Mathematica  Notebooks

Mathematica Player Interactive Demonstrations

Word    Graphs   P (PDF)

PDF Class Info
1.1  How to graph cylindrical surfaces, cylinders, planes and spheres in 3-Space using Plot3D, Shapes and Graphics3D
1.1 Parabola generates a cylindrical surface parallel to an axis of choice
12.1 Cylindrical surfaces P
 
1.2  How to add and subtract vectors, multiply vectors by a scalar, find the norm, components and the resultant force
1.2 Vector addition, subtraction, multiplication by a scalar, and norm
12.2 Vector operations P
CLASS SCHEDULE
1.3  How to find the angle between vectors and  use scalar product to find projections,  parallel and orthogonal vectors
1.3 Maximum and minimum angle between two special unit vectors
 12.3 Vector angle, dot pr. P
SYLLABUS   
1.4  How to use cross and triple product to find the area of a parallelogram and the volume of a parallelepiped in 3-Space
1.4 Area and Volume in 3 space using cross and triple products
 12.4 Cross product P  
1.5  How to find parametric equations of lines in 3-Space, intersecting and skew lines, the distance from a point to a line
1.5 Determine if given lines are skew, intersect or parallel, distance
 12.5 Skew,intersecting lines P  

Homework  Answers

1.6  How to find equations of planes, normal vectors, the distance form point to a plane, plane determined by skew lines
1.6 Determine if a line and a plane intersect, find the point or distance
 12.6 Line and a plane P
11.1  11.2  11.3  11.4 

1.7  How to graph ellipsoids, cone, paraboloid, hyperboloid in 3-Space using Plot3D, Implicit graphing and Graphics3D
1.7 Traces of a hyperbolic paraboloid in z=a, y=b, x=c planes
 12.7 Quadrics P
11.5  11.6  11.7  11.8
1.8  How to use spherical and cylindrical coordinates,  graph and convert equations to spherical, cylindrical coordinates
2.1 Cone cut by a plane produces a 3-Space conic section curve
ImpPlot3D Add On Pack 
12.1  12.2  12.3 
2.1  How to graph curves, find parametric equations for curve of intersection of surfaces; Trefoil, Torus, 8-Shape Knots
2.1 Cylinder cut by a plane yields an elliptic curve in 3-Space
Implicit3D  Examples 
2.2  How to find limits, derivatives and integrals of vector valued functions and graph the position and derivative vectors
2.2 Graphing position and derivative vectors for a vector function
 12.8 Revolution plots P
13.1  13.2   13.3  13.4
2.3  How to find arc length and arc length parametrization and choose the correct solution for  parameter t  in terms of   s
2.3 Step by step interactive tutorial on arc length parametrization
13.1 Knots: Trefoil, Torus, P
   13.5  13.6   13.7  13.8 
2.4  How to find unit tangent, inward normal, binormal vectors and osculating, rectifying, normal planes and TNB frame
2.4 Unit tangent, normal, binormal slide along the curve = TNB  Frame
Deep Forrest , 99 Linking #
  14.1  14.2  14.3
2.5  How to find curvature for parametric curves, radius, center of curvature, osculating circles, evolutes of basic curves
2.5 Centers of osculating circles for all points on the curve form evolute 
 13.2 Position derivative P
      14.4  14.5  14.7    
2.6  How to find velocity, speed, distance, acceleration, vector, scalar normal and tangential components of acceleration
2.6 Velocity, tangential, normal acceleration vectors slide along the curve  
13.4 TNB Frame P
15.1  15.2  15.3   15.4 
3.1  How to plot functions of two variables, make contour and density plots, find traces, level curves and level surfaces
2.6 Finds and graphs vector and scalar tangential, normal acceleration 
13.5 Evolute P
15.5  15.6  15.7   15.8  
3.2  How to find and compare directional and general limits for functions of two variables, Plucker cone and ridge surface
2.6 (M) Graphs of motion components with respect to arc length
13.6 Motion components P  
3.3  How to find partial derivatives, slopes in x and y directions, mixed and higher order partial derivatives, tangent lines
3.2 Directional limits are different, hence the limit does not exist
 14.1 Density, contour plots P
Practice Exams
3.4  How to find linear approximation for multivariable functions, use total differential to approximate changes and error
3.4 Linear approximation error approaches zero faster than the distance
 14.2 Directional limits P
3.5  How to apply one and two variable chain rules for multivariable functions and solve various related rates problems
3.6 Directional derivatives, gradients are normal to level curves
 14.6 Gradients, level curves P  
3.6  How to find gradients, directional derivatives, maximal rate of change, phase plane for a heat seeking bug on a plate

3.6 Path taken by a heat seeking bug on a heated plate

 14.7 Tangent planes P
3.7  How to find total differential, linear approximation and tangent planes and normal liones for multivariable functions
3.7 Tangent planes are graphs of linear approximations
14.8 Optimization problems P
3.8  How to solve optimization problems for multivariable functions, use extreme value theorem and second partials test
3.8 Absolute extrema on the boundary or interior of the region         
15.1 Double integrals  P
Ch 14 Prc Test (M)
4.1  How to find volumes of 3-Space regions over rectangular bases using double integrals and  RegionPlot3D command
3.8 Quadratic model of minimum to maximum through cylindrical surface
 15.2 Double integrals P
4.2  How to set up limits of integration for double integrals over type I and II regions and reverse the order of integration
4.1 Change the order of integration in double integrals
 15.3 Polar regions P
4.3  How to change to and set up limits of integration for double integrals in polar coordinates over simple polar regions
4.6 Polygon centroid of a 2-space region using double integrals
15.4 Parametric surfaces P
4.4  Parametric torus, cylinders, cones, spheres, astroidal sphere, helicoid, pseudosphere, Klein bottle and Mobius strip
4.4 Torus, how to graph parametric surfaces and find unit normals
15.5 Triple integrals P
 MATHEMATICA
4.5  How to set up limits of integration in triple integrals over simple xy, xz, zy solids and change the order of integration
4.5 Interactive volume of a cylindrical wedge changes with constraints
Chapter 15 Practice Test P
PROJECT  Due Date
4.8  How to apply change of variables in double integrals, graph transformations and find their images and find Jacobians
4.8 Change of variables transforming a rectangle into hyperbolic region
 16.1 Vector fields plots P
is May 20 at 3:15 pm
5.1  How to plot vector fields, find divergence and curl, properties of inverse square fields, potential functions and Nabla
 4.8 Transformation of square into triangle, differentiable, piecewise linear 16.2 Line integrals P  
5.2  How to evaluate ds, dr, dx, dy, dz   line integrals, find work done by a vector field and mass of a negligibly thin wire
5.6 (M) How to plot vector fields on the sphere,  (x,y,z)  or spherical
 16.3 Conservative fields P
MATHEMATICA
5.3  How to test and find potential function for conservative vector fields, use the Fundamental theorem of line integrals
5.6 Failed attempts at Hairy Ball theorem including field with one cowlick
 16.4 Green's Theorem P
LINKS
5.4  How to evaluate 2-Space line integrals using Green' theorem and find areas as line integrals, area of an ellipse, astroid
5.6 (M) How to plot vector fields on the torus,  (x,y,z)  or spherical
 16.5 Surface integrals P   Download Free Player
5.5  How to evaluate surface integrals and find area of parametric surfaces, how to find mass of negligibly thin membrane
5.6 Torus Wrap phase flows, fields, closed and dense trajectories
16.6 Finding flux P
Mathematica Main Page
5.6  How to find flux of a vector field, graph vector fields on the sphere and torus in rectangular or spherical coordinates
5.6 Flux of an arbitrary linear vector field through the unit sphere
 16.7 Divergence Theorem P
Mathematica Tutorial
5.7  How to find flux of a vector field using the Divergence (Gauss) theorem, graph closed piecewise parametric surfaces
5.7 Divergence Theorem for capped solids    16.7 Gauss Theorem fails
 16.8 Stokes' Theorem P
Video  Part I   Part II 
5.8  How to evaluate 3-Space line integrals using Stokes' theorem and find matching orientation of surface and boundary
5.8 Choice of surface with the given boundary in Stokes Theorem
 16.8 Oriented disk    P     
Demos from Wolfram