Multiple Integrals

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. Transformation of double integrals. - 7. Improper integrals. - 8. Volumes. - Exercises. - 3. Surface Integrals. - 1. Preliminary remarks about surfaces. - 2. The area of 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. - Solutions to Exercises. Language: English