Calculus II
Published:
Teaching Semesters
Course Specification (Official)
This is the official course description. Please note that some of the information and requirements stated herein may not reflect my personal views.
Acknowledgement
I gratefully acknowledge Pearson for kindly providing me with complimentary sample copies of their textbooks for my teaching. I appreciate their trust and support. These resources have informed the development of some of my personal teaching materials below.
Personal Teaching Materials & Resources
Supplementary Notes on Textbooks and References
- Textbook: Thomas’s Calculus
- Editions 12 to 15 are all acceptable for use, as discrepancies between them are minimal.
- The course structure (sequence) is primarily based on the 12th Edition, with slight differences compared to later editions (13th, 14th, 15th).
- The 14th Edition is available as a reprinted version (the most cost-effective choice).
- The 15th Edition is the latest update of the textbook.
- Chinese Translation Note: The newest Chinese translated version is based on the 10th Edition, which is outdated and not recommended.
- For more reference recommendations, check out my Study Resources & Advice page.
Personal Slides
This version was carefully adapted for my actual lectures, refined to reflect my teaching style and the needs of my students. The modifications include reworded explanations, added examples, exercises, and annotated notes to support classroom use. Copyright © Xiaozhou Li — CC BY-NC-ND 4.0
Note: Minor updates or in-class adjustments may not be reflected here in real time; slides are usually updated after each chapter is completed.
Course Overview Slide
- Chapter 10. Infinite Sequences and Series Slide
- 10.1 Sequences
- 10.2 Infinite Series
- 10.3 The Integral Test
- 10.4 Comparison Tests
- 10.5 Absolute Convergence; The Ratio and Root Tests
- 10.6 Alternating Series and Conditional Convergence
- 10.7 Power Series
- 10.8 Taylor and Maclaurin Series
- 10.9 Convergence of Taylor Series
- 10.10 The Binomial Series and Applications of Taylor Series
- Chapter 11. Parametric Equations and Polar Coordinates Slide
- 11.1 Parametrizations of Plane Curves
- 11.2 Calculus with Parametric Curves
- 11.3 Polar Coordinates
- 11.4 Graphing Polar Coordinate Equations
- 11.5 Areas and Lengths in Polar Coordinates
- 11.6 Conic Sections
- 11.7 Conics in Polar Coordinates
- Chapter 12. Vectors and the Geometry of Space Slide
- 12.1 Three-Dimensional Coordinate Systems
- 12.2 Vectors
- 12.3 The Dot Product
- 12.4 The Cross Product
- 12.5 Lines and Planes in Space
- 12.6 Cylinders and Quadric Surfaces
- Chapter 13. Vector-Valued Functions and Motion in Space Slide
- 13.1 Curves in Space and Their Tangents
- 13.2 Integrals of Vector Functions; Projectile Motion
- 13.3 Arc Length in Space
- 13.4 Curvature and Normal Vectors of a Curve
- 13.5 Tangential and Normal Components of Acceleration
- 13.6 Velocity and Acceleration in Polar Coordinates
- Chapter 14. Partial Derivatives Slide
- 14.1 Functions of Several Variables
- 14.2 Limits and Continuity in Higher Dimensions
- 14.3 Partial Derivatives
- 14.4 The Chain Rule
- 14.5 Directional Derivatives and Gradient Vectors
- 14.6 Tangent Planes and Differentials
- 14.7 Extreme Values and Saddle Points
- 14.8 Lagrange Multipliers
- 14.9 Taylor’s Formula for Two Variables
- 14.10 Partial Derivatives with Constrained Variables
- Chapter 15. Multiple Integrals Slide
- 15.1 Double and Iterated Integrals over Rectangles
- 15.2 Double Integrals over General Regions
- 15.3 Area by Double Integration
- 15.4 Double Integrals in Polar Form
- 15.5 Triple Integrals in Rectangular Coordinates
- 15.6 Moments and Centers of Mass
- 15.7 Triple Integrals in Cylindrical and Spherical Coordinates
- 15.8 Substitutions in Multiple Integrals
- Chapter 16. Integrals and Vector Fields Slide
- 16.1 Line Integrals
- 16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux
- 16.3 Path Independence, Conservative Fields, and Potential Functions
- 16.4 Green’s Theorem in the Plane
- 16.5 Surfaces and Area
- 16.6 Surface Integrals
- 16.7 Stokes’ Theorem
- 16.8 The Divergence Theorem and a Unified Theory
Supplementary Learning Materials
- 微积分中英名词对照：源自《托马斯微积分第10版》（中文翻译版）附录，仅作课程教学辅助，若涉侵权请联系本人删除。
- Problem Sets: A curated collection of problems from my courses, designed to deepen your understanding and sharpen your problem-solving skills.
- More Comprehensive Support：For general study tips, course-specific advice, and academic guidance, you can also refer to my Study Resources & Advice