Book:Walter Ledermann/Multiple Integrals

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Walter Ledermann: Multiple Integrals

Published $1966$, Routledge & Kegan Paul.


Subject Matter


Contents

Preface
1. Line Integrals
1. Preliminary remarks about curves
2. Definition of a curvilinear integral
3. Area
Exercises
2. Double Integrals
1. Definition of a double integral
2. Double integrals over a rectangle
3. Double integrals over normal regions
4. Green's Theorem in two dimensions
5. Change of variables
6. Transformations of double integrals
7. Improper integrals
8. Volumes
Exercises
3. Surface Integrals
1. Preliminary remarks about surfaces
2. The area of a surface
3. Surface integrals
Exercises
4. Volume Integrals
1. Definition of a volume integral
2. Reduction to repeated integral
3. Gauss's Theorem (divergence theorem)
4. Change of variables
5. Stokes's Theorem
Exercises
Appendix
Solutions to Exercises
Index