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Introduction to Vectors
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Classroom Contents
Calculus 3
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- 1 Introduction to Vectors
- 2 Vector Length and Unit Vectors
- 3 Dot Product
- 4 The Two Definitions of Dot Product Are Equivalent
- 5 Cross Product
- 6 Jusification of the Properties of Cross Product
- 7 Cross Product and Areas of Parallelograms
- 8 More Properties of Cross Product
- 9 Equations of Lines and Planes in 3-D Space
- 10 More Examples of Lines and Planes in 3D
- 11 Parallel and Perpendicular Lines and Planes
- 12 Distances between Points, Lines, and Planes
- 13 Vector Functions and Space Curves
- 14 Closest Point on a Curve
- 15 Derivatives and Integrals of Vector Functions
- 16 Arclength of Parametric Curves
- 17 Functions of Several Variables
- 18 Limits of Functions of Several Variables
- 19 Proof that sin x is smaller in magnitude than x.
- 20 Tricky Limit
- 21 Partial Derivatives
- 22 The Chain Rule for Functions of Several Variables
- 23 Justification of the Chain Rule
- 24 Directional Derivatives
- 25 Tangent Plane
- 26 Local Max and Min Values for Functions of Two Variables
- 27 The Second Derivatives Test
- 28 Proof of the Second Derivatives Test
- 29 Lagrange Multipliers
- 30 Double Integrals and Riemann Sums
- 31 Iterated Integrals
- 32 Double Integrals Over General Regions
- 33 Double Integrals in Polar Coordinates
- 34 Justification of the Area Element when Integrating in Polar Coordinates
- 35 The Area under the Normal Curve is 1
- 36 Center of Mass
- 37 Triple Integrals
- 38 Triple Integrals in Cylindrical Coordinates
- 39 Spherical Coordinates
- 40 Triple Integrals in Spherical Coordinates
- 41 Vector Fields
- 42 Line Integrals with respect to Arclength
- 43 Line Integrals in Terms of Riemann Sums
- 44 Line Integrals with Respect to x and y
- 45 Line Integrals and Parametrizations
- 46 Simple Closed Curves - Definitions
- 47 Types of Regions of the Plane - Definitions
- 48 Conservative Vector Fields and Independence of Path
- 49 Green’s Theorem
- 50 Proof of Green’s Theorem
- 51 Parametric Surfaces
- 52 Surface Area of Parametric Surfaces
- 53 Divergence
- 54 Curl
