Multivariable Calculus (Calc III) - Complete Semester Course
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1 modules • 109 lessons • 29.5 hours of video
Multivariable Calculus (Calc III) - Complete Semester Course
109 lessons
• 29.5 hours
Multivariable Calculus (Calc III) - Complete Semester Course
109 lessons
• 29.5 hours
- Multivariable Calculus Unit 1 Lecture 01: Welcome to (x,y,z) space R3 19:21
- Multivariable Calculus Unit 1 Lecture 02: Five examples in R3 13:45
- Multivariable Calculus Unit 1 Lecture 03: Five examples in R3 25:50
- Introduction to vectors, Multivariable Calculus Unit 1 Lecture 04 20:59
- Vector Magnitude and the Standard Basis Vectors, Multivariable Calculus Unit 1 Lecture 05 18:49
- Multivariable Calculus: Force with vectors 10:21
- The Dot Product, Multivariable Calculus 23:33
- Vector Projection, Multivariable Calculus 15:25
- Multivariable Calculus: Work (Unit 1 Lecture 09) 06:35
- Vector Cross Product, Multivariable Calculus 23:19
- Multivariable Calculus: Quick right-hand rule demo 01:17
- Cross Product Areas and Volumes, Multivariable Calculus 13:27
- Torque, Multivariable Calculus 07:51
- Multivariable Calculus: Lines in R2 10:32
- Vector Equation of a Line, Multivariable Calculus 20:11
- Vector Equation of a Plane and General Form, Multivariable Calculus 28:36
- How to find lines and planes, Multivariable Calculus 31:05
- Multivariable Calculus: Distance from a point to a plane 12:21
- Intersection of two planes: the line and the angle, Multivariable Calculus 24:47
- Introduction to vector-valued functions and curves, Multivariable Calculus 16:01
- Multivariable Calculus: Calculus on vector-valued functions (Curves) 23:02
- Parametrized Curves, Multivariable Calculus 11:54
- Multivariable Calculus: Parameterize the curve of intersection 08:37
- Multivariable Calculus: Velocity and Acceleration 15:22
- Multivariable Calculus: Newton's second law and projectile motion 18:48
- Projectile motion: optimal angle, landing time and location in Multivariable Calculus 13:30
- Multivariable Calculus: The unit tangent vector T 09:10
- Multivariable Calculus: Arc length and the arc length function 09:06
- Example arc length computation with calculus 09:39
- Reparametrization with respect to arc length, Multivariable Calculus 14:40
- Multivariable Calculus: Curvature κ(t) for a parametrized curve 17:36
- Vectors N and B with visuals, Multivariable Calculus 20:12
- Compute T, N, and B for a parameterized curve, Multivariable Calculus 16:24
- Examples with T, N, B, κ and the osculating circle, Multivariable Calculus 20:41
- Example finding the osculating plane and TNB, Multivariable Calculus 14:03
- Example finding the osculating circle, Multivariable Calculus 14:40
- Osculating plane and circle, Multivariable Calculus 10:55
- The decomposition of acceleration in Multivariable Calculus 16:12
- Multivariable Calculus: Introduction to functions of multiple variables 14:32
- Quadric Surfaces, Multivariable Calculus 17:32
- Level sets and contour maps, Multivariable Calculus 08:34
- Parametric surfaces r(u,v), Multivariable Calculus 15:57
- Multivariable limits and continuity 24:43
- Partial derivatives, Multivariable Calculus 21:57
- Directional Derivatives, Multivariable Calculus 09:25
- Clairaut's Theorem and higher order derivatives, Multivariable Calculus 12:20
- Proof of Clairaut's Theorem, Real Analysis II 43:02
- Tangent Planes in Multivariable Calculus 13:06
- Multivariable Calculus: Find the point on the sphere closest to a plane 12:49
- Multivariable Calculus Unit 3 Lecture 10: General definition of differentiability 27:29
- Differentials and linearization in Multivariable Calculus 06:50
- Linearize a solution to the heat equation, Multivariable Calculus 07:09
- Multivariable Calculus: Directional derivatives and the gradient 10:32
- The Chain Rule in Multivariable Calculus 16:34
