課程資訊

Calculus (general Mathematics) (a)(1)

107-1

MATH1201

201E101A1

05

4.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1071Calculus_A05

Differentiation and Integration, or, collectively, Calculus, on functions of a single variable together with their profound applications in various subject areas are introduced in this course. On differentiation, it includes the definitions of limits and continuity, techniques of differentiation, strategies in solving extreme-value problem and so on; on integration, it includes the definition of integrals, the Fundamental Theorem of Calculus, techniques of integration, finding areas and volumes, solving elementary differential equations and more.

Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of Calculus in various fields are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sections in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.

Students would be familiar with Calculus as a tool and be able to apply it in various subjects after finishing this course. "Calculus A (1) and (2)" provide the basis for the study of various advanced courses like Engineering Mathematics, Analysis and Differential Equations.

Students participating in the course should be already skilled in high school mathematics. They are expected to attend and participate actively in lectures as well as discussion sections.

Office Hours

Textbook: James Stewart, Calculus Early Transcendentals, 8th edition.

Reference book: Maurice D. Weir and Joel Hass,
Thomas' Calculus: Early Transcendentals, 13th Edition in SI units

Website of the unified course on Calculus A:
http://www.math.ntu.edu.tw/~mathcal/a/

WeBWorK system for online exercises:
http://webwork.math.ntu.edu.tw/webwork2/1071MATH1201_05/

NTU past-papers on Calculus A:
http://www.math.ntu.edu.tw/~mathcal/a/?page_id=7

Episte Math:
http://episte.math.ntu.edu.tw/cgi/mathfield.pl?fld=cal

Free online Desmos Graphing Calculator:
https://www.desmos.com/calculator

Online computational knowledge engine:
https://www.wolframalpha.com

James Stewart, Calculus: Early Transcendentals, 8th Edition (course textbook)

(僅供參考)

 No. 項目 百分比 說明 1. Mid-term exam 35% Contents include materials from Sections 1.4 ~ 4.9. 2. Final exam 35% Contents include materials from Sections 5.1 ~ 10.4. 3. Others 30% Including homework assignments, WeBWork online exercises, in-class quizzes and other possible bonuses.

 課程進度
 週次 日期 單元主題 第1週 9/12,9/14 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms 2.1 The Tangent and Velocity Problems 第2週 9/19,9/21 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit 第3週 9/26,9/28 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function 第4週 10/03,10/05 3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 第5週 10/12 ※10/10(Wed) Double Tenth Day 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions 3.8 Exponential Growth and Decay (✽) 第6週 10/17,10/19 3.9 Related Rates 3.10 Linear Approximations and Differentials 3.11 Hyperbolic Functions (✽) 4.1 Maximum and Minimum Values 第7週 10/24,10/26 4.2 The Mean Value Theorem 4.3 How Derivatives Affect the Shape of a Graph 4.4 Indeterminate Forms and l'Hospital's Rule 第8週 10/31,11/02,11/3 4.5 Summary of Curve Sketching 4.7 Optimization Problems 4.9 Antiderivatives ※Mid-term exam 11/3(Sat) 09:00~11:30 contents: 1.4~4.9 第9週 11/07,11/09 5.1 Areas and Distances 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule 第10週 11/14,11/16 6.1 Areas Between Curves 6.2 Volume 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function 第11週 11/21,11/23 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 第12週 11/28,11/30 7.4 Integration of Rational Functions by Partial Fractions 7.5 Strategy for Integration 7.8 Improper Integrals 第13週 12/05,12/07 8.1 Arc Length 8.2 Area of a Surface of Revolution 第14週 12/12,12/14 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 第15週 12/19,12/21 10.4 Areas and Lengths in Polar Coordinates 9.1 Modeling with Differential Equations 第16週 12/26,12/28 9.3 Separable Equations 9.4 Models for Population Growth 第17週 1/02,1/04,1/5 9.5 Linear Equations ※Final exam 1/5(Sat) 09:00~11:30 contents: 5.1~10.4