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Vector Analysis
University of California - Davis
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Luis Rademacher

Shiqian Ma

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MAT 21D

MAT 21D Study Guide - Final Guide: Unit Vector, Dot Product

|(cid:3049) | : example: a straight line is parameterized by (cid:1870) (cid:4666)(cid:1872)(cid:4667)=(cid:2835) +(cid:1872) (cid:3642)(cid:1870) (cid

MAT 21D

MAT 21D Study Guide - Final Guide: Cross Product, Unit Vector, Dot Product

If (cid:1870) (cid:4666)(cid:1872)(cid:4667)=(cid:1858)(cid:4666)(cid:1872)(cid:4667)(cid:2835) +(cid:1859)(cid:4666)(cid:1872)(cid:4667)(cid:2836) + (

MAT 21D

MAT 21D Study Guide - Final Guide: Cylindrical Coordinate System, Spherical Coordinate System, Ice Cream Cone

Mat 21d lecture 8 triple integrals in cylindrical and spherical coordinates: example: consider a 2-d plane, a thin plate. The triangular region is boun

MAT 21D

MAT 21D Study Guide - Final Guide: Centroid, Angular Velocity

Mat 21d lecture 7 moments of inertia, second moments: for a 3-d solid, the mass, =(cid:1518)(cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667). First

MAT 21D

MAT 21D Study Guide - Final Guide: Unit Disk, Cartesian Coordinate System, Unit Circle

Based on the sketch of the region r, our new region g: (cid:882) (cid:2870),(cid:882) (cid:1870) (cid:883)(cid:3642) (cid:1516) (cid:1516)(cid:4666)(ci

MAT 21D

MAT 21D Final: MAT 21D – Lecture 12 – Arc Length in Space

MAT 21D

MAT 21D Final: MAT 21D – Lecture 10 – Substitutions in Triple Integrals

Mat 21d lecture 10 substitutions in triple integrals: we have a region g in uvw-space and a region d in xyz-space with (cid:4666)(cid:1876),(cid:1877),

MAT 21D

MAT 21D Final: MAT 21D – Lecture 14 – Tangential and Normal Components of Acceleration

Mat 21d lecture 14 tangential and normal components of acceleration: the tangent vector, =(cid:3031)(cid:3045) (cid:3031)(cid:3046)= | |. Normal vector

MAT 21D

MAT 21D Final: MAT 21D – Lecture 6 – Moments and Centers of Mass

MAT 21D

MAT 21D Study Guide - Final Guide: Multiple Integral, Cartesian Coordinate System

MAT 21D

MAT 21D Study Guide - Final Guide: Multiple Integral, Hypotenuse

Integrating (cid:1858)(cid:4666)(cid:1870),(cid:4667) over a region, r: partition a region into slices of pizza. The total sum for the volume of each s

Class Notes

Taken by our most diligent verified note takers in class covering the entire semester.

MAT 21D Lecture Notes - Lecture 1: Multiple Integral, Divergence Theorem, Riemann Sum

Mat 21d lecture 1 double integrals over rectangles: compute the area underneath the curve bounded by (cid:1877)=(cid:4666)(cid:1876)(cid:4667)=(cid:187

MAT 21D Lecture Notes - Lecture 2: Multiple Integral

MAT 21D Lecture Notes - Lecture 3: Multiple Integral

MAT 21D Lecture 11: MAT 21D – Lecture 11 – Substitutions in Triple Integrals

Mat 21d lecture 11 substitutions in triple integrals: we have a region g in uvw-space and a region d in xyz-space with (cid:4666)(cid:1876),(cid:1877),

MAT 21D Lecture Notes - Lecture 12: Cross Product, Unit Vector

If (cid:1870) (cid:4666)(cid:1872)(cid:4667)=(cid:1858)(cid:4666)(cid:1872)(cid:4667)(cid:2835) +(cid:1859)(cid:4666)(cid:1872)(cid:4667)(cid:2836) + (

MAT 21D Lecture 13: MAT 21D – Lecture 13 – Arc Length in Space

MAT 21D Lecture Notes - Lecture 14: Unit Vector, Dot Product

|(cid:3049) | : example: a straight line is parameterized by (cid:1870) (cid:4666)(cid:1872)(cid:4667)=(cid:2835) +(cid:1872) (cid:3642)(cid:1870) (cid

MAT 21D Lecture 15: MAT 21D – Lecture 15 – Tangential and Normal Components of Acceleration

Mat 21d lecture 15 tangential and normal components of acceleration: the tangent vector, =(cid:3031)(cid:3045) (cid:3031)(cid:3046)= | |. Normal vector

MAT 21D Lecture 15: MAT 21D – Lecture 15 – Line Integrals

MAT 21D Lecture 16: MAT 21D – Lecture 16 – Line Integrals

MAT 21D Lecture Notes - Lecture 16: 2D Computer Graphics, Mathematical Notation, Dot Product

Mathematical: the vector field in 3d space is represented by (cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667)=(cid:1839)(cid:4666)(cid:1876),(cid:1

MAT 21D Lecture Notes - Lecture 17: Dot Product, Cross Product, Curve

Mat 21d lecture 17 work and circulation flux. =(cid:2869: the vector, =(cid:1839)(cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667)(cid:2835) +(cid:1

MAT 21D Lecture Notes - Lecture 17: 2D Computer Graphics, Mathematical Notation, Dot Product

Mathematical: the vector field in 3d space is represented by (cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667)=(cid:1839)(cid:4666)(cid:1876),(cid:1

MAT 21D Lecture Notes - Lecture 18: Conservative Vector Field, Partial Derivative

1) flow is counterclockwise, and, 2) the curve is closed. Mat 21d lecture 18 conservative fields and potential functions: flux = (cid:1866) (cid:1856)(

MAT 21D Lecture Notes - Lecture 18: Dot Product, Cross Product, Curve

Mat 21d lecture 18 work and circulation flux. =(cid:2869: the vector, =(cid:1839)(cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667)(cid:2835) +(cid:1

MAT 21D Lecture Notes - Lecture 19: Conservative Vector Field, Partial Derivative

1) flow is counterclockwise, and, 2) the curve is closed. Mat 21d lecture 19 conservative fields and potential functions: flux = (cid:1866) (cid:1856)(

MAT 21D Lecture Notes - Lecture 27: Curve, Conservative Vector Field, Partial Derivative

MAT 21D Lecture Notes - Lecture 28: Cylindrical Coordinate System, Cross Product

MAT 21D Lecture Notes - Lecture 29: Implicit Surface, Surface Integral, Multiple Integral

MAT 21D Lecture Notes - Lecture 30: Surface Integral, Cross Product

MAT 21D Lecture Notes - Lecture 31: Curve, Ellipse, Conservative Vector Field

MAT 21D Lecture Notes - Lecture 32: Divergence Theorem, Spherical Coordinate System, Cross Product