Absolute Analysis

Introduction 1
I. Linear Algebra 4
1. The Linear Space with Real Multiplier Domain 4
2. Finite Dimensional Linear Spaces 10
3. Linear Mappings 13
4. Bilinear and Quadratic Functions 26
5. Multilincar Functions 41
6. Metrization of affine Space 56
II. Differential Calculus 74
1. Derivatives and Differential 74
2. Taylor's Formula 80
3. Partial Differentiation 95
4. Implicit Functions 99
III. Integral Calculus 118
1. The Affine Integral 118
2. Theorem of Stokes 124
3. Applications of Stoke's Theorem 140
IV. Differential Equations 148
1. Normal System 148
2. The General Differential Equation of First Order 158
3. The Linear Differential Equation of Order One 163
V. Theory of Curves and Surfaces 181
1. Regular Curves and Surfacer 181
2. Curve Theory 183
3. Surface Theory 193
4. Vectors and Tensor 202
5 Integration of the Derivative Formulas 221
6. Thcorcma Egregium 228
7. Parallel Translation 232
8. The Gauss-Bonnet Theorem 240
VI. Riemannian Geometry 247
1. Affine Differential Geommtry 248
2. Riemannian Geometry 257
Bibliography 261
Index 264