Homepage » ALL COURSE » College of Science » Department of Applied Mathematics » Calculus I (A) Academic Year 109 | Department of Applied Mathematics Prof. Cheng-Fang Su
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.
The course of Calculus I (A) primarily focuses on single-variable functions, covering both differential and integral calculus. The content includes topics such as limits and continuity of functions, differential theory in calculus, as well as definite and indefinite integrals and their related applications. The goal is to provide students with a solid understanding of single-variable calculus, preparing them for the more advanced topics in Calculus I (B), which involve vector-valued functions and multivariable calculus.
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 |
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Course Credits | 4 Credits |
Academic Year | 109 Academic Year |
Level | Undergraduate Student |
Prior Knowledge | High school mathematics |
Related Resources | Course Video Course Syllabus Learning Notes |
Week | Course Content | Course Video |
---|---|---|
Syllabus and Teaching Philosophy | Watch Online | |
Preliminaries and Notations | Watch Online | |
Chapter 1 Limits and Derivatives 1.1 Limits of Sequences 1.2 Limits of Functions | Watch Online | |
1.2 Limits of Functions 1.3 Evaluating Limits Analytically | Watch Online | |
1.3 Evaluating Limits Analytically | Watch Online | |
1.4 Continuous Functions | Watch Online | |
1.5 Limits at infinity; Asymptotes 1.6 Differentiation | Watch Online | |
1.6 Differentiation | Watch Online | |
1.6 Differentiation Chapter 2 Rules of Differentiation 2.1 Rules of Differentiation | Watch Online | |
2.1 Rules of Differentiation 2.2 Chain Rule 2.3 Implicit Differentiation | Watch Online | |
2.3 Implicit Differentiation 2.4 The Differentiation of the Inverse Functions | Watch Online | |
2.4 The Differentiation of the Inverse Functions 2.5 Differential and Linear Approximation Chapter 3 Applications of Differentiation 3.1 Extreme Values on an Interval | Watch Online | |
3.1 Extreme Values on an Interval | Watch Online | |
3.2 The First Derivative Test 3.3 Concavity and the Second Derivative Test | Watch Online | |
3.3 Concavity and the Second Derivative Test 3.4 Summary of Curve Sketching | Watch Online | |
3.4 Summary of Curve Sketching 3.5 Rolle’s Theorem and the Mean Value Theorem | Watch Online | |
3.5 Rolle’s Theorem and the Mean Value Theorem 3.6 Indeterminate Forms and L'Hospital’s Rule | Watch Online | |
3.6 Indeterminate Forms and L'Hospital’s Rule 3.7 Antiderivative 4.4 Indefinite Integrals Chapter 5 Techniques of Integrals (1)The Substitution Rule | Watch Online | |
Chapter 5 Techniques of Integrals (1)The Substitution Rule (2) Integration by Parts (3) Trigonometric Integrals I | Watch Online | |
Chapter 5 Techniques of Integrals Review of (1)-(3) (4) Trigonometric Integrals II (5) Trigonometric Substitution | Watch Online | |
Chapter 5 Techniques of Integrals (5) Trigonometric Substitution (6) Half-Angle Substitution (7) Integration of Rational Functions by Partial Fractions | Watch Online | |
Chapter 5 Techniques of Integrals (7) Integration of Rational Functions by Partial Fractions | Watch Online | |
Chapter 4 Integration 4.1 Area | Watch Online | |
4.1 Area 4.2 Properties of Integrals 4.3 Fundamental Theorem of Calculus | Watch Online | |
Chapter 5 Techniques of Integrals (8) Improper Integrals | Watch Online | |
Chapter 6 Applications of Integration 6.1 Area of a Region Between Two Curves 6.2 Volume | Watch Online | |
6.2 Volume 6.3 Arc Length | Watch Online | |
7.1 Curves Defined by Parametric Equations 7.2 Calculus with Parametric Curves | Watch Online | |
7.3 Polar Coordinates 7.4 Calculus with Parametric Curves | Watch Online | |
Polar Curves | Watch Online | |
Review | Watch Online | |
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 |
課程目標
微積分在物理學、生物學、統計學、天文學、經濟學、資訊科學與財務工程等領域都是相當重要的基礎工具,它同時也是許多課程的先備知識,例如工程數學、微分方程、統計學與金融數學。
而微積分甲(一)的課程主要先從單變數函數的觀點出發,講述單變數函數的微分學與積分學,內容大致有微分學中的函數的極限、連續性、微分理論,與積分學中的定積分、不定積分與其相關的應用,先讓同學對單變數函數的微積分有一定程度的掌握與理解,以便良好地銜接微積分甲(二)中向量值函數與多變數函數相關理論的學習。。
課程章節
章節 | 章節內容 |
Chapter 1 Limits and Derivatives | 1.1 Limits of Sequences 1.2 Limits of Functions 1.3 Evaluating Limits Analytically 1.4 Continuous Functions 1.5 Limits at infinity; Asymptotes 1.6 Differentiation |
Chapter 2 Rules of Differentiation | 2.1 Rules of Differentiation 2.2 Chain Rule 2.3 Implicit Differentiation 2.4 The Differentiation of the Inverse Functions 2.5 Differential and Linear Approximation |
Chapter 3 Applications of Differentiation | 3.1 Extreme Values on an Interval 3.2 The First Derivative Test 3.3 Concavity and the Second Derivative Test 3.4 Summary of Curve Sketching 3.5 Rolle’s Theorem and the Mean Value Theorem 3.6 Indeterminate Forms and L'Hospital’s Rule 3.7 Antiderivative |
Chapter 4 Integration | 4.4 Indefinite Integrals |
Chapter 5 Techniques of Integrals | 5.1 The Substitution Rule 5.2 Integration by Parts 5.3 Trigonometric Integrals I 5.4 Trigonometric Integrals II 5.5 Trigonometric Substitution 5.6 Half-Angle Substitution 5.7 Integration of Rational Functions by Partial Fractions |
Chapter 4 Integration | 4.1 Area 4.2 Properties of Integrals 4.3 Fundamental Theorem of Calculus |
Chapter 5 Techniques of Integrals | 5.8 Improper Integrals |
Chapter 6 Applications of Integration | 6.1 Area of a Region Between Two Curves 6.2 Volume 6.3 Arc Length |
Chapter 7 | 7.1 Curves Defined by Parametric Equations 7.2 Calculus with Parametric Curves 7.3 Polar Coordinates 7.4 Calculus with Parametric Curves |
Polar Curves | |
上學期總複習影片 |
課程書目
Stewart, James. Calculus: Early Transcendentals., 8th ed. Cengage Learning, 2015.
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) |