Lesson 7 of 33
How long is a curve?? The Arclength Formula in 3D
Lessons33 lessons
- 1What are the big ideas of Multivariable Calculus?? Full Course Intro
- 2Angle between vectors leads to defining the Dot Product | Multivariable Calculus
- 3Geometrically Defining the Cross Product | Multivariable Calculus
- 4The Vector Equation of Lines | Multivariable Calculus
- 5Equations of Planes: Vector & Component Forms | Multivariable Calculus
- 63D Curves and their Tangents | Intro to Vector-Valued Functions
- 7How long is a curve?? The Arclength Formula in 3D
- 8How curvy is a curve? Intro to Curvature & Circles of Curvature | Multi-variable Calculus
- 9Torsion: How curves twist in space, and the TNB or Frenet Frame
- 10Tangential and Normal components of Acceleration | Multi-variable Calculus
- 11Visualizing Multi-variable Functions with Contour Plots
- 12Limits are...weird...for multi-variable functions | Limits along paths
- 13Computing Multivariable Limits Algebraically
- 14What are derivatives in 3D? Intro to Partial Derivatives
- 15Continuity vs Partial Derivatives vs Differentiability | My Favorite Multivariable Function
- 16What is differentiability for multivariable functions??
- 17The Multi-Variable Chain Rule: Derivatives of Compositions
- 18Directional Derivatives | What's the slope in any direction?
- 19Geometric Meaning of the Gradient Vector
- 20How to find the TANGENT PLANE | Linear approximation of multi-variable functions
- 21Multi-variable Optimization & the Second Derivative Test
- 22Multivariable Optimization with Boundaries
- 23Lagrange Multipliers | Geometric Meaning & Full Example
- 24Lagrange Multipliers with TWO constraints | Multivariable Optimization
- 25Intro to Gradient Descent || Optimizing High-Dimensional Equations
- 26Defining Double Integration with Riemann Sums | Volume under a Surface
- 27Double Integration Example over General Regions --- two ways!
- 28Change the order of integration to solve tricky integrals
- 29Double Integration in Polar Coordinates | Example & Derivation
- 30The Gaussian Integral // Solved Using Polar Coordinates
- 31Triple Integrals in Cartesian Coordinates | Volume between Surfaces
- 32Integration in Spherical Coordinates
- 33Change of Variables & The Jacobian | Multi-variable Integration