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Lectures on integral calculus of functions of one variable and series theory
18. Taylor series
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Table of contents
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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Real analytic functions and their expansions into Taylor series
Real analytic functions and the property of infinite differentiability
Sufficient condition for the existence of a Taylor series. Expansions of exponent, sine, and cosine into a Taylor series
Taylor series expansion of a power function
Taylor series expansions of the logarithm and arcsine
19. Fourier series in Euclidean space
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20. Fourier series in the space of integrable functions
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References
Index
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