1 Analytic Geometry in Three Dimensions -- 2 Vectors -- 3 Infinite Series -- 4 Partial Derivatives. Applications -- 5 Multiple Integration -- 6 Fourier Series -- 7 Implicit Function Theorems. Jacobians -- 8 Differentiation under the Integral Sign. Improper Integrals. -- 9 Vector Field Theory -- 10 Green's and Stokes' Theorems -- Appendix 1 -- Matrices and Determinants -- 1. Matrices -- 2. Matrices, Continued. Double Sums and Double Sequences -- 3. Determinants -- 4. Properties of Determinants -- 5. Cramer's Rule -- 6. The Rank of a Matrix. Elementary Transformations -- 7. General Linear Systems -- Appendix 2 -- Proofs of Theorems 6, 10, 16, and 17 of Chapter 2 -- Appendix 3 -- to the Use of a Table of Integrals -- A Short Table of Integrals -- Answers to Odd-Numbered Problems.