Handbook of mathematics for engineers and scienteists part 2

Below, the graphs of the inverse hyperbolic functions are given. These are obtained from the graphs of the corresponding hyperbolic functions by mirror reflection with respect to the straight line y = x (with the domain of each function being taken into account). | Contents vii . Line and Plane in Space. 124 . Plane in Space . 124 . Line in Space . 131 . Mutual Arrangement of Points Lines and Planes . 135 . Quadric Surfaces Quadrics . 143 . Quadrics Canonical Equations . 143 . Quadrics General Theory . 148 References for Chapter 4 . 153 5. Algebra. 155 . Polynomials and Algebraic Equations. 155 . Polynomials and Their Properties . 155 . Linear and Quadratic Equations. 157 . Cubic Equations. 158 . Fourth-Degree Equation. 159 . Algebraic Equations of Arbitrary Degree and Their Properties . 161 . Matrices and Determinants . 167 . Matrices . 167 . Determinants . 175 . Equivalent Matrices. Eigenvalues . 180 . Linear Spaces . 187 . Concept of a Linear Space. Its Basis and Dimension . 187 . Subspaces of Linear Spaces . 190 . Coordinate Transformations Corresponding to Basis Transformations in a Linear Space . 191 . Euclidean Spaces . 192 . Real Euclidean Space. 192 . Complex Euclidean Space Unitary Space . 195 . Banach Spaces and Hilbert Spaces . 196 . Systems of Linear Algebraic Equations. 197 . Consistency Condition for a Linear System . 197 . Finding Solutions of a System of Linear Equations . 198 . Linear Operators . 204 . Notion of a Linear Operator. Its Properties . 204 . Linear Operators in Matrix Form. 208 . Eigenvectors and Eigenvalues of Linear Operators . 209 . Bilinear and Quadratic Forms . 213 . Linear and Sesquilinear Forms . 213 . Bilinear Forms . 214 . Quadratic Forms. 216 . Bilinear and Quadratic Forms in Euclidean Space . 219 . Second-Order Hypersurfaces . 220 . Some Facts from Group Theory . 225 . Groups and Their Basic Properties . 225 . Transformation Groups . 228 . Group Representations. 230 References for Chapter 5 . 233 viii Contents 6. Limits and Derivatives . 235 . Basic Concepts of Mathematical Analysis . 235 .