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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 AMS (Journals and MathSciNet): The American Mathematical Society is a professional society that advances research and connects the diverse global mathematical community through publications, meetings and conferences, professional services and awareness programs. AMS peer-reviewed journals are of the highest quality in mathematical research and cover a broad range of mathematics. MathSciNet is 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.
Global Science Press Journals: Communications in Computational Physics, Journal of Computational Mathematics, Numerical Mathematics: Theory, Methods and Applications, East Asian Journal on Applied Mathematics, Advances in Applied Mathematics and Mechanics
SIAM journals: Society for Industrial and Applied Mathematics (SIAM) is a nonprofit organization that conveys 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.
Project Euclid Journals: Project Euclid, now jointly managed by the Cornell Library and Duke University Press, was originally created to provide a platform for small scholarly publishers of mathematics and statistics journals to move from print to electronic in a cost-effective way.
AIMS Journals: The American Institute of Mathematical Sciences (AIMS) is an international organization for the advancement and dissemination of mathematical and applied sciences. This publisher is known for its Discrete and Continuous Dynamical Systems journal.
IP Journals: International Press of Boston (IP), Inc. is a scholarly publishing company founded near Harvard University. It currently publishes 20 peer-reviewed e-journals and two annual books dealing with various fields of current research in pure and applied mathematics, including Acta Mathematica, Journal of Differential Geometry.
MSP Journals: Mathematical Sciences Publishers (MSP) is focused on developing software for publishing and on assisting and creating top-level scientific-research publications and strives to offer the highest quality at the lowest sustainable prices. Its top-ranked journals include Geometry & Topology, Algebraic & Geometric Topology, Comm. in Appl. Math. and Computational Science.
EMS Journals: The European Mathematical Society(EMS) is a very prestigious society for mathematicians in Europe. It is a non-profit organization dedicated to the publication of high-quality peer-reviewed journals and high-quality books, on all academic levels and in all fields of pure and applied mathematics.