Intermediate Calculus

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.