Calculus III - Multivariable Calculus - Vectors, Curves, Partial Derivatives, Multiple Integrals, Optimization

Calculus III - Multivariable Calculus - Vectors, Curves, Partial Derivatives, Multiple Integrals, Optimization

DrTreforBazett via YouTube Direct link

What are derivatives in 3D? Intro to Partial Derivatives

14 of 32

14 of 32

What are derivatives in 3D? Intro to Partial Derivatives

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Classroom Contents

Calculus III - Multivariable Calculus - Vectors, Curves, Partial Derivatives, Multiple Integrals, Optimization

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  1. 1 What are the big ideas of Multivariable Calculus?? Full Course Intro
  2. 2 Angle between vectors leads to defining the Dot Product | Multivariable Calculus
  3. 3 Geometrically Defining the Cross Product | Multivariable Calculus
  4. 4 The Vector Equation of Lines | Multivariable Calculus
  5. 5 Equations of Planes: Vector & Component Forms | Multivariable Calculus
  6. 6 3D Curves and their Tangents | Intro to Vector-Valued Functions
  7. 7 How long is a curve?? The Arclength Formula in 3D
  8. 8 How curvy is a curve? Intro to Curvature & Circles of Curvature | Multi-variable Calculus
  9. 9 Torsion: How curves twist in space, and the TNB or Frenet Frame
  10. 10 Tangential and Normal components of Acceleration | Multi-variable Calculus
  11. 11 Visualizing Multi-variable Functions with Contour Plots
  12. 12 Limits are...weird...for multi-variable functions | Limits along paths
  13. 13 Computing Multivariable Limits Algebraically
  14. 14 What are derivatives in 3D? Intro to Partial Derivatives
  15. 15 Continuity vs Partial Derivatives vs Differentiability | My Favorite Multivariable Function
  16. 16 What is differentiability for multivariable functions??
  17. 17 The Multi-Variable Chain Rule: Derivatives of Compositions
  18. 18 Directional Derivatives | What's the slope in any direction?
  19. 19 Geometric Meaning of the Gradient Vector
  20. 20 How to find the TANGENT PLANE | Linear approximation of multi-variable functions
  21. 21 Multi-variable Optimization & the Second Derivative Test
  22. 22 Multivariable Optimization with Boundaries
  23. 23 Lagrange Multipliers | Geometric Meaning & Full Example
  24. 24 Lagrange Multipliers with TWO constraints | Multivariable Optimization
  25. 25 Defining Double Integration with Riemann Sums | Volume under a Surface
  26. 26 Double Integration Example over General Regions --- two ways!
  27. 27 Change the order of integration to solve tricky integrals
  28. 28 Double Integration in Polar Coordinates | Example & Derivation
  29. 29 The Gaussian Integral // Solved Using Polar Coordinates
  30. 30 Triple Integrals in Cartesian Coordinates | Volume between Surfaces
  31. 31 Integration in Spherical Coordinates
  32. 32 Change of Variables & The Jacobian | Multi-variable Integration

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