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Lectures on integral calculus of functions of one variable and series theory
1. Antiderivative and indefinite integral
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Preface
Video lectures
1. Antiderivative and indefinite integral
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Definition of an antiderivative and indefinite integral
Table of indefinite integrals
The simplest properties of an indefinite integral
Change of variables in an indefinite integral
Formula of integration by parts
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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References
Index
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