Calculus III: Multivariable Calculus (Vectors, Curves, Partial Derivatives, Multiple Integrals, Optimization, etc) **Full Course **
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What you'll learn
This course includes
- 5.5 hours of video
- Certificate of completion
- Access on mobile and TV
Course content
1 modules • 33 lessons • 5.5 hours of video
Calculus III: Multivariable Calculus (Vectors, Curves, Partial Derivatives, Multiple Integrals, Optimization, etc) **Full Course **
33 lessons
• 5.5 hours
Calculus III: Multivariable Calculus (Vectors, Curves, Partial Derivatives, Multiple Integrals, Optimization, etc) **Full Course **
33 lessons
• 5.5 hours
- What are the big ideas of Multivariable Calculus?? Full Course Intro 16:50
- Angle between vectors leads to defining the Dot Product | Multivariable Calculus 06:11
- Geometrically Defining the Cross Product | Multivariable Calculus 05:13
- The Vector Equation of Lines | Multivariable Calculus 05:30
- Equations of Planes: Vector & Component Forms | Multivariable Calculus 04:28
- 3D Curves and their Tangents | Intro to Vector-Valued Functions 10:07
- How long is a curve?? The Arclength Formula in 3D 07:10
- How curvy is a curve? Intro to Curvature & Circles of Curvature | Multi-variable Calculus 07:48
- Torsion: How curves twist in space, and the TNB or Frenet Frame 10:48
- Tangential and Normal components of Acceleration | Multi-variable Calculus 10:48
- Visualizing Multi-variable Functions with Contour Plots 07:54
- Limits are...weird...for multi-variable functions | Limits along paths 05:38
- Computing Multivariable Limits Algebraically 12:17
- What are derivatives in 3D? Intro to Partial Derivatives 08:53
- Continuity vs Partial Derivatives vs Differentiability | My Favorite Multivariable Function 09:11
- What is differentiability for multivariable functions?? 14:35
- The Multi-Variable Chain Rule: Derivatives of Compositions 10:47
- Directional Derivatives | What's the slope in any direction? 12:01
- Geometric Meaning of the Gradient Vector 14:51
- How to find the TANGENT PLANE | Linear approximation of multi-variable functions 09:23
- Multi-variable Optimization & the Second Derivative Test 13:36
- Multivariable Optimization with Boundaries 15:08
- Lagrange Multipliers | Geometric Meaning & Full Example 12:24
- Lagrange Multipliers with TWO constraints | Multivariable Optimization 16:29
- Intro to Gradient Descent || Optimizing High-Dimensional Equations 11:04
- Defining Double Integration with Riemann Sums | Volume under a Surface 09:41
- Double Integration Example over General Regions --- two ways! 10:26
- Change the order of integration to solve tricky integrals 07:39
- Double Integration in Polar Coordinates | Example & Derivation 11:11
- The Gaussian Integral // Solved Using Polar Coordinates 07:52
- Triple Integrals in Cartesian Coordinates | Volume between Surfaces 07:13
- Integration in Spherical Coordinates 07:52
- Change of Variables & The Jacobian | Multi-variable Integration 10:07
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