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Lesson 16A Infinite Series Absolute Convergence, Ratio Test and Root Test

Somali: Somalibesttutor waxaad ka heleysaa koorsooyin Xisaab iyo Kimisreti lagu sharxay af Soomaali, waxaadna ka baran kartaa meel kasta oo aad dunida ka joogto. English: Somalibesttutor is an online educational platform that offers high-quality courses of Mathematics and Chemistry to Somali students at any level wherever they are. Subscribe, Share and Like to get the next videos Facebook: https://www.facebook.com/Somalionline... Contact us: [email protected] Enjoy! INTRODUCTON Calculus 2 (Integral Calculus) 1. Antiderivatives and Indefinite Integration o Definition of Antiderivative o Definition of Indefinite Integration o Integral Notation o Integration Rules o Differential Integrals o General Solution o Particular Solution o Slope Fields ( Directional Field ) o Projectiles o Position Function o Velocity Function o Acceleration Function 2. Area under a Curve o Sigma Notation o Sigma Properties o Summations o Series to Sigma Notation o Lower Sum and Upper Sum o Infinite Number of Rectangles (Limit) 3. Riemann Sums and Definite Integrals o Definition of Riemann Sums o Definite Integrals 4. The Fundamental Theorem of Calculus o Fundamental Theorem of Calculus o Average Value of a Function on a closed Interval o Mean Value Theorem for Integrals o Second Fundamental Theorem of Calculus 5. Integration Techniques: Integration by Substitution o Integration by Substitution ( Indefinite Integrals ) o Integration by Substitution ( Definite Integrals ) 6. Integration Techniques: Integration of Even and Odd Functions o Definition of Even Function and Odd Function o Integrating Even Functions o Integrating Odd Functions 7. Numerical Integration o Trapezoidal Rule o Simpson’s Rule o Parabola Rule o Trapezoidal Error o Simpson’s Error 8. Integration of Natural Logarithm and Trigonometric Functions o Integration of Natural Logarithmic Functions o Integration of Trigonometric Functions 9. Integration of Inverse Trigonometric Functions o Integration of Inverse Trigonometric Functions by Using Substitution o Integration of Inverse Trigonometric Functions by Using Completing the Square 10. Hyperbolic Functions o Definition of Hyperbolic Functions o Hyperbolic Identities o Derivatives and Integrals of Hyperbolic Functions o Inverse Hyperbolic Functions 11. Infinite Sequences (Convergent and Divergent Sequences) o Definition of the Limit of Infinite Sequences o Definition of Convergence and Divergences o Properties of the Limit of Infinite Sequences o Squeeze Theorem for Infinite Sequences o Absolute Value of Infinite Sequences o Monotonic Sequences o Bounded Sequences 12. Infinite Series o Definition of the Limit of Infinite Series o Telescoping Series o Geometric Series o Harmonic Series o Divergence Test ( Corrolary Theorem ) o Properties of convergent Series 13. Infinite Series o Integral Test for Convergence and Divergence o P-Series 14. Infinite Series o Comparison Test for Infinite Series o The Limit Comparison Test for Infinite Series 15. Infinite Series o Alternating Series Test for Convergence o Alternating Harmonic Series 16. Infinite Series o Absolute Convergence o Ratio Test o Root Test 17. Infinite Series o Power Series o Interval of Convergence (Domain of the Function). o Radius of Convergence o Calculus of Power Series o Integration of Power Series o Differentiation of Power Series 18. Infinite Series o Definition of Taylor and Macluarin Series o Differentiation of Taylor and Macluarin Series o Common Macluarin Series and Alternative Method 19. Infinite Series o Approximation of Function by Taylor Polynomials o Remainder (Error) of Taylor Polynomials o When does a Function have Taylor Polynomials Representation? 20. The Area under a Curve o Area under a Curve o Area enclosed by Curves and its Properties 21. The Integration of Volumes o Volumes of Revolution o Disk Method o Washer Method o Shell Method 22. L’hopital’s Rule o L’hopital’s Rule