Author(s): M. L. Krasnov, A. I. Kiselev, G. I. Makarenko
Publisher: Mir Publishers
Year: 1983
Language: English
City: Moscow
Preface
CHAPTER I. THE VECTOR FUNCTION OF A SC A LA R ARGUMENT
Sec. 1. The hodograph of a vector function
Sec. 2. The limit and continuity of a vector function of a scalar argument
Sec. 3. The derivative of a vector function with respect to a scalar argument
Sec. 4. Integrating a vector function of a scalar argument
Sec. 5. The first and second derivatives of a vector with respect to the arc length of a curve. The curvature of a curve. The principal normal
Sec. 6. Osculating plane. Binormal. Torsion. The Frenet formulas
CHAPTER II. SCALAR FIELDS
Sec. 7. Examples of scalar fields. Level surfaces and level lines
Sec. 8. Directional derivative
Sec. 9. The gradient of a scalar field
CHAPTER III. VECTOR FIELDS
Sec. 10. Vector lines. Differential equations of vector lines
Sec. 11. The flux of a vector field. Methods of calculating flux
Sec. 12. The flux of a vector through a closed surface. The Gauas-Ostrogradaky theorem
Sec. 13. The divergence of a vector field. Solenoidal fields
Sec. 14. A line integral in a vector field. The circulation of a vector field
Sec. 15. The curl (rotation) of a vector field
Sec. 16. Stokes' theorem
Sec. 17. The independence of a line integral of the path of integration. Green’s formula
CHAPTER IV. POTENTIAL FIELDS
Sec. 18. The criterion for the potentiality of a vector field
Sec. 19. Computing a line integral in a potential field
CHAPTER V. THE HAMILTONIAN OPERATOR. SECOND-ORDER DIFFERENTIAL OPERATIONS. THE LAPLACE OPERATOR
Sec. 20. The Hamiltonian operator del
Sec. 21. Second-order differential operations. The Laplace operator
Sec. 22. Vector potential
CHAPTER VI. CURVILINEAR COORDINATES. BASIC OPERATIONS OF VECTOR ANALYSIS IN CURVILINEAR COORDINATES
Sec. 23. Curvilinear coordinates
Sec. 24. Basic operations of vector analysis in curvilinear coordinates
Sec. 25. The Laplace operator in orthogonal coordinates
ANSWERS
APPENDIX I
APPENDIX II
BIBLIOGRAPHY
INDEX
