The fundamentals of mathematical analysis are a convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations.
It shows the utility of abstract concepts and teaches an understanding construction of proofs.
Topic to be cover:
Less abstract definitions and proofs, and gives application where possible.
More demanding and more mathematical maturity, it places more emphasis from the beginning on point-set topology and n-space, whereas point 1 is concerned primarily with analysis on the real line, saving for the last weeks work in 2 spaces (the plane) and its point set topology
Further instruction and practice in written and oral communication.
Principles of Mathematical Analysis 3rd ed. By McGraw-Hill
Mathematical Analysis 2nd ed. By Pearson Education
Calculus 4th ed. By California University
Multivariable Calculus, Differential Equations, and Honors of Differential Equations.
Problem sets (28 variants), Writing Assignment.