Calculus II is an important compulsory basic theory course for engineering and economic management undergraduates in Colleges and universities, which belongs to the basic mathematics course. It is the necessary foundation of most science and engineering courses. This course is the first key basic course for undergraduate students after enrollment. It plays an important role in establishing scientific thinking method, learning mathematical modeling ability, training scientific, rigorous and assiduous learning attitude.
Overview
Syllabus
- Chapter11 Infinite Sequences and Series
- 11.1 Sequences
- 11.2 Series
- 11.3. The Integral Test and Estimates of Sums
- 11.4. The Comparison Tests
- 11.5. Alternating Series
- 11.6. Absolute Convergence and the Ratio and Root Tests
- 11.7. Strategy for Testing Series
- 11.8. Power Series
- 11.9. Representations of Functions as Power Series
- 11.10. Taylor and Maclaurin Series
- 11.11. Applications of Taylor Polynomials
- Chapter12 Vectors and the Geometry of Space
- 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
- Chapter13 Vector Functions
- 13.1. Vector Functions and Space Curves
- 13.2. Derivatives and Integrals of Vector Functions
- 13.3. Arc Length and Curvature
- 13.4. Motion in Space: Velocity and Acceleration
- Chapter14 Partial Derivatives
- 14.1. Functions of Several Variables
- 14.2. Limits and Continuity
- 14.3. Partial Derivatives
- 14.4. Tangent Planes and Linear Approximations
- 14.5. The Chain Rule
- 14.6. Directional Derivatives and the Gradient Vector
- 14.7. Maximum and Minimum Values
- 14.8. Lagrange Multipliers
- Chapter15 Multiple Integrals
- 15.1. Double Integrals over Rectangles
- 15.2. Iterated Integrals
- 15.3. Double Integrals over General Regions
- 15.4. Double Integrals in Polar Coordinates
- 15.5. Applications of Double Integrals
- 15.6. Surface Area
- 15.7. Triple Integrals
- 15.8. Triple Integrals in Cylindrical Coordinates
- 15.9. Triple Integrals in Spherical Coordinates
- 15.10. Change of Variables in Multiple Integrals
- Chapter16 Vector Calculus
- 16.1. Vector Fields
- 16.2. 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
- 16.7. Surface Integrals
- 16.8. Stokes’ Theorem
- 16.9. The Divergence Theorem
- 16.10. Summary
- Chapter17 Second-Order Differential Equations
- 17.1. Second-Order Linear Equations
- 17.2. Nonhomogeneous Linear Equations
- 17.3. Applications of Second-Order Differential Equations
- 17.4. Series Solutions
Taught by
Qing Wu
