The present course of Mathematical Analysis covers the Di§erential Calculus part only. It is assumed that students have the basic skills to compute simple limits, di§erentials and the integrals of some elementary functions.

Contents

• Chapter 1. The real line.
• Chapter 2. Series of numbers
• Chapter 3. Sequences and series of functions
• Chapter 4. Taylor series
• Chapter 5. Power series
• Chapter 6. The normed space R m
• Chapter 7. Partial derivatives. Di§erentiability
• Chapter 8. Taylorís formula for several variables.
• Chapter 9. Contractions and fixed points
• Chapter 10. Local extremum points
• Chapter 11. Implicitly deÖned functions

Summary on tutorial Mathematical analysis I (differential calculus)

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