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