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Tensor Calculus

Track :

Science

Lessons no : 23

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What will you learn in this course?
  • Master tensor operations including contraction, raising, lowering, and index manipulation for complex mathematical modeling
  • Apply tensor calculus to solve problems in physics such as general relativity and continuum mechanics
  • Utilize tensor notation to simplify and analyze multidimensional data structures in engineering and data science
  • Implement tensor differentiation and integration techniques for advanced mathematical analysis
  • Develop proficiency in transforming tensors between coordinate systems for practical applications
  • Interpret tensor equations to model physical phenomena in electromagnetism and fluid dynamics
  • Employ tensor algebra to optimize computational algorithms in scientific computing
  • Analyze the role of tensors in describing curvature, stress, and strain in various scientific fields
  • Apply tensor calculus principles to formulate and solve real-world engineering problems
  • Enhance problem-solving skills using tensor calculus for research and technological innovation

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Lessons | 23
Calculus 3 Tensors 1 of 28 What is a Tensor
00:04:53

Calculus 3 Tensors 1 of 28 What is a Tensor
Calculus 3 Tensors 2 of 28 Tensors Represented in a Matrix
00:03:08

Calculus 3 Tensors 2 of 28 Tensors Represented in a Matrix
Calculus 3 Tensors 3 of 28 What is a Dyad A Graphical Representation
00:05:38

Calculus 3 Tensors 3 of 28 What is a Dyad A Graphical Representation
Calculus 3 Tensors 4 of 28 The Dyad 3 Vectors Define Stress at the 3 Planes
00:04:34

Calculus 3 Tensors 4 of 28 The Dyad 3 Vectors Define Stress at the 3 Planes
Calculus 3 Tensors 5 of 28 Tensor for Crystal Structure Orthorombic
00:02:13

Calculus 3 Tensors 5 of 28 Tensor for Crystal Structure Orthorombic
Calculus 3 Tensors 6 of 45 Potential for Confusion
00:03:55

Calculus 3 Tensors 6 of 45 Potential for Confusion
Calculus 3 Tensors 7 of 45 Tensors for Crystal Structures Monoclinic
00:04:35

Calculus 3 Tensors 7 of 45 Tensors for Crystal Structures Monoclinic
Calculus 3 Tensors 8 of 45 Tensors for Crystal Structures Triclinic
00:03:07

Calculus 3 Tensors 8 of 45 Tensors for Crystal Structures Triclinic
Calculus 3 Tensors 9 of 45 Stress in Tensor in 2 Dimensions
00:04:21

Calculus 3 Tensors 9 of 45 Stress in Tensor in 2 Dimensions
Calculus 3 Tensors 10 of 45 Tensor of Rank 3 The Triad
00:05:20

Calculus 3 Tensors 10 of 45 Tensor of Rank 3 The Triad
Calculus 3 Tensors 11 of 45 Tensor of Rank 3 The Triad A 2nd Look
00:03:15

Calculus 3 Tensors 11 of 45 Tensor of Rank 3 The Triad A 2nd Look
Calculus 3 Tensors 12 of 45 Tensor of Rank 3 The Triad A 3rd Look
00:03:08

Calculus 3 Tensors 12 of 45 Tensor of Rank 3 The Triad A 3rd Look
Calculus 3 Tensors 13 of 45 What is the Inertia Tensor
00:04:40

Calculus 3 Tensors 13 of 45 What is the Inertia Tensor
Calculus 3 Tensors 14 of 45 Angular Momentum the Inertia Tensor Diagonal Elements
00:05:05

Calculus 3 Tensors 14 of 45 Angular Momentum the Inertia Tensor Diagonal Elements
Calculus 3 Tensors 15 of 45 The OFF Diagonal Elements of the Inertia Tensor
00:03:33

Calculus 3 Tensors 15 of 45 The OFF Diagonal Elements of the Inertia Tensor
Calculus 3 Tensors 16 of 45 The Complete Inertia Tensor
00:03:23

Calculus 3 Tensors 16 of 45 The Complete Inertia Tensor
Calculus 3 Tensors 17 of 45 The Inertia Tensor A Simple Example
00:05:06

Calculus 3 Tensors 17 of 45 The Inertia Tensor A Simple Example
Calculus 3 Tensors 18 of 45 The Inertia Tensor A LESS Simple Example
00:03:47

Calculus 3 Tensors 18 of 45 The Inertia Tensor A LESS Simple Example
Calculus 3 Tensors 19 of 45 The Inertia Tensor A 3 D Simple Example
00:02:42

Calculus 3 Tensors 19 of 45 The Inertia Tensor A 3 D Simple Example
Calculus 3 Tensors 20 of 45 What is the Meaning of the OFF Diagonal Elements
00:06:05

Calculus 3 Tensors 20 of 45 What is the Meaning of the OFF Diagonal Elements
Calculus 3 Tensors 21 of 45 A 2 Mass Example
00:04:03

Calculus 3 Tensors 21 of 45 A 2 Mass Example
Calculus 3 Tensors 22 of 45 The Inertia Tensor for a Mass Distribution Diagonal
00:06:04

Calculus 3 Tensors 22 of 45 The Inertia Tensor for a Mass Distribution Diagonal
Calculus 3 Tensors 23 of 45 The Inertia Tensor for a Mass Distribution OFF Diagonal
00:04:50

Calculus 3 Tensors 23 of 45 The Inertia Tensor for a Mass Distribution OFF Diagonal


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Tensor Calculus course, in this course Explore the advanced mathematical framework for tensors, vital in physics, engineering, and multidimensional data analysis.