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高等数学立体图册
高等数学立体图册

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数理化

  • 电子书积分:8 积分如何计算积分?
  • 作 者:刘光旭,李荫国编著
  • 出 版 社:北京:高等教育出版社
  • 出版年份:1982
  • ISBN:13010·0814
  • 页数:125 页
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上一篇:光谱线波长表下一篇:初等数论
《高等数学立体图册》目录

40 球面x2+y2+z2=1与平面x=0,y=0,z=0围在第一卦限的区域(The Solid in the First Octant Bounded by the Sphere x2+y 2

一、圆锥曲线(Conic Sections)(F.上.57) 2

1 椭圆(Ellipse) 2

2 双曲线(Hyperbola) 4

3 抛物线(Parabola) 6

二、空间直角坐标与矢量代数 (Rectangular Coordinates in 3-Space;Vector Algebra) 8

4 直角坐标系的八个卦限 (Eight Octants of Rectangular CoordinateSystem) (F.上.103) 8

5 矢量在轴上的投影 (Projection of Vector on Axis)(F.上.115) 10

6 矢量在平面上的投影(Projection of Vector on Plane) 12

7 矢量积的分配律(Distributive Law of Vector Product)(F.上.129) 14

8 欧拉角(Euler s Angles) 16

三、二次柱面(Quadric Cylinders) 18

9 双曲柱面(Hyperbolic Cylinder)(F.上.139) 18

10 抛物柱面(Parabolic Cylinder)(F.上.139) 20

四、空间曲线、曲面的参数方程(Parametric Equations of SpaceCurves and Surfaces ) 22

11 螺旋线(Circular Helix)(F.上.141) 22

12 正螺面(Right helicoid) 24

五、二次曲面(Quadric Surfaces) 28

13 旋转曲面(Surface of Revolution)(F.上.165) 28

14 椭球面 (Ellipsoid)(F.上.167) 28

15 单叶双曲面(Hyperboloid of One Sheet)(F.上.169) 30

16 单叶双曲面是直纹曲面 (Hyperboloid of One Sheet is a RuledSurface)(F.上.169) 32

17 双叶双曲面(Hyperboloid of Two Sheets)(F.上.171) 34

18 椭圆抛物面(Elliptic Paraboloid)(F.上.173) 36

19 双曲抛物面 (Hyperbolic Paraboloid)(F.上.174) 38

20 双曲抛物面是直纹曲面 (Hyperbolic Paraboloid is a RuledSurface) 40

六、多元函数的微分法(The Derivatives of a Function of SeveralVariables) 40

24 全微分的几何意义(Geometric Significance of TotalDiff erential)(F.下.83) 48

25 方向导数(Directional Derivative)(F.下.85) 50

26 多元函数的极值(Extreme Value of Function of SeveralVariables)(F.下.103) 52

七、重积分(Multiple Integrals)27 平面x=a,y=a,z=a,x+y+z=?a 在第一卦限所围区域 (Solidin the First octantBounded by the Planes x=a,y=a,z=a,and x+y+z=?a 54

28 V=?dx?(x2+y2)dy的积分区域 (Integral Region ofV=?dx?(x2+y2)dy) 56

29 ?(T.7.35),(F.上.143) 58

30 旋转抛物面z=x2+y2+1与平面x=0,x=4,y=0,y=4所围区域(The Solid Bounded by the Paraboloid of Revolutionz=x2+y2+1 and Planes x=0,x=4,y=0,and y=4)(T.22. 61

31 抛物面z=x2+y2+1与平面x+y=4及三个坐标平面所围区域 (TheSolid Bounded by the Paraboloid z=x2+y2+1 and the Planesx+y=4,x=0,y=0,and z=0)(T.9.13(g)也可供T.9.13(c),T.22.62参考) 62

32 抛物柱面z=4-x2,平面2x+y=4与三个坐标平面所围区域 (TheSolid Bounded by the Parabolic Cvlinder z=4-x2theCoordinate Planes,and Plane 2x+y=4)(T.9.13(e),T.22.63) 64

33 抛物柱面2y2=x,平面?+?+?=1与平面z=0所围区域(TheSolid Bounded by the Parabolic Cvlinder 2y2=x and thePlanes?+?+?=1 and z=0)(T.22.64) 66

34 圆柱面x2+y2=R2与圆柱面x2+z2=R2所围区域 (The SolidBounded by the Cylinders x2+y2=R2 and x2+z2=R2)(T.9.13(j)T.22.65;T.22.93) 68

35 抛物柱面y=?与平面y=0,z=0,x+z=?所围区域 (The SolidBounded by the Parabolie Cylinder y=?and the Planesy=0,z=0,and x+z=?)(T.22.70) 70

