Calculus II

Chapter 1 Application of Integration

• Area of a Region Between Two Curves
• Surface of Revolution
• The Disc Method Part I
• The Disc Method Part II
• Volume of Solids with Known Cross Section Part I
• Volume of Solids with Known Cross Section Part II
• The Shell Method Part I
• The Shell Method Part II
• Arc Length Part I
• Arc Length Part II
• Area of a Surface of Revolution fory = f (x)
• Example of the Surface of Revolution for y = f (x)
• Area of a Surface of Revolution for x = f (y)
• Example of the Surface of Revolution for x = f (y)



Chapter 2 Integration Techniques

• Integration by Parts
• Wallis’s Formulas
• Trigonometric Substitution Integrals Involving√a2-u2
• Trigonometric Substitution Integrals Involving√a2+u2
• Trigonometric Substitution Integrals Involving√u2-a2
• Special Integration Formulas
• L'Hôpital's Rule
• Improper Integrals with Infinite Integration Limits
• Improper Integrals with Infinite Discontinuities
• A Special Type of Improper Integral



Chapter 3 Sequence

• Definition of Sequence
• Limit of a Sequence
• Convergence and Divergence of a Sequence
• Properties of Limits of Sequences
• Squeeze Theorem
• Absolute Value Theorem
• Monotonic Sequence
• Definition of a Bounded Sequence
• Bounded Monotonic Sequences


Chapter 4 Series and Tests for Convergence and Divergence

• Infinite Series
• Sum of the Series
• nth Partial Sum of a Sequence
• Properties of Infinite Series
• Convergent and Divergent Series
• Convergence of a Geometric Series
• nth Term Test of a Convergent Series
• nthTerm Test for Divergence
• The Integral Test
• Convergence of pSeries
• Direct Comparison Test
• Limit Comparison Test
• Alternating Series Test
• Absolute Convergence
• Absolute and Conditional Convergence
• Ratio Test
• Root Test
• nth Taylor Polynomial
• nth Maclaurin Polynomial
• Taylor’s Theorem
• Power Series
• Convergence of a Power Series
• Properties of Function Defined by Power Series
• Operations with Power Series
• The Form of Convergent Power Series
• Convergence of a Taylor Series
• Taylor and Maclaurin Series

Chapter 5 Conics

• Standard Equation of a Parabola Part I
• Standard Equation of a Parabola Part II
• Standard Equation of an Ellipse Part I
• Standard Equation of an Ellipse Part II
• Eccentricity of an Ellipse
• Standard Equation of a Hyperbola Part I
• Standard Equation of a Hyperbola II
• Eccentricity of a Hyperbola


Chapter 6 Parametric Equation and Polar Coodinate

• Parametric Equation
• Explaning on Parametric Equation
• Parametric Equation of Smooth Curve
• Improper Integrals with Infinite Discontinuities
• Arc Length in Parametric Form
• Area of a Surface of Revolution
• Coordinate Conversion
• Slope in Polar Form
• Tangent Lines at the Pole
• Area in Polar Coordinates
• Arc Length of a Polar Curve
• Bounded Sequence
• Classification of Conics and Eccentricity
• Conics in Polar Equations
• Detail on Polar Equations of Conics Part I
• Detail on Polar Equations of Conics Part II/IV
• Detail on Polar Equations of Conics Part III/IV
• Detail on Polar Equations of Conics Part IV/IV

Appendix