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.