Books on analysis can be found in the Mathemathics Library Stacks shelved under call number range 515 to 516.
"Analysis is a broad area of mathematics with roots in calculus, inequalities, and other classical subjects. Today Analysis includes measure theory, complex variables, ordinary and partial differential equations, harmonic analysis, probability, dynamical systems, and other parts of mathematics." from Professor John P. D'Angelo.
See the Department of Mathematics Analysis page for the departmental faculty with interest in Analysis.