Chegg and similar platforms have solutions for Apostol. However, be extremely cautious.
2.1 Real-Valued Functions of Several Variables * Exercises: 1-15 (pp. 43-45) * Solutions: + Exercise 3: $f(x, y) = x^2 + y^2$ + Exercise 9: $\nabla f(x, y) = (2x, 2y)$ 2.2 Partial Derivatives * Exercises: 1-19 (pp. 54-57) * Solutions: + Exercise 5: $\frac\partial f\partial x = 2x, \frac\partial f\partial y = 2y$ + Exercise 13: $\frac\partial^2 f\partial x^2 = 2, \frac\partial^2 f\partial y^2 = 2$ 2.3 The Gradient and the Derivative * Exercises: 1-13 (pp. 65-67) * Solutions: + Exercise 3: $\nabla f(x, y) = (2x, 2y), f'(x, y) = \beginpmatrix 2x & 2y \endpmatrix$ tom m apostol calculus volume 2 solutions
Several university professors maintain archival pages containing homework solutions for courses taught directly out of Apostol's textbook. These can be highly valuable as they often feature alternative explanations and added intuition not found in standard manuals. Online Mathematics Forums Chegg and similar platforms have solutions for Apostol
These are often written in clean LaTeX, making them easier to read than hand-written scans. 43-45) * Solutions: + Exercise 3: $f(x, y)
In Volume 2, Apostol categorizes problems differently than other authors:
Mapping spaces and calculating determinants.