Book:Walter Ledermann/Multiple Integrals

Subject Matter

 * Integral Calculus

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