A youtube Calculus Workbook (Part II)
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740306194
Table of contents: title: Content; title: Preface; title: 1. M1: Natural Logarithm and Exponential; title: 1.1. Natural Logarithm: definition and logarithm laws; title: 1.2. Calculus of Logarithms; title: 1.3. Logarithmic Differentiation; title: 1.4. One-to-one functions and inverse functions; title: 1.5. Finding inverse functions; title: 1.6. Calculus of inverse functions; title: 1.7. Natural Exponential: definition and properties; title: 1.8. Derivatives and integrals with exponentials; title: 1.9. Exponential and logarithmic equations and inequalities; title: 2. M2: More transcendental functions; title: 2.1. General exponential functions; title: 2.2. General logarithm functions; title: 2.3. Inverse trig functions: arcsine; title: 2.4. Inverse trig functions: other inverse trig functions; title: 2.5. Inverse trig functions: derivative and integrals; title: 2.6. Hyperbolic functions; title: 2.7. Inverse hyperbolic functions; title: 3. M3: Rule of De l’Hospital; title: 3.1. Rule of De L’Hospital: statement and proof; title: 3.2. Rule of de l’Hospital: examples (quotients); title: 3.3. Rule of De L’Hospital: indeterminate products; title: 3.4. Rule of De L’Hospital: indeterminate powers; title: 4. M4: Integration review and Integration by parts; title: 4.1. Review of Integration: basics and completing the square; title: 4.2. Review of Integration: trig formulas and manipulating fractions; title: 4.3. Integration by parts: indefinite integrals; title: 4.4. Integration by parts: definite integrals; title: 4.5. Integration by parts: one more example; title: 5. M5: Trigonometric integrals and trigonometric substitutions; title: 5.1. Powers of sine and cosine; title: 5.2. Products of sine and cosine; title: 5.3. (co)secant, (co)tangent and their powers; title: 5.4. Trig substitutions; title: 6. M6: Partial Fractions; title: 6.1. Partial fractions: generalities; long division; title: 6.2. only non-repeated linear factors; title: 6.3. with repeated linear factors; title: 6.4. with irreducible quadratic factors; title: 6.5. with repeated irreducible quadratic factors; title: 7. M7: Improper Integrals; title: 7.1. Improper integrals of type I; title: 7.2. Improper integrals of type II; title: 7.3. Comparison for improper integrals; title: 8. M8: Parametric Curves; title: 8.1. Introduction to parametric curves; title: 8.2. Tangent lines to parametric curves; title: 8.3. Symmetry; concavity; title: 8.4. plane areas; title: 8.5. arc length; title: 8.6. Surface area of surface of revolutions; title: 9. M9: Polar Curves; title: 9.1. Polar coordinates; title: 9.2. Polar regions and polar curves; title: 9.3. tangent lines to polar curves; title: 9.4. arc length for polar curves; title: 9.5. area enclosed by a sector of a polar curve; title: 10. M10: Sequences and Series; title: 10.1. Sequences; title: 10.2. limit of sequences; title: 10.3. abstract properties of sequences; title: 10.4. limit of sequences defined inductively; title: 10.5. fixed points and limits of sequences defined inductively; title: 10.6. Series; title: 10.7. Series: a criterion for divergence; title: 10.8. Geometric Series; title: 10.9. Telescoping sums; title: 11. M11: Integral Test and Comparison Test; title: 11.1. Integral Test; title: 11.2. p-series; title: 11.3. Estimating the sum; title: 11.4. Direct Comparison Test; title: 11.5. Limit Comparison Test; title: 11.6. Estimating sums revisited; title: 12. M12: Alternating Series Test; title: 12.1. Alternating Series Test; title: 12.2. Absolute and conditional convergence; title: 12.3. Estimating sums with the Alternating Series Test; title: 13. M13: Ratio and Root Tests; title: 13.1. Ratio Test (Statement and proof); title: 13.2. Ratio Test: examples; title: 13.3. Root Test; title: 13.4. Strategies to test series for convergence (M14); title: 14. M15: Power Series and Taylor Series; title: 14.1. Power series; title: 14.2. Intervals of convergence; title: 14.3. Representation of functions as power series; title: 14.4. term-by-term differentiation and integration of power series; title: 14.5. more power series representations; title: 14.6. Power series and sums of numerical series; title: 14.7. Taylor and MacLaurin series; title: 14.8. Examples of Taylor Series; title: 14.9. Convergence of Taylor Series; title: 14.10. More examples of Taylor Series; title: 15. M16: Applications of power series; title: 15.1. Power series and sums of numerical series; title: 15.2. Estimating integrals; title: 15.3. Calculating limits; title: 15.4. More power series: products; title: 15.5. More power series: Binomial series; title: 16. Notations; title: 17. Index; title: 18. Endnotes