Notes for Calculus 3 Spring 2001

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9.1  Vectors in the Plane

 

 
bulletLength of a Vector
bulletAddition of Vectors
bulletVector Arithmetic
bulleti, j components
bulletPerpendicular Vectors?
bullet2D Vector Introduction
9.2  Dot Products
bulletPerpendicular Vectors
bulletDot Products
9.3  Vector Valued Functions
bullet2D Parametric
9.4  Projectile Motion
bullet2D Parametric
9.5  Polar Coordinates
bulletPolar Grapher
bulletPolar vs. Rectangular
9.6  The Calculus of Polar Curves
10.1  3D Coordinates and Vectors
bulletIntro To 3D
bulletDistance in 3D
bulletEquation of Sphere
bulletGraph of Sphere
bulletVector Arithmetic
bulleti, j, k Notation
10.2  Dot and Cross Product
bulletDot Product in 3D
bulletAngle Between Vectors
bulletDirection Angles
bulletParallel and Perp Components
bulletDot and Cross Product
bullet2 x 2 Determinant
bullet3 x 3 Determinant
bulletCross Product of 2 Vectors
bulletArea of Triangle
bulletCross of 2 Vectors
bulletVolume of Pyramid
bulletCo-Planar Vectors?
10.3  Lines and Planes in Space
bulletLine Through 2 Points
bulletSymmetric Eqs of a Line
bulletPlane Given Point and Normal
bulletPlane Through 3 Points
bulletAngle Between Planes
10.4  Cylinders and Quadric Surfaces
bulletTraces of a Plane
bulletTraces of a Cylinder
bulletFigure 8 Cylinder
bulletElliptic Cylinder
bulletParabolic Cylinder
bulletEllipsoid of Revolution
bulletCone
bulletGeneral Ellipsoid
bulletQuadric Surfaces
bulletAnimated Hyperboloids
bulletElliptic Paraboloid
bulletElliptic Cone
bulletHyperboloid of One Sheet
bulletHyperboloid of Two Sheets
bulletHyperbolic Paraboloid
bulletRotated Ellipse
bulletRotated Hyperbolic Paraboloid
bulletRotated Ellipsoid
10.5  Vector Valued Functions and Space Curves
bulletParametric Curves in 3D
bulletTrefoil Knot
bulletBorromean Rings
bulletHelix
bulletTangent Line to Helix
bulletv and a on a Circle
bulletv and a on a Parabola
bulletv and a on a Helix
bulletFind r given a
bulletDrop a Bail of Hay
bulletProjectile
10.6  Arc Length and the Unit Tangent Vector
bulletArc Length on a Helix
bulletVelocity on a Helix
bulletCurvature on a Circle
bulletT and N on a Parabola
bulletCurvature on a Helix
bulletT, N and k on a Cubic
10.7  TNB Frames
bulletTangential and Normal Components of Acceleration
bulletTNB Frames
bulletCircle of Curvature
bulletSatellite Motion
bulletMore Satellite Motion
11.1  Functions of Several Variables
bulletA Plane
bulletParaboloid
bulletContours of a Paraboloid
bulletContours of a Hyperbolic Paraboloid
bulletLevel Surfaces
bulletA Strange Surface
bulletCircular Waves
bulletQuartic Surface
11.2  Limits and Continuity
bulletLimit of xy
bulletDiscontinuous on a Circle
bulletLimit of xy at (a, b)
bulletLimit of a Polynomial
bulletLimit of a Composition
bulletLimit of 0/0
bulletNon-Limit of 0/0
bulletRemovable Discontinuity
11.3  Partial Derivatives
bulletPartials of a Polynomial
bulletPartials of a Product
bulletPartials Evaluated at a Point
bulletPartials of Ideal Gas Volume
bulletSlopes of a Surface
bulletTangent Plane to a Surface
bulletHigher Order Partials
11.4  The Chain Rule
bulletw = f(x,y), x=g(t), y=h(t)
bulletMelting Ice
bulletw = f(x,y,z), x, y and z are functions of t
bulletz = f(u,v), u and v are functions of x and y
bulletPolar Conversion
bulletLots of Variables
bulletImplicit Partials to find Tangent Plane
bulletPolar Transformation
bulletPolar Derivative Matrix
11.5  Directional Derivatives, Gradient Vectors
bulletGradients and Contours
bulletGradient with 3 Variables
bulletDirectional Temperature Derivative
bulletChange in Temp of a Flying Hawk
bulletFastest Warming Bumble Bee
bulletUse Gradient to Find Tangent Plane of a Surface
bulletPlane Normal to the Curve of intersection of Two Surfaces
bulletTangent Line to an implicit function
11.6  Linearization and Differentials
bulletDifferential of Polynomial
bulletDifferential of Square Root
bulletDifferential of Ideal Gas
bulletFind a Nearby Point on a Curve
bulletError in V = xyz
11.7  Extreme Values and Saddle Points
bulletLocal and Absolute Extema
bulletMax, Min and Saddle Points
bulletFinding Local Extrema
bulletFinding Extrema on a Region
bulletExtrema on a Triangular Region
bulletMaximize a function
bulletExtrema with 3 Variables
bullet2nd Partials Test on Cubic
bullet2nd Partials Test on Monkey Saddle
bullet2nd Partials Test on Quartic
12.1  Double Integrals
bulletFinding Regions
12.2  Area, Average Value
12.3  Double Integrals in Polar Form
12.4  Triple Integrals
Extra: Cylindrical and Spherical Coordinates
bulletCylindrical to Rectangular
bulletRectangular to Cylindrical
bulletSurfaces in Cylindrical Coordinates
bulletA Region between two Cylindrical Surfaces
bulletSpherical to Rectangular
bulletRectangular to Spherical
bulletParaboloid in Spherical
bulletShifted Sphere
bulletAnother Shifted Sphere
bulletGreat Circle Distance
Extra: LaGrange Multipliers
bulletTwo Variable Function and Constraint
bulletMaximize Rectangle in Ellipsoid
bulletMaximize Box in Ellipsoid
bulletHighest Point on Intersection of Plane and Paraboloid
 

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