At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous functions and emphasize the proofs’ development. Define the derivative of a function of one and several variable, prove various theorems about the derivatives of functions and emphasize the proofs’ development. Define a cluster point and an accumulation point, prove, Rolles’s Theorem, extreme value theorem, boundedness theorem and the Mean Value theorem and emphasize the proofs’ development. Define Multiple and surface integrals and their evaluation techniques.
Principles of Mathematical Analysis by 
