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.

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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

 

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

ChapterContent
Chapter 8 Sequences, Series, and Power Series8.1 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 Space9.1 Vectors in the Plane
9.2 Vectors in Space
9.3 The Dot Product of Two Vectors in Space
Chapter 10 Vector Functions10.1 Vector Functions and Space Curves
10.2 Differentiation and Integration of Vector Function
10.3 Arc Length and Curvature
Chapter 11 Partial Derivatives11.1 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 Integrals12.1 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
ChapterDownload Link
1. 單變數純量函數—極限與連續PDF
2. 單變數純量函數—導數(概念篇)PDF
3. 單變數純量函數—導數(應用篇)PDF
4. 單變數純量函數—積分(概念篇)PDF
5. 單變數純量函數—積分(技巧篇)PDF
6. 單變數純量函數—瑕積分PDF
7. 單變數純量函數—積分(應用篇)PDF
8. 參數方程式PDF
9. 數列與級數PDF
10. 單變數向量函數(概念篇)PDF
11. 單變數向量函數(應用篇)PDF
12. 多變數純量函數—極限與連續PDF
13. 多變數純量函數—偏導數(概念篇)PDF
14. 多變數純量函數—偏導數(應用篇)PDF
15. 多變數純量函數—重積分PDF
16. 筆記(全)PDF
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