- Gradients and Tangent Planes, Multivariable Calculus 21:40
- Tangent Plane and Normal Line using a gradient, Multivariable Calculus 13:38
- Optimization in Multivariable Calculus 14:53
- Optimization over bounded regions, Multivariable Calculus 20:23
- Lagrange Multipliers, Multivariable Calculus 13:32
- Multivariable Calculus: Definition of Double Riemann integration 27:49
- Fubini's Theorem, Multivariable Calculus Unit 4 Lecture 2 22:50
- Double integration over general regions, Multivariable Calculus Unit 4 Lecture 3 22:11
- Applications of double integrals, Multivariable Calculus 16:41
- Introduction to Triple integrals in Multivariable Calculus 30:23
- Applications of triple integrals, Multivariable Calculus Unit 4 Lecture 6 17:22
- Introduction to polar coordinates and integration, Multivariable Calculus 20:47
- Examples of integrating with polar coordinates, Multivariable Calculus 11:43
- Areas between circles with double integrals, Multivariable Calculus 28:19
- Double integral in polar example, Multivariable Calculus 07:49
- Example: double integral over a disk in polar coordinates, Multivariable Calculus 12:47
- Average value with polar coordinates example, Multivariable Calculus 04:58
- Integrate e^(-x^2) using a double integral, Multivariable Calculus 08:39
- Triple integration with cylindrical (polar) coordinates, Multivariable Calculus 24:04
- Introduction to spherical coordinates, Multivariable Calculus 15:59
- Spherical coordinates integration examples, Multivariable Calculus 14:36
- Spherical Integration Example, Multivariable Calculus 20:58
- Computing a volume with double and triple integrals, Multivariable Calculus 29:09
- Compute a volume with a triple integral, three set ups 42:22
- Vector Fields, Multivariable Calculus 16:37
- Conservative Vector Fields, Multivariable Calculus 10:06
- Finding potential functions, Multivariable Calculus 17:45
- Introduction to line integrals, Multivariable Calculus 07:10
- Scalar line integrals, Multivariable Calculus 13:14
- How to set up a scalar line integral, Multivariable Calculus 02:44
- Scalar line integrals practice and properties, Multivariable Calculus 08:11
- Vector line integrals, Multivariable Calculus 14:43
- Work done by a vector field computed with a line integral, Multivariable Calculus 06:15
- Circulation line integrals, Multivariable Calculus 07:55
- Fundamental Theorem for Line Integrals (FTLI), Multivariable Calculus 10:58
- Conservation of Energy, Multivariable Calculus 07:16
- Examples of scalar and vector line integrals, Multivariable Calculus 08:20
- Surface Area with a Surface Integral, Multivariable Calculus 36:57
- Example computing surface area with a surface integral, Multivariable Calculus 10:44
- Scalar surface integrals, Multivariable Calculus 15:57
- Surface Area cut out by two cylinders, Multivariable Calculus 16:45
- Surface Integrals: Why 'r' Isn't Needed When Parametrizing with Polar Coordinates 07:38
- Example of a scalar surface integral (spherical and cylindrical coordinates), Multivariable Calculus 13:37
- Flux Integrals, Multivariable Calculus 22:05
- Example of a flux integral, Multivariable Calculus 11:17
- Curl and divergence of a vector field, Multivariable Calculus 16:07
- Green's Theorem, Multivariable Calculus 26:55
- Example using Green's Theorem to compute a circulation integral 05:52
- Green's Theorem Example, Multivariable Calculus 09:54
- Green's theorem for flux, Multivariable Calculus 18:07
- Stokes' Theorem, Multivariable Calculus 21:24
- Line integral along a plane and sphere intersection, with Stokes and without 29:59
- Divergence Theorem, Multivariable Calculus 18:20
- One flux example two ways: using Stokes' and the Divergence Theorem 24:12
- Flux across a hemisphere, with and without the Divergence Theorem, Multivariable Calculus 25:36
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