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Lectures on integral calculus of functions of one variable and series theory
20. Fourier series in the space of integrable functions
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Оглавление
Preface
Video lectures
1. Antiderivative and indefinite integral
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2. Integration of rational functions
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3. Integration of trigonometric functions
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4. Integration of irrational functions
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5. Definite integral and Darboux sums
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6. Classes of integrable functions. Properties of a definite integral
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7. Integral with a variable upper limit. Newton-Leibniz formula
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8. Calculation of areas and volumes
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9. Curves and calculating their length
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10. Improper integrals: definition and properties
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11. Absolute and conditional convergence of improper integrals
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12. Numerical series
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13. Convergence tests for numerical series with non-negative terms
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14. Alternating series and conditional convergence
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15. Functional sequences and series
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16. Properties of uniformly converging sequences and series
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17. Power series
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18. Taylor series
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19. Fourier series in Euclidean space
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20. Fourier series in the space of integrable functions
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Euclidean space of integrable functions
Constructing an orthonormal sequence of integrable functions
Constructing a formal Fourier series for integrable functions
Convergence of the Fourier series in mean square in the case of periodic continuous functions
Convergence of the Fourier series in mean square in the case of piecewise continuous functions
Pointwise convergence of the Fourier series
Uniform convergence of the Fourier series
Decreasing rate of Fourier coefficients for differentiable functions
References
Index
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