Analytic geometry with calculus

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Author(s): Robert Carl Yates
Series: Mathematics series
Publisher: Prentice-Hall
Year: 1961

Language: English
Pages: 258

Cover......Page 1
Title Page......Page 2
Copyright......Page 3
Preface......Page 4
Contents......Page 6
I. THE PLANE......Page 12
1.1 The Real Number System and the Continuum Axiom......Page 14
1.2. Coordinate Systems in the Plane......Page 15
1.3. Graphs: Mathematical Statements......Page 16
1.4. Graphs, Rectangular (General Remarks)......Page 19
1.5. Guide Lines (Rectangular Coordinates)......Page 24
* 1.6. Techniques (Rectangular Coordinates)......Page 26
1.7. Graphs, Polar......Page 31
2.1. Distance. Midpoint of a Segment......Page 36
2.2. Direction Cosines. Direction Numbers......Page 37
2.3. Angle Between Two Line Segments......Page 39
2.4. Parallel and Perpendicular Line Segments......Page 40
2.5. Slope......Page 41
2.7. Angle of Triangle Formed by P1P2P3......Page 42
3.2. Function......Page 44
3.4. Limits. The Symbol......Page 45
3.5. Geometric Progressions......Page 47
3.6. A Special Limit......Page 48
3.8. Continuity......Page 50
4.1. The Derivative in Rectangular Coordinates......Page 55
4.2. Slope of a Curve y = f (x)......Page 57
4.3. Maximum-minimum in Rectangular Coordinates......Page 58
4.4. The Derivative in Polar Coordinates......Page 60
4.5. Derivatives of uv, u/v, u"......Page 63
4.6. Differentiation of Implicit Functions......Page 65
5.1. Determination of the Function......Page 67
5.2. Area. Rectangular Coordinates......Page 70
5.3. Area. Polar Coordinates......Page 72
5.4. Area. Parametric Equations......Page 74
6.1. Concept......Page 77
6.2. Slope......Page 80
6.3. Families......Page 81
6.4. Concurrency......Page 85
6.6. Angle Bisectors......Page 88
7. The Circle......Page 91
7.1. General Equations 8o......Page 0
7.2. Families of Circles......Page 94
7.3. Power of a Point......Page 100
7.4. Radical Axis......Page 102
8.1. General. Discussion......Page 106
8.2. Special Properties......Page 109
8.3. Equations of the Conics......Page 113
8.4. More General Equations......Page 116
8.5. Constructions I......Page 20
9. The Conies: Their Properties and Applications......Page 123
9.1. The Reflective Property......Page 124
9.2. Tangents......Page 127
* 9.3. Areas......Page 128
9.4. The Parabolic Cable......Page 130
9.5. Plane Motion of a Point......Page 131
9.6. LORAN......Page 135
10.1. Instantaneous Center......Page 138
10.2. The Trammel (Ladder)......Page 139
10.3. The Conchoid......Page 140
10.4. The Cycloids......Page 141
10.6. Linkage Motion......Page 146
10.8. Cams......Page 150
10.9. Line Motion Linkages......Page 152
10.10. The Lemniscate......Page 153
11.2. Rotation......Page 156
11.3. Illustrations......Page 157
11.4. Removal of the xy-Term......Page 159
11.5. Identification of Conics......Page 161
11.6. Diameters of Conics......Page 164
11.7. Principal Diameters......Page 166
12.1. Translations......Page 170
12.2. Rotations......Page 171
12.3. The Affine Linear Transformation......Page 174
12.4. Inversion......Page 180
12.5. The Joukowski Airfoil......Page 184
II. THREE-SPACE......Page 186
13.1. Coordinate Systems......Page 188
13.2. Distance......Page 191
13.3. Angle Between Two Line Segments......Page 192
13.4. Parallelism......Page 193
14.1. Definition......Page 195
14.2. Definition......Page 197
14.3. Families of Planes Through a Line. Projection Planes of a Line......Page 199
14.4. Normal to a Plane......Page 200
14.5. Distance from Point to Plane......Page 201
14.6. Determination of Equations of Planes......Page 203
14.8. Determination of Equations of Lines......Page 206
15.1. Definition......Page 211
15.2. Definition......Page 212
15.3. Graphical Representation of a Surface......Page 213
15.4. Families of Surfaces and Projection Cylinders......Page 215
16.1. Tangent Line and Normal Plane to a Curve......Page 218
16.2. Tangent Plane and Normal Line to a Surface......Page 221
17.1. Surfaces of Revolution......Page 225
17.2. Ruled Surfaces......Page 229
17.3. The Cone and Cylinder......Page 233
17.4. Gears......Page 237
18.1. General Discussion......Page 239
18.2. Illustrations......Page 240
19.1. Plane Sections......Page 247
19.3. Diametral Planes......Page 248
19.4. Principal Planes......Page 250
19.5. Classification of Quadric Surfaces......Page 252
Index......Page 256