Calculus I Syllabus - Calculus 1 | Trường Đại học Quốc tế, Đại học Quốc gia Thành phố HCM

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Môn: Calculus 1 (MA001IU)

Trường: Trường Đại học Quốc tế, Đại học Quốc gia Thành phố Hồ Chí Minh

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Profile Mai Nguyệt
COURSE OUTLINE
for
CALCULUS I
Instructor: Assoc. Prof. