Introduction to the Algebra and Geometry of Euclidean Space
来源:互联网 发布:淘宝推广手段 编辑:程序博客网 时间:2024/05/15 10:48
Introduction to the Algebra and Geometry of Euclidean Space
- Sage Notebook: Vectors with Sage [.sws]
- Dot products, cross products and magnitudes with Sage.
- Sage Notebook: Lines and Planes with Sage [.pdf][.sws]
- Examples of finding Lines and Planes with Sage in 3D.
- Vectors
- Introduction to the concept of vector. Magnitud, direction, addition.
- Vector Geometry
- Cartesian and spherical coordinate systems. Describing, surfaces, lines, points with vectors.
- Working with vectors in Maple
- Using maple to compute addition of vectors, magnitudes, angles. The plane in the wind problem is here...
- Simple Examples of Vectors with Maple
- computing lenths, unit vectors, solving simple vector equations and the proof that the medians of a triangle intersect at a single point.
- The Dot Product
- Introducing the inner product. Scalar and vector projections.
- The Cross Product
- Definition. Cross products of the i,j,k basis vectors. Examples.
- The Law of cosines
- The famous law of cosines and the formula for the inner product in terms of the coordinates of the vectors.
- Properties of Cross products
- Maple proofs of the distributivity and anti-commutatitivity properties of cross products.
- Cross products are NOT associative.
- Maple proof that cross products are not associative.
- Applications of the cross product: planes, volumes
- Triple products. The volume generated by 3 vectors. Projected Area.
- Lines with Maple
- Position vector plus t times the velocity vector: Howto with maple.
- The plane through 3 points
- The equation of the plane containing 3 given points. The maple procedure P3points for computing it is here...
- The plane containing two lines
- The equation of the plane containing two given lines. The maple procedure interlines for finding the point of intersection of two lines in 3D is here...
- The distance from a point to a line
- How far away is this point from that line?
The maple proc d2line is here... - The distance from a point to a plane
- How far is that point from this plane ?
The maple proc p2plane is here... - Plane containing two lines: Example1
- Given two lines in symmetric form, maple is used to find the plane that contains them. A picture of the plane with the two lines is here...
- Example: angle of diagonals
- Simple Maple proof that when the diagonals of a rectangle intersect at right angles then the rectangle is a square.
- Example: bisecting the angle betweenu and v
- Length of u times v plus length of v times u does it! The proof with maple is here...
- Two planes and one point
- The equation of the plane that contains the line of intersection of two other planes and a given point.
- Two planes, angle, line..
- Finding the angle between two planes and the line of intersection in symmetric form.
- A few review exercises
- Seven problems on lines, planes, angles, innerprods etc...
- More review exercises
- Seven problems on planes, lines and vectors.
Carlos Rodriguez <carlos@math.albany.edu>Last modified: Tue Jan 30 15:39:46 EST 2001 e Algebra and Geometry of Euclidean Space
The maple proc d2line is here...
The maple proc p2plane is here...
- Introduction to the Algebra and Geometry of Euclidean Space
- Introduction to The Design and Analysis of Algorithms (1)
- Introduction to The Design and Analysis of Algorithms (2)
- Euclidean Geometry
- Euclidean Geometry
- Introduction to Linear Algebra Lecture 1
- Introduction to Linear Algebra 学习笔记(一)
- the introduction of gcc and g++
- The introduction and application of PLC
- The Introduction of Windows Programming and WTL
- 入手《Introduction to the Theory of Computation》
- Introduction to the calculus of variations
- An Introduction to the Theory of Computation
- Minds and Computers: An Introduction to the Philosophy of Artificial Intelligence
- Understanding Windows CardSpace: An Introduction to the Concepts and Challenges of Digital Identitie
- "Introduction to the Theory of Computation" Reading notes - Ch. 0 and 1
- Introduction to Languages and the Theory of Computation--Chapter 1 学习笔记
- Euclidean Geometry(数学)
- 笔记
- MS是彻底抛弃makefile了,他新一代的build system 是MS Build.
- SDL2.0 ubuntu complie
- ARC 与内存管理
- 添加 WinJS 控件
- Introduction to the Algebra and Geometry of Euclidean Space
- 《启示录》读书笔记系列--笔记十二
- cocos2d-x(精灵类)
- c++中常量指针(int const * p),指针常量(int * const p )
- ERP系统容灾方案典型架构
- 设计模式之:工厂方法(Factory Method)
- 如何实现窗口阴影效果 (SysShadow、分层窗口、DWM)
- poj 2886 Who Gets the Most Candies?
- Ruby for Rails 实践2