# Mathematical analysis. Differential calculus

#### Detalii

Anul apariției
2014
Autor(i)
Dan Dăianu
Pagini
492
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#### Descriere

Scrisă într-un limbaj elevat, dar pe deplin accesibilă, presărată cu sute de exemple care lămuresc materialul teoretic al acestei discipline fundamentale, răspunzând şi cerinţelor actuale ale învăţării prin exemple, cartea se constituie într-un instrument deosebit de util pentru studenţii unei universităţi de prestigiu.

CONTENTS

Preface

Part I. Analysis of Function of a Single Real Variable

1. Numerical Sequences and Series

- 1.1. Sequences

- 1.2. Definitions. general Criteria

- 1.3. Series with Nonnegative terms

- 1.4. Approximate Computation of Sums

- 1.5. Improper Integrals and Series

- 1.6. Finite Products

- 1.7. Solved Problems

- 1.8. Exercises

1. Approximations with Taylor Polynomials

- 2.1. Derivatived

- 2.2. Differentiability

- 2.3. Taylor’s Formula

- 2.4. Approximation of Functions

- 2.5. Finding the Extrema

- 2.6. Algebric Application

- 2.7. Solved Problems

- 2.8. Exercises

1. Sequences and Series of Functions

- 3.1. Convergence of Sequences of Functions

- 3.2. Series of Functions

- 3.3. Powers Series

- 3.4. Taylor Series

- 3.5. Other Polynomial Approximations

- 3.6. Fourier Series

- 3.7. Solved Problems

- 3.8. Exercises

1. Metric Spaces. Fixed Point Theorems

- 4.1. Metrics, Norms, Inner-products

- 4.2. Elements of Topology

- 4.3. Sequences

- 4.4. Fixed Point Theorems

- 4.5. Solved Problems

- 4.6. Exercises

Part II. Analysis of Functions of Several Real Variables

1. Limit and continuity in

- 5.1. Limits of Sequences

- 5.2. Vectorial Functions

- 5.3. Limit of a Function

- 5.4. Continuous Functions

- 5.5. Solved Problems

- 5.6. Exercises

1. Differentiable mapping

- 6.1. Partial Derivatives

- 6.2. Directional Derivatives

- 6.3. Differentiability

- 6.4. The Differentials and Derivatives of Composite Functions

- 6.5. Homogenous Functions

- 6.6. Differential of Higher Order

- 6.7. Elements of calculus in the Teheory of Fields

- 6.8. Solved Problems

- 6.9. Exercises

1. Differentiable isomorphisms

- 7.1. Regular transformations

- 7.2. Implicit Functions

- 7.3. Functional Dependence

- 7.4. Changes of Variables

- 7.5. Solved problems

- 7.6. Exercises

1. Polynomial approximations

- 8.1. Taylor’s Formula

- 8.2. Local Extrema

- 8.3. Conditional extrema

- 8.4. Solved Problems

- 8.5. Exercises

Bibliography

Index