**I****nstructor: Prof.Dr.Kenan TaÅŸ**

**Catalogue Description: **The real line and Euclidean space. The topology of Euclidean space (open sets, interior of a set, closed sets, accumulation points, closure of a set, boundary of a set, sequences, completeness). Compact and connected sets (compactness, the Heine-Borel theorem, nested set property, path-connected sets, connected sets). Continuous mappings (continuity, images of compact and connected sets, operations on continuous mappings, the boundedness of continuous functions on compact sets, uniform continuity, differentiation and integration of functions of one variable). Uniform convergence (pointwise and uniform convergence, the Weierstrass M-test, integration and differentiation of series, the space of continuous functions, the Arzela-Ascoli theorem).

**Textbook: 1) J. E. Marsden and M.J. Hoffman, Elementary classical analysis, W.H. Freeman, 1993.**

**2) John Srdjan Petrovic, Advanced Calculus, Theory and Practice, 2014, CRC Press**

### You can download pdf-file of the first textbook from the following address:

### http://math.cankaya.edu.tr/~kenan/Elementary%20Classical%20Analysis.pdf

**Reference Book:** R.C. Buck, Advanced calculus, McGraw-Hill, 1956.

### SAMPLE Midterm Questions and Solutions is : here

**Evaluation:**

Midterm Exam : %30

Take Homes and Presentations: %30 * *

Final: %40

**Midterm EXAM ****APRIL 24, 2017 Monday **

**Warning : Students are responsible for checking this web page regularly for announcements and homework assignments.**

**Attendance: Is required and your grade will be penalized if you miss too many classes. **

**Remember to sign -in sheet every class. **