36 双曲抛物面z=xy与平面x+y=1,z=0所围区域 (The SolidBounded by the Hyperbo1ic Paraboloid z=xy and the Planesx+y=1and z=0)(T.22.71) 72

37 旋转抛物面z=x2+y2,抛物柱面y=x2与平面y=1,z=0所围区域(The Solid Bounded by the Paraboloid of Revolution z=x2+y2,the Parabolic Cylinder y=x2,and Planes y=1,z=*0++(T.22.72) 74

38 双曲抛物面cz=xy(c>0),椭圆柱面?+?=1与平面z=0围在第一卦限的区域(The Solid in the First octant Bounded by theHyperbolic Paraboloid cz=xy(c>0),the Elliptic Cylinder?+?=1,and the Plane z=0)(T.22.73) 76

+z2=1,Planes x=0, y=0,and z=0 )(T.22. 77

39 椭圆抛物面3x2+y2=z与抛物柱面z=1-x2所围区域 (The SolidBounded by the Elliptic Paraboloid 3x2+y2=z and theParabolic Cylinder z=1-x2)(T.22.74) 78

41 平面y=0,z=0,3x+y=6,3x+2y=12,x+y+z=6所围区域(The Solid Bounded by the Planes y=0,z=0,3x+y=6,3x+2y=12,and x+y+z=6) (T.22.83) 82

43 双曲抛物面z=?,圆柱面x2+y2=ax(a>0)与平面z=0所围区域(The Solid Bounded by the Hyperbolic Paraboloid z=?theCylinder x2+y2=ax(a>0),and the Plane z=0)(T.9.13(i)T.22.85) 86

44 圆柱面x2+y2=2ax,旋转抛物面az=x2+y2与平面z=0所围区域,其中a>0 (The Solid Bounded by the Cylinder x2+y2=2ax,theParaboloid of Revolution az=x2+y2(a>0),and the Planez=0)(T.22.87) 88

42 锥面z=?与抛物柱面z2=2x所围区域 (The Solid Boundedby the Cone z=?and the Parabolic Cylinder z2=2x )(T.22. 90

45 旋转抛物面x2+y2=az与圆锥面z=2a-?(a>0)所围区域(TheSolid Bounded by the Paraboloid of Revolution x2+y2=az andthe Circular Cone z=2a-?(a>0))(T.22.88) 90

46 半球面z=?与旋转抛物面x2+y2=2az所围立体之表面积,其中a>0(Surface Area of the Solid Bounded by TheSemi-Sphere z=?and the Paraboloid of Revolutionx2+y2=2az,a>0)(T.22.92) 92

47 球x2+y2+z2=a2与圆柱面x2+y2=ax(a>0)所围区域 (TheSolid Bounded by the Sphere x2+y2+z2=a2 and the Cylinderx2+y2=ax,a>0) (T.22.66;T.22.95) 94

48 抛物柱面y=?y=2?与平面z=0,z+x=6所围区域 (TheSolid Bounded by the Parabolic Cylinders y=?,y=2?and the Planes z=0,z+x=6)(T.9.13(d);T.22.119) 96

49 双纽线柱面(x2+y2)2=x2-y2,旋转抛物面2z=x2+y2与平面z=0所围区域(The Solid Bounded by the Lemniscate Cylinder(x2+y2)2=x2-y2,the Paraboloid of Revolution 2z=x2+y2,and the Plane z=0 ) 98

50 旋转抛物面x=?,抛物柱面x=?与平面y=1所围区域(The Solid Bounded by the Paraboloid of Revolution x=?,the Parabolic Cylinder x=?,and the Plane y=1) 100

51 柱面坐标(Cylindrical Coordinates)(F.下.131) 102

52 柱面坐标下的体积元素(Cylindrical Element of Volume)(F.下.132) 104

53 球面坐标(Spherical Coordinates)(F.下.133) 106

54 球面坐标下的体积元素(Spherical Element of Volume)(F.下.134) 108

55 曲面的面积(Area of Surface)(F.下.135) 110

八、其它(Miscellaneous)56 球极射影(Spherical Polar Projection) 112

57 单叶旋转双曲面的平行曲面作为圆柱族的内包络面(The ParallelSurface of the Rotating Hyperboloid of One Sheet As theInterior Envelope of the Family of Cylinders) 114

58 环面(Torus) 116

59 环面的三角剖分(A Triangulation of Torus) 118

60 ?面与圆柱面相交 (The Intersection of a Torus and a Cylinder) 120

61 元函数f(x,y)=?的图形(The Graph of Function of Two Variablesf(x,y)=? 122

62 ?鞍面(Monkey Saddle)z=x3-3xy2 124

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