Calculus I (B) - Academic Year 109
This course is provided by the NYCU Department of Applied Mathematics .
Calculus is a fundamental tool in various fields such as physics, biology, statistics, astronomy, economics, computer science, and financial engineering. It also serves as a prerequisite for many courses, such as engineering mathematics, differential equations, statistics, and financial mathematics.
Calculus I (B) builds upon the knowledge from Calculus I (A), covering topics such as the convergence and applications of sequences and series, limits and continuity of multivariable functions, partial derivatives, directional derivatives, gradients, and differentiability of functions. The course will also introduce the computation and applications of multiple integrals and conclude with the basics of vector calculus. These topics are crucial for analyzing practical problems in fields such as electromagnetism, fluid mechanics, and economics. This course aims to help students establish a solid understanding of the fundamental theories and computational techniques of multivariable calculus, which will be useful for subsequent courses and research.
Textbook：
Stewart, James. Calculus: Early Transcendentals., 8th ed. Cengage Learning, 2015.
For perfect learning results, please buy textbooks!
| Instructor(s) | Department of Applied Mathematics Prof. Cheng-Fang Su |
|---|---|
| Course Credits | 4 Credits |
| Academic Year | 109 Academic Year |
| Level | College Students |
| Prior Knowledge | High school mathematics |
| Related Resources | Course Video Course Syllabus Learning Notes |
| Week | Course Content | Course Video |
|---|---|---|
| 1 | Chapter 8 Sequences, Series, and Power Series Introduction 8.1 Sequences | Watch Online |
| 2 | 8.1 Sequences 8.2 Series 8.3 The Integral Test | Watch Online |
| 3 | 8.1-8.3的補充例題 (Other Examples for 8.1-8.3) 8.4 Comparison Tests | Watch Online |
| 4 | 正項級數斂散性的複習 (Review of the Test for Convergence of Series with Non-negative Terms) 8.5 The Ratio and Root Tests | Watch Online |
| 5 | 8.6 Alternating Series and Absolute Convergence | Watch Online |
| 6 | 8.7 Power Series 8.8 Representation of Functions as Power Series(1/2) | Watch Online |
| 7 | 8.8 Representation of Functions as Power Series(2/2) 8.9 Taylor Series and Maclaurin Series(1/3) | Watch Online |
| 8 | 8.9 Taylor Series and Maclaurin Series(2/3) | Watch Online |
| 9 | 8.9 Taylor Series and Maclaurin Series(3/3) | Watch Online |
| 10 | Rearrangement of Series and Binomial Series | Watch Online |
| 11 | Chapter 9 Vector and the Geometry of Space 9.1 Vectors in the Plane 9.2 Vectors in Space 9.3 The Dot Product of Two Vectors in Space | Watch Online |
| 12 | Chapter 10 Vector Functions 10.1 Vector Functions and Space Curves(1/2) | Watch Online |
| 13 | 10.1 Vector Functions and Space Curves(2/2) 10.2 Differentiation and Integration of Vector Function(1/2) | Watch Online |
| 14 | 10.2 Differentiation and Integration of Vector Function(2/2) 10.3 Arc Length and Curvature(1/2) | Watch Online |
| 15 | 10.3 Arc Length and Curvature(2/2) Chapter 11 Partial Derivatives 11.1 Functions of Several Variables 11.2 Limits and Continuity(1/3) | Watch Online |
| 16 | 11.2 Limits and Continuity(2/3) | Watch Online |
| 17 | 11.2 Limits and Continuity(3/3) | Watch Online |
| 18 | 11.3 Partial Derivatives 11.4 Tangent Plane and Linear Approximation(1/2) | Watch Online |
| 19 | 11.4 Tangent Plane and Linear Approximation(2/2) 11.5 The Chain Rule(1/2) | Watch Online |
| 20 | 11.5 The Chain Rule(2/2) 11.6 Directional Derivatives and the Gradient Vector(1/3) | Watch Online |
| 21 | 11.6 Directional Derivatives and the Gradient Vector(2/3) | Watch Online |
| 22 | 11.6 Directional Derivatives and the Gradient Vector(3/3) 11.7 Maximum and Minimum Values(1/2) | Watch Online |
| 23 | 11.7 Maximum and Minimum Values(2/2) 11.8 Lagrange Multiplier Method | Watch Online |
| 24 | Chapter 12 Multiple Integrals 12.1 Iterated Integrals(1/2) | Watch Online |
| 25 | 12.1 Iterated Integrals(2/2) 12.2 Double Integrals(1/2) | Watch Online |
| 26 | 12.2 Double Integrals(2/2) | Watch Online |
| 27 | 12.3 Double Integrals in Polar Coordinates 12.4 Surface Area | Watch Online |
| 28 | 12.5 Triple Integrals(1/2) | Watch Online |
| 29 | 12.5 Triple Integrals(2/2) 12.6 Triple Integrals in Cylindrical Coordinates | Watch Online |
| 30 | 12.7 Triple Integrals in Spherical Coordinates | Watch Online |
| 31 | 12.8 Change of Variables in Multiple Integrals | Watch Online |
Course Objectives
Calculus is a fundamental tool in various fields such as physics, biology, statistics, astronomy, economics, computer science, and financial engineering. It also serves as a prerequisite for many courses, such as engineering mathematics, differential equations, statistics, and financial mathematics.
Calculus I (B) builds upon the knowledge from Calculus I (A), covering topics such as the convergence and applications of sequences and series, limits and continuity of multivariable functions, partial derivatives, directional derivatives, gradients, and differentiability of functions. The course will also introduce the computation and applications of multiple integrals and conclude with the basics of vector calculus. These topics are crucial for analyzing practical problems in fields such as electromagnetism, fluid mechanics, and economics. This course aims to help students establish a solid understanding of the fundamental theories and computational techniques of multivariable calculus, which will be useful for subsequent courses and research.
Course Chapter
| Chapter | Content |
| Chapter 8 Sequences, Series, and Power Series | 8.1 Sequences 8.2 Series 8.3 The Integral Test) 8.4 Comparison Tests 8.5 The Ratio and Root Tests 8.6 Alternating Series and Absolute Convergence 8.7 Power Series 8.8 Representation of Functions as Power Series8.9 Taylor Series and Maclaurin Series Rearrangement of Series and Binomial Series |
| Chapter 9 Vector and the Geometry of Space | 9.1 Vectors in the Plane 9.2 Vectors in Space 9.3 The Dot Product of Two Vectors in Space |
| Chapter 10 Vector Functions | 10.1 Vector Functions and Space Curves 10.2 Differentiation and Integration of Vector Function 10.3 Arc Length and Curvature |
| Chapter 11 Partial Derivatives | 11.1 Functions of Several Variables 11.2 Limits and Continuity 11.3 Partial Derivatives 11.4 Tangent Plane and Linear Approximation 11.5 The Chain Rule 11.6 Directional Derivatives and the Gradient Vector 11.7 Maximum and Minimum Values 11.8 Lagrange Multiplier Method |
| Chapter 12 Multiple Integrals | 12.1 Iterated Integrals 12.2 Double Integrals 12.3 Double Integrals in Polar Coordinates 12.4 Surface Area 12.5 Triple Integrals 12.6 Triple Integrals in Cylindrical Coordinates 12.7 Triple Integrals in Spherical Coordinates 12.8 Change of Variables in Multiple Integrals |
Textbooks
Stewart, James. Calculus: Early Transcendentals., 8th ed. Cengage Learning, 2015.
學習筆記 Learning Notes
| 學習筆記-由光電工程學系陳啟馼同學提供 | |
| Chapter | Download Link |
| 1. 單變數純量函數—極限與連續 | |
| 2. 單變數純量函數—導數（概念篇） | |
| 3. 單變數純量函數—導數（應用篇） | |
| 4. 單變數純量函數—積分（概念篇） | |
| 5. 單變數純量函數—積分（技巧篇） | |
| 6. 單變數純量函數—瑕積分 | |
| 7. 單變數純量函數—積分（應用篇） | |
| 8. 參數方程式 | |
| 9. 數列與級數 | |
| 10. 單變數向量函數（概念篇） | |
| 11. 單變數向量函數（應用篇） | |
| 12. 多變數純量函數—極限與連續 | |
| 13. 多變數純量函數—偏導數（概念篇） | |
| 14. 多變數純量函數—偏導數（應用篇） | |
| 15. 多變數純量函數—重積分 | |
| 16. 筆記（全） | |
