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开设学校:北京交通大学;学科:理学、
Practice more, learn more! Wish you enjoy this course and get profits from our lectures.
-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
--Exercises 11.4
-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
--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
-12.1. Three-Dimensional Coordinate Systems
--12.1.Three-Dimensional Coordinate Systems
-12.2. Vectors
-12.3. The Dot Product
-12.4. The Cross Product
-12.5. Equations of Lines and Planes
-12.6. Cylinders and Quadric Surfaces
--12.6.Cylinders and Quadric Surfaces
-Quiz 12
-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
-13.3. Arc Length and Curvature
--13.3.1.Arc Length and Curvature
-13.4. Motion in Space: Velocity and Acceleration
--13.4.Motion in Space: Velocity and Acceleration
-Quiz 13
-14.1. Functions of Several Variables
--14.1.Functions of Several Variables
-14.2. Limits and Continuity
-14.3. Partial Derivatives
-14.4. Tangent Planes and Linear Approximations
--14.4.1.Tangent Planes and Linear Approximations
-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
-Quiz 14
-15.1. Double Integrals over Rectangles
--15.1.Double Integrals over Rectangles
-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
-15.7. 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
-16.1. Vector Fields
-16.2. Line Integrals
--16.2.1.Line Integrals with respect to Arc Length
-16.3. The Fundamental Theorem for Line Integrals
--16.3.The Fundamental Theorem for Line Integrals
-16.4. Green’s Theorem
-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
-16.8. Stokes’ Theorem
-16.9. The Divergence Theorem
-16.10. Summary
-Quiz 16
-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
-Quiz 17
1988年6月 于中国科学院系统所获得理学硕士学位; 1988年7月至今依次在青岛大学、石油大学(北京)、北京交通大学任教; 2008年8月作为访问学者在美国 Montclair State University工作六个月。 2009获得北京交通大学优秀教师称号。 任教期间,曾经讲授过微积分、线性代数、空间解析几何、微分几何、一般拓扑学、离散数学等等。自2011年开始,从事微积分全英文及双语教学工作。