MATH 1010-3

Brief

11210MATH101003 is a calculus course intended for those studying engineering majors. The following topics are presented with applications in the engineering world: limits, continuity, differentiation, integration of elementary functions with applications, transcendental functions and techniques of integration. Each textbook section has an accompanying homework set to help the student better understand the material. This material is found in Chapters 1-8 of the text. The goals of this course are for you to: 1. understand the concepts of calculus (explain “why?” and “what’s going on?”); 2. become proficient with the techniques, calculations, and procedures characteristic of calculus; 3. be able to use techniques from calculus to model “real-world” situations and solve “applied” problems; and 4. be able to write original, complete, well-organized, logically correct solutions to problems and responses to questions.

Description

一、課程說明(Course Description) 講解微積分基本知識，訓練學生思維能力。 二、指定用書(Text Books) Thomas’Calculus Joel R. Hass, Christopher Heil, Maurice D. Weir, 13th Edition in SI units Pearson/Addison Wesley, 2017 三、參考書籍(References) None 四、教學方式(Teaching Method) Lectures 五、教學進度(Syllabus) (1) Limits and Continuous Functions (3 weeks) (2) Derivatives (3 weeks) (3) Integration (3 weeks) (4) Applications of Integration (3 weeks) (5) Techniques of Integration (3 weeks) Chap. 2 Limits and Continuity Sect 2.2 Limit of a Function and Limit Laws Sect 2.3 The Precise Definition of a Limit Sect 2.4 One-Sided Limits Sect 2.5 Continuity Sect 2.6 Limits Involving Infinity; Asymptotes of Graphs Chap. 3 Differentiation Sect 3.1 Tangents and the Derivative at a Point Sect 3.2 The Derivative as a Function Sect 3.3 Differentiation Rules Sect 3.5 Derivatives of Trigonometric Functions Sect 3.6 The Chain Rule Sect 3.7 Implicit Differentiation Sect 3.9 Linearization and Differentials Chap. 4 Applications of Derivatives Sect 4.1 Extreme Values of Functions Sect 4.2 The Mean Value Theorem Sect 4.3 Monotonic Functions and the First Derivative Test Sect 4.4 Concavity and Curve Sketching Sect 4.5 Applied Optimization Sect 4.7 Antiderivatives Chap. 5 Integrals Sect 5.3 The Definite Integral Sect 5.4 The Fundamental Theorem of Calculus Sect 5.5 Indefinite Integrals and the Substitution Method Sect 5.6 Definite Integrals Substitution and the Area between Curves Chap. 6 Applications of Definite Integrals Sect 6.1 Volumes Using Cross-Sections Sect 6.2 Volumes Using Cylindrical Shells Sect 6.3 Arc Length Sect 6.4 Areas of Surfaces of Revolution Chap. 7 Transcendental Functions Sect 7.2 Natural Logarithms Sect 7.3 Exponential Functions Sect 7.5 Indeterminate Forms and L'Hôital's Rule Sect 7.6 Inverse Trigonometric Functions Sect 7.7 Hyperbolic Functions Chap. 8 Techniques of Integration Sect 8.1 Using Basic Integration Formulas Sect 8.2 Integration by Parts Sect 8.3 Trigonometric Integrals Sect 8.4 Trigonometric Substitutions Sect 8.5 Integration of Rational Functions by Partial Fractions Sect 8.6 Integral Tables and Computer Algebra Systems Sect 8.8 Improper Integrals 六、成績考核(Evaluation) Your grade is based primarily on your scores on the Quizzes, Midterm exam, Final exam, and Your class participation as follows: Final Grade = 20% Quizzes + 30% Midterm exam + 40% Final exam + 10% Your class participation. 七、學生使用AI的聲明: 生成式人工智慧倫理聲明：禁止使用。 經仔細考量後，本課程授課教師認為不宜於此門課程當中使用生成式人工智慧於課堂學習當中。因本課程的內容於生成式AI容易影響學生對基礎核心知識之判讀。 八、可連結之網頁位址 None

Prerequisites

Timetable

Scores

Average GPA 2.64

Std. Deviation 1.07

Remarks

含實中科學班,演習課時間M19:00-21:00,地點物019,501,504

Restrictions

物理系大學部1年級優先，第3次選課起開放全校修習

Compulsory

Elective

Cross Discipline

First Specialization

Second Specialization