Introduction to Analysis II

Introduction to Analysis II is the sequel to Introduction to Analysis I, and together these two courses constitute the foundations of real analysis in mathematics. This course is designed to prepare students for future advanced analysis and functional analysis courses. It lays the foundation for several other areas, such as complex analysis, topology, dynamical systems, quantum mechanics, and mathematical statistics. The rigorous treatment of the subject in terms of theory and examples gives students the flavor of mathematical reasoning and intuition for other advanced topics in mathematics. Differentiability and Riemann integrals are introduced and their properties are studied in details. Topics covered are open, closed, and compact sets of real numbers. Sequences and series of functions, point wise and uniform convergence. Power series and Taylor series. Metric spaces: basic notions generalized from the setting of the real numbers. 

Schedule and Grading Breakup:

Lecture Schedule:  Monday/Wednesday  3:00-4:15  SDSB-305

Office Hours: TBA
Assignment(s): 15%

Due dates: 23rd Sept for A1, 7th Oct for A2, 21st Oct for A3, 11th Nov for A4, 25th Nov for A5

Quiz(s): 20%

30th Sep for Q1, 14th Oct for Q2, 18th Nov for Q3, 29th Nov for Q4

Project: 10% (dates for presentations will be announced later)

Every student will be assigned a topic/Theorem. Your task is to write a short note and a presentation on your assigned topic. The write-up should contain your original explanation with elaborated examples. Topics will be announced later.

Midterm Examination: 20% (28th Oct class time)

Final Examination (Written and Oral): 35% (As per Zambeel)

Dates for graded components:

The date for assignments, quizzes and exams will be strictly adhered to and late submissions will not be entertained, unless faced with some unforeseen circumstances.