Calculus Ⅱ课程列表：

Chapter11 Infinite Sequences and Series

-11.1 Sequences

--11.1.1.Precise Definition for the Limits of Sequences

--11.1.2.Calculating the Limits of Sequences

--Exercises 11.1

-11.2 Series

--11.2.1.Series-Geometric Series

--11.2.2.Series-Harmonic Series

--Exercises 11.2

-11.3. The Integral Test and Estimates of Sums

--11.3.The Integral Test and Estimates of Sums

-11.4. The Comparison Tests

--11.4.The Comparison Tests

--Exercises 11.4

-11.5. Alternating Series

--11.5.Alternating Series

-11.6. Absolute Convergence and the Ratio and Root Tests

--11.6.1.Absolute Convergence and Conditional Convergence

--11.6.2.The Ratio and Root Test

--Exercise 11.6

-11.7. Strategy for Testing Series

--11.7.Strategy for Testing Series

-11.8. Power Series

--11.8.Power Series

--Exercises 11.8

-11.9. Representations of Functions as Power Series

--11.9.Representations of Functions as Power Series

-11.10. Taylor and Maclaurin Series

--11.10.1.The Taylor and Maclaurin series

--11.10.2.The Convergence of Taylor series

--Exercises 11.10

-11.11. Applications of Taylor Polynomials

--11.11.Applications of Taylor Polynomials

-Practice Exercises 11

Chapter12 Vectors and the Geometry of Space

-12.1. Three-Dimensional Coordinate Systems

--12.1.Three-Dimensional Coordinate Systems

-12.2. Vectors

--12.2.Vectors

-12.3. The Dot Product

--12.3.The Dot Product

-12.4. The Cross Product

--12.4.The Cross Product

-12.5. Equations of Lines and Planes

--12.5.1.Equations of Lines

--12.5.2.Equations of Planes

-12.6. Cylinders and Quadric Surfaces

--12.6.Cylinders and Quadric Surfaces

-Quiz 12

-Practice Exercises 12

Chapter13 Vector Functions

-13.1. Vector Functions and Space Curves

--13.1.Vector Functions and Space Curves

-13.2. Derivatives and Integrals of Vector Functions

--13.2.Derivatives and Integrals of Vector Functions

--13.2.Limits and Continuity

-13.3. Arc Length and Curvature

--13.3.1.Arc Length and Curvature

--13.3.2.TNB Frame

-13.4. Motion in Space: Velocity and Acceleration

--13.4.Motion in Space: Velocity and Acceleration

-Quiz 13

-Practice Exercises 13

Chapter14 Partial Derivatives

-14.1. Functions of Several Variables

--14.1.Functions of Several Variables

-14.2. Limits and Continuity

--14.2.Limits and Continuity

-14.3. Partial Derivatives

--14.3.Partial Derivatives

-14.4. Tangent Planes and Linear Approximations

--14.4.1.Tangent Planes and Linear Approximations

--14.4.2.Differentials

-14.5. The Chain Rule

--14.5.The Chain Rule

-14.6. Directional Derivatives and the Gradient Vector

--14.6.Directional Derivatives and the Gradient Vector

-14.7. Maximum and Minimum Values

--14.7.Maximum and Minimum Values

-14.8. Lagrange Multipliers

--14.8.Lagrange Multipliers

-Quiz 14

-Practice Exercises 14

Chapter15 Multiple Integrals

-15.1. Double Integrals over Rectangles

--15.1.Double Integrals over Rectangles

-15.2. Iterated Integrals

--15.2.Iterated Integrals

-15.3. Double Integrals over General Regions

--15.3.Double Integrals over General Regions

-15.4. Double Integrals in Polar Coordinates

--15.4.Double Integrals in Polar Coordinates

-15.5. Applications of Double Integrals

--15.5.Applications of Double Integrals

-15.6. Surface Area

--15.6.Surface Area

-15.7. Triple Integrals

--15.7.Triple Integrals

-15.8. Triple Integrals in Cylindrical Coordinates

--15.8.Triple Integrals in Cylindrical Coordinates

-15.9. Triple Integrals in Spherical Coordinates

--15.9.Triple Integrals in Spherical Coordinates

-15.10. Change of Variables in Multiple Integrals

--15.10. Change of Variables in Multiple Integrals

-Quiz 15

-Pactice Exercises 15

Chapter16 Vector Calculus

-16.1. Vector Fields

--16.1.Vector Fields

-16.2. Line Integrals

--16.2.1.Line Integrals with respect to Arc Length

--16.2.2.Work Integrals

-16.3. The Fundamental Theorem for Line Integrals

--16.3.The Fundamental Theorem for Line Integrals

-16.4. Green’s Theorem

--16.4.Green’s Theorem

-16.5. Curl and Divergence

--16.5.Curl and Divergence

-16.6. Parametric Surfaces and Their Areas

--16.6.Parametric Surfaces and Their Areas

-16.7. Surface Integrals

--16.7.1.Surface Integrals with respect to surface area

--16.7.2.Flux Integrals

-16.8. Stokes’ Theorem

--16.8.Stokes’ Theorem

-16.9. The Divergence Theorem

--16.9.The Divergence Theorem

-16.10. Summary

--16.10. Summary

-Quiz 16

-Practice Exercise 16

Chapter17 Second-Order Differential Equations

-17.1. Second-Order Linear Equations

--17.1.Second-Order Linear Equations

-17.2. Nonhomogeneous Linear Equations

--17.2.1.Method of Undetermined Coefficients

--17.2.2.Method of Variation of Parameters

-17.3. Applications of Second-Order Differential Equations

--17.3.Applications of Second-Order Differential Equations

-17.4. Series Solutions

--17.4.Series Solutions

-Quiz 17

-Practice Exercises 17

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