Academa Multivariable Calculus

Vectors and the Geometry of the Space

Lecture 1 Vectors

Lecture 2 Dot Product

Vector Projections and Determinants

Lecture 3 Vector Projections and Determinants

Lecture 4 Cross Product

Planes and Lines

Lecture 5 Planes and Lines

Planes and Lines (cont.)

Lecture 6 Planes and Lines (cont.)

Vector Functions

Parametric Curves

Lecture 7 Parametric Curves

Parametric Curves (cont.)

Lecture 8 Parametric Curves (cont.)

Partial Derivatives

Partial Derivatives

Lecture 9 Partial Derivatives

Partial Derivatives (cont.)

Lecture 10 Partial Derivatives (cont.)

Tangent Plane, Normal Vector to Surface

Lecture 11 Tangent Plane, Normal Vector to Surface

Lecture 12 Chain Rule

Directional Derivative and the Gradient

Lecture 13 Directional Derivative and the Gradient

Maximization and Minimization

Lecture 14 Maximization and Minimization

Lagrange Multipliers

Lecture 15 Lagrange Multipliers

Multiple Integrals

Double Integration

Lecture 16 Double Integration

Double Integration over General Regions

Lecture 17 Double Integration over General Regions

Applications of Double Integration

Lecture 18 Applications of Double Integration

Lecture 19 Double Integration in Polar Coordinates

Lecture 20 Triple Integration

Lecture 21 Applications of Triple Integration

Lecture 22 Cylindrical and Spherical Coordinates

Lecture 23 Integration in Cylindrical and Spherical Coordinates

Lecture 24 General Change of Variables

Vector Calculus

Lecture 25 Vector Fields and Line Integrals

Lecture 26 Gradient Fields and the Fundamental Theorem of Line Integrals

Lecture 27 More on Conservative Fields

Lecture 28 Green's Theorem

Lecture 29 Curl and Divergence

Lecture 30 More on Div and Curl

Lecture 32 More on Parametric Surfaces, Surface Integrals

Lecture 33 Big Picture of Integration, Stokes' Theorem

Lecture 35 Curl Free World, Div Free World

Lecture 2: Dot Product

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