Calculus I

Teaching Semesters

• 2025 Fall, 2024 Fall, 2023 Fall, 2022 Fall.

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  • Chinese Translation Note: The newest Chinese translated version is based on the 10th Edition, which is outdated and not recommended.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 1. Functions Slide, Lecture Note
  • 1.1 Functions and Their Graphs
  • 1.2 Combining Functions; Shifting and Scaling Graphs
  • 1.3 Trigonometric Functions
  • 1.4* Graphing with Software
• Chapter 2. Limits and Continuity Slide, Lecture Note
  • 2.1 Rates of Change and Tangents to Curves
  • 2.2 Limit of a Function and Limit Laws
  • 2.3 The Precise Definition of a Limit
  • 2.4 One-Sided Limits
  • 2.5 Continuity
  • 2.6 Limits Involving Infinity; Asymptotes of Graphs
• Chapter 3. Differentiation Slide, Lecture Note
  • 3.1 Tangents and the Derivative at a Point
  • 3.2 The Derivative as a Function
  • 3.3 Differentiation Rules
  • 3.4 The Derivative as a Rate of Change
  • 3.5 Derivatives of Trigonometric Functions
  • 3.6 The Chain Rule
  • 3.7 Implicit Differentiation
  • 3.8 Related Rates
  • 3.9 Linearization and Differentials
• Chapter 4. Applications of Derivatives Slide, Lecture Note
  • 4.1 Extreme Values of Functions
  • 4.2 The Mean Value Theorem
  • 4.3 Monotonic Functions and the First Derivative Test
  • 4.4 Concavity and Curve Sketching
  • 4.5 Applied Optimization
  • 4.6 Newton’s Method
  • 4.7 Antiderivatives
• Chapter 5. Integration Slide, Lecture Note
  • 5.1 Area and Estimating with Finite Sums
  • 5.2 Sigma Notation and Limits of Finite Sums
  • 5.3 The Definite Integral
  • 5.4 The Fundamental Theorem of Calculus
  • 5.5 Indefinite Integrals and the Substitution Method
  • 5.6 Definite Integral Substitutions and the Area Between Curves
• Chapter 6. Applications of Definite Integrals Slide, Lecture Note
  • 6.1 Volumes Using Cross-Sections
  • 6.2 Volumes Using Cylindrical Shells
  • 6.3 Arc Length
  • 6.4 Areas of Surfaces of Revolution

• Chapter 7. Transcendental Functions Slide

• Chapter 8. Techniques of Integration Slide

• Chapter 9. Ordinary Differential Equations Slide

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