In the second edition of Apostol's Mathematical Analysis he comments: "The material on line integrals, vector analysis, and surface integrals has been deleted." The contents from the 1st Edition (I think, stolen from an Amazon comment) are: Real and Complex Number Systems; Fundamental Notions of Set Theory; Elements of Point-Set Theory; The Concepts of Limit and Continuity; Differentiation of Real-Valued Functions; Differentiation of Functions of Several Variables; Applications of Partial Differentiation; Functions of Bounded Variation, Rectifiable Curves, and Connected Sets; Riemann-Stieltjes Integration Theory; Multiple Integrals and Line Integrals; Vector Analysis; Infinite Series and Products; Sequences of Functions; Improper Riemann-Stieltjes Integrals; Fourier Series and Fourier Integrals; Cauchy's Theorem and Calculus of Residues; & the contents of the second edition are: Real and Complex Number Systems; Fundamental Notions of Set Theory; Elements of Point-Set Theory; Limits and Continuity; Derivatives; Functions of Bounded Variation & Rectifiable Curves; The Riemann-Stieltjes Integral; Infinite Series and Products; Sequences of Functions; The Lebesgue Integral; Fourier Series and Fourier Integrals; Multivariable Differential Calculus Implicit Functions & Extremum Problems Multiple Riemann Integrals; Multiple Lebesgue Integrals; Vector Analysis; Cauchy's Theorem and the Residue Calculus; so really the only major differences are the exclusion of vector analysis, line & surface integrals to what you gain in Lebesgue integration. My question is whether the material on line & surface integrals & the vector analysis material from the first edition is any better than the exposition he gives of in his Calculus II? Keep in mind that the differences between the first edition of his calculus & second aren't really that major, a bit more linear algebra (I only browsed the book but it looked pretty close to the second edition) but the difference between his Calculus & Mathematical Analysis books is pretty big so I really have no idea whether he approaches the material from a higher perspective. If you've ever compared the old & new editions of volume 2 of Courant you'll see the drastic change in the approach to the material so I can only hope for a similar occurrence with Apostol.