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This course teaches fundamental principles of mathematical analysis for one-variable functions, based on rigorous theory. Topics include the real number system, sequences and series, limits, basic topology, real-valued functions, continuity and differentiation, Riemann-Stieltjes integrals, sequences and series of functions, uniform convergence, power series, Fourier series, differentiation and integration of multivariate functions.
Principles of Mathematical Analysis by 
Principles of Mathematical Analysis by 
Understanding Analysis by 
Foundations of Mathematical Analysis by 
Mathematical Analysis by MathSciNet: an electronic publication offering access to a carefully maintained and easily searchable database of reviews, abstracts and bibliographic information for much of the mathematical sciences literature. Link to MathSciNet
SIAM: Society for Industrial and Applied Mathematics (SIAM) was incorporated in 1952 as a nonprofit organization to convey useful mathematical knowledge to other professionals who could implement mathematical theory for practical, industrial, or scientific use. SIAM fosters the development of applied mathematical and computational methodologies needed in various application areas. Link to SIAM