Outline of Advanced Mathematics Review

All + All -

advanced mathematics

• + - 08 vector and Analytic Geometry
  • + - concept
    • How to describe a vector algebraically
    • How to find a unit vector
    • Angle: angle between the positive direction of the coordinate axis
    • The direction cosine: direction cosine of the angle
  • + - operator
    • + - subtraction
      • Geometry: parallel quadrilateral and triangular rule Rule
      • Algebra: addition and subtraction corresponding position
    • + - Take
      • = The number of the dot product = product; multiplied by the corresponding values ​​are added; background: work
      • Cross product; the two vectors and then double-write applications determinant; Background: normals
  • + - Application
    • + - Equation
      • + - plane equation
        • French point: Vector face of a little known law of peace
        • Intercept the formula: it is known and the plane of intersection of the three axes
        • General formula: point can be determined by French
      • + - linear equation
        • = Symmetrical point to the formula: A few (two known points on a straight line) and a known linear direction vector
        • Parameters of formula: Another point is equal to the equation t French re simplification
        • General Formula: two simultaneous equations plane
    • + - angle
      • + - wire line angle
        • 1, taken on two points in a straight line direction vector
        • 2、cosθ
      • + - things to angle
        • 1, the method for finding the vector {A, B, C}
        • 2、cosθ
      • + - line plane angle
        • 1, taken on two points in a straight line direction vector
        • 2, taken {A, B, C} practice vector
        • 3、sinθ
    • + - Distance
      • Little bit of
      • + - point and area
        • 1, the vector Seeking
        • 2, a plane take any point
        • 3, the normal vector connecting the two points projected
      • + - dotted line
        • 1, seeking direction vector
        • 2, taken on the line to any point
        • 3, projection
    • + - plane beam
      • f1(x,y,z) + λf2(x,y,z) = 0
  • + - curved surface
    • + - establish equation
      • 1, take a little curved office
      • From equation 2, between the points
    • Surface of revolution: Who turn around, who unchanged
  • + - Space Curve
    • General Formula: two simultaneous equations plane
    • Parameters formula: x = cos (t) ...
    • Point to the type (only for straight-line)
• Differential Calculus and Applications
  • The basic concept of the Differential Calculus
  • Partial derivative
  • Total differential
  • How far is in line with the law of derivation function
  • Implicit function derivation
  • Geometric multivariate Function Differential
  • Gradient and directional derivative
  • Algebra: Extreme Value of the Function