Introduction to mathematical analysis / Igor Kriz, Aleš Pultr

1, Preliminaries
2. Metric and topological spaces I
3. Multivariable differential calculus
4. Integration I: multivariable Riemann integral and basic ideas toward the Lebesgue integral
5. Integration II: measurable functions, measure and the techniques of Lebesgue integration
6. Systems of ordinary differential equations
7. Systems of linear differential equations
8. Line integrals and Green's theorem
9. Metric and topological spaces II
10. Complex analysis I: basic concepts
11. Multilinear algebra
12. Smooth manifolds, differential forms and Stokes' theorem
13. Complex Analysis II: further topics
14. Calculus of variations and the geodesic equation
15. Tensor calculus and Riemannian geometry
16. Banach and Hilbert spaces: elements of functional analysis
17. A few applications of Hilbert spaces
A. Linear algebra I: vector spaces
B. Linear algebra II: more about matrices.

Includes bibliographical references (p. 501) and indexes.

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The book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, the Lebesgue integral, vector calculus and differential equations. After having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today.-- Source other than Library of Congress.