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PROFESSOR: | Dr. Jenny X. Li
Office: 220 McAllist Building
Phone: 863-9106
office hours: Mon. 3:30pm-4:30pm, Wed. 3:30-4:30pm or by appointment
E-mail: li@math.psu.edu
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COURSE: | An introduction to rigorous mathematical proofs which
involving properties of real numbers, sequences, continuity, series of
function, differentiation and integration.
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TEXTBOOK: | Elementary Analysis: The Theory of Calculus
by Kenneth A. Ross 12th Ed., Springer
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REFERENCE: | Introduction to Analysis by Arthur Mattuck, latest edition
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PREREQUISITES: | Math 141
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| GRADE:
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- Homework and Quizes (25%): Every week.
- Midterm (35%): March 2 at regular lecture time.
- Final Exam (40%): Time and place will be announced.
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| POLICIES:
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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
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