.
Much, much more!

The course requires a solid understanding of algebra. In order to progress past the first few chapters, an understanding of trigonometry, exponentials and logarithms is useful, though I give a brief introduction to each.

Please note: This course is not linked to the US syllabus Calc 1, Calc 2 & Calc 3 courses, and not designed to prepare you specifically for these. The course will be helpful for students working towards these, but that's not the aim of this course.
Who this course is for:
Data scientists
People studying calculus
Engineers
Financial analysts
Anyone looking to expand their knowledge of mathematics

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After finishing my studies at Oxford University I worked for a year in India before moving to London, which is where I have been ever since.I have taught mathematics in some of the best performing schools in the country for over 10 years, where I have taught all levels of school maths, including GCSE, A-Level, Further Maths and Oxbridge entrance paper preparation. I also have 1000's of hours of tutoring experience working one-to-one with students on A-level maths and further maths.Alongside this I have worked with businesses to train their staff in mathematical skills, such as statistics, data analysis and mathematical software packages.Away from my work I love music and long-distance cycling, and recently cycled from London to Istanbul.

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