PROFESSOR:  Dr. Jenny X. Li
Office: 220 McAllist Building
Phone: 8639106
office hours: Tue. 11:3012:30, Friday 11:3012:30 or by appointment
Email: li@math.psu.edu

COURSE:  An introduction to rigorous mathematical proofs which
involving properties of real numbers, sequences, continuity, series of
function, differentiation and integration.

TEXTBOOK:  Elementary Analysis: The Theory of Calculus
by Kenneth A. Ross 2th edition., Springer

REFERENCE:  Introduction to Analysis by Arthur Mattuck, latest edition

PREREQUISITES:  Math 141

GRADE:

 Homework and Quizzes (25%): Every week.
 Midterm (35%): Oct.15 at regular lecture time.
 Final Exam (40%): Time and place will be announced.

POLICIES:

 NO late homework will be accepted, but the lowest grade of homework will be dropped. Also there will be NO makeup midterm.
 Quizzes will occur whenever it is necessary. They will be announced in advance, also No makeup quizzes.
 Bonus questions will be given throughout the semester which will be added to the final grade.
 NO books, notes, calculators or other electronic devices are permitted in the quizzes, midterm or final exam.

TENTATIVE OUTLINE: 
 PART I Introduction
 Review
 The sets of Naturally and Rational Numbers
 The set of Real Numbers
 The Completeness Axiom
 PART II Sequences
 Limits of Sequence
 Monotone Sequences and Cauchy Sequences
 Lim sup's and lim inf's
 Alternating Series and Integral Tests
 PART III Continuity
 Continuous Functions
 Properties of Continuous Functions
 Uniform Continuity
 Limits of Functions
 Topological Concepts in Metric Spaces
 More on Metric Space: Continuity and Connectedness
 PART IV Sequences and Series of Functions
 Uniform Convergence
 Differentiation and Integration of Power Series
 Weierstrass's Approximation Theorem
 PART V Differentiation
 Basic Properties of the Derivative
 The Mean Value Theorem
 L'Hospital's Rule
 Taylor's Theorem
