A youtube Calculus Workbook (Part II)
Publisher: Bookboon
Published: 2013
ISBN-13: 9788740306194
Table of contents: title: Innhold; title: Preface; title: M1: Natural Logarithm and Exponential; title: Natural Logarithm: definition and logarithm laws; title: Calculus of Logarithms; title: Logarithmic Differentiation; title: One-to-one functions and inverse functions; title: Finding inverse functions; title: Calculus of inverse functions; title: Natural Exponential: definition and properties; title: Derivatives and integrals with exponentials; title: Exponential and logarithmic equations and inequalities; title: M2: More transcendental functions; title: General exponential functions; title: General logarithm functions; title: Inverse trig functions: arcsine; title: Inverse trig functions: other inverse trig functions; title: Inverse trig functions: derivative and integrals; title: Hyperbolic functions; title: Inverse hyperbolic functions; title: M3: Rule of De l’Hospital; title: Rule of De L’Hospital: statement and proof; title: Rule of de l’Hospital: examples (quotients); title: Rule of De L’Hospital: indeterminate products; title: Rule of De L’Hospital: indeterminate powers; title: M4: Integration review and Integration by parts; title: Review of Integration: basics and completing the square; title: Review of Integration: trig formulas and manipulating fractions; title: Integration by parts: indefinite integrals; title: Integration by parts: definite integrals; title: Integration by parts: one more example; title: M5: Trigonometric integrals and trigonometric substitutions; title: Powers of sine and cosine; title: Products of sine and cosine; title: (co)secant, (co)tangent and their powers; title: Trig substitutions; title: M6: Partial Fractions; title: Partial fractions: generalities; long division; title: only non-repeated linear factors; title: with repeated linear factors; title: with irreducible quadratic factors; title: with repeated irreducible quadratic factors; title: M7: Improper Integrals; title: Improper integrals of type I; title: Improper integrals of type II; title: Comparison for improper integrals; title: M8: Parametric Curves; title: Introduction to parametric curves; title: Tangent lines to parametric curves; title: Symmetry; concavity; title: plane areas; title: arc length; title: Surface area of surface of revolutions; title: M9: Polar Curves; title: Polar coordinates; title: Polar regions and polar curves; title: tangent lines to polar curves; title: arc length for polar curves; title: area enclosed by a sector of a polar curve; title: M10: Sequences and Series; title: Sequences; title: limit of sequences; title: abstract properties of sequences; title: limit of sequences defined inductively; title: fixed points and limits of sequences defined inductively; title: Series; title: Series: a criterion for divergence; title: Geometric Series; title: Telescoping sums; title: M11: Integral Test and Comparison Test; title: Integral Test; title: p-series; title: Estimating the sum; title: Direct Comparison Test; title: Limit Comparison Test; title: Estimating sums revisited; title: M12: Alternating Series Test; title: Alternating Series Test; title: Absolute and conditional convergence; title: Estimating sums with the Alternating Series Test; title: M13: Ratio and Root Tests; title: Ratio Test (Statement and proof); title: Ratio Test: examples; title: Root Test; title: Strategies to test series for convergence (M14); title: M15: Power Series and Taylor Series; title: Power series; title: Intervals of convergence; title: Representation of functions as power series; title: term-by-term differentiation and integration of power series; title: more power series representations; title: Power series and sums of numerical series; title: Taylor and MacLaurin series; title: Examples of Taylor Series; title: Convergence of Taylor Series; title: More examples of Taylor Series; title: M16: Applications of power series; title: Power series and sums of numerical series; title: Estimating integrals; title: Calculating limits; title: More power series: products; title: More power series: Binomial series; title: Notations; title: Index; title: Endnotes