Author(s): A. S. Solodovnikov, G. A. Toropova
Publisher: Mir Publishers
Year: 1990
Language: English
City: Moscow
Front Cover
Title Page
CONTENTS
PREFACE
Part One ANALYTIC GEOMETRY
Chapter 1 VECTORS IN THE PLANE AND IN SPACE. CARTESIAN COORDINATE SYSTEM
1.1. VECTORS
1.2. VECTOR BASIS IN THE PLANE AND IN SPACE
1.3. CARTESIAN COORDINATE SYSTEM ON A STRAIGHT LINE, IN THE PLANE, AND IN SPACE
Exercises to Chapter 1
Chapter 2 RECTANGULAR CARTESIAN COORDINATES. SIMPLE PROBLEMS IN ANALYTIC GEOMETRY
2.1. PROJECTION OF A VECTOR ON AN AXIS
2.2. RECTANGULAR CARTESIAN COORDINATE SYSTEM
23. SCALAR PRODUCT OF VECTORS
2.4. POLAR COORDINATES
Exercises to Chapter 2
Chapter 3 DETERMINANTS
3.1. SECOND-ORDER DETERMINANTS. CRAMER’S RULE
3.2. THIRD-ORDER DETERMINANTS
3.3. nth-ORDER DETERMINANTS
3.4. TRANSPOSITION OF A DETERMINANT
3.5. EXPANSION OF A DETERMINANT BY ROWS AND COLUMNS
3.6. PROPERTIES OF nth-ORDER DETERMINANTS
3.7. MINORS. EVALUATION OF nth-ORDER DETERMINANTS
3.8. CRAMER'S RULE FOR AN n x n SYSTEM
3.9. A HOMOGENEOUS n x n SYSTEM
Exercises to Chapter 3
Chapter 4 THE EQUATION OF A LINE IN THE PLANE. A STRAIGHT LINE IN THE PLANE
4.1. THE EQUATION OF A LINE
4.2. PARAMETRIC EQUATIONS OF A LINE
43. A STRAIGHT LINE IN THE PLANE AND ITS EQUATION
4.4. RELATIVE POSITION OF TWO STRAIGHT LINES IN THE PLANE
4.5. PARAMETRIC EQUATIONS OF A STRAIGHT LINE
4.6. DISTANCE BETWEEN A POINT AND A STRAIGHT LINE
4.7. HALF-PLANES DEFINED BY A STRAIGHT LINE
Exercises to Chapter 4
Chapter 5 CONIC SECTIONS
5.1. THE ELLIPSE
5.2. THE HYPERBOLA
53. THE PARABOLA
Exercises to Chapter 5
Chapter 6 THE PLANE IN SPACE
6.1. THE EQUATION OF A SURFACE IN SPACE. THE EQUATION OF A PLANE
6.2. SPECIAL FORMS OF THE EQUATION OF A PLANE
6.3. DISTANCE BETWEEN A POINT AND A PLANE. ANGLE BETWEEN TWO PLANES
6.4. HALF-SPACES
Exercises to Chapter 6
Chapter 7 A STRAIGHT LINE IN SPACE
7.1. EQUATIONS OF A LINE IN SPACE. EQUATIONS OF A STRAIGHT LINE
7.2. GENERAL EQUATIONS OF A STRAIGHT LINE
7.3. RELATIVE POSITION OF TWO STRAIGHT LINES
7.4. RELATIVE POSITION OF A STRAIGHT LINE AND A PLANE
Exercises to Chapter 7
Chapter 8 QUADRIC SURFACES
8.1. THE ELLIPSOID
8.2. THE HYPERBOLOID
8.3. THE PARABOLOID
Part Two LINEAR ALGEBRA
Chapter 9 SYSTEMS OF LINEAR EQUATIONS
9.1. ELEMENTARY TRANSFORMATIONS OF A SYSTEMOF LINEAR EQUATIONS
9.2. GAUSSIAN ELIMINATION
Exercises to Chapter 9
Chapter 10 VECTOR SPACES
10.1. ARITHMETIC VECTORS AND OPERATIONS WITH THEM
10.2. LINEAR DEPENDENCE OF VECTORS
10.3. PROPERTIES OF LINEAR DEPENDENCE
10.4. BASES IN SPACE R"
10.5. ABSTRACT VECTOR SPACES
Exercises to Chapter 10
Chapter 11 MATRICES
11.1. RANK OF A MATRIX
11.2. PRACTICAL METHOD FOR FINDING THE RANK OF A MATRIX
11.3. THEOREM ON THE RANK OF A MATRIX
11.4. RANK OF A MATRIX AND SYSTEMS OF LINEAR EQUATIONS
11.5. OPERATIONS WITH MATRICES
11.6. PROPERTIES OF MATRIX MULTIPLICATION
11.7. INVERSE OF A MATRIX
11.8. SYSTEMS OF LINEAR EQUATIONS IN MATRIX FORM
Exercises to Chapter 11
Chapter 12 EUCLIDEAN VECTOR SPACES
12.1. SCALAR PRODUCT. EUCLIDEAN VECTOR SPACES
12.2. SIMPLE METRIC CONCEPTS IN EUCLIDEAN VECTOR SPACES
12.3. ORTHOGONAL SYSTEM OF VECTORS. ORTHOGONAL BASIS
12.4. ORTHONORMAL BASIS
Exercises to Chapter 12
Chapter 13 AFFINE SPACES. CONVEX SETS AND POLYHEDRONS
13.1 THE AFFINE SPACE A"
13.2. SIMPLE GEOMETRIC FIGURES IN An
13.3. CONVEX SETS OF POINTS IN A". CONVEX POLYHEDRONS
Exercises to Chapter 13
INDEX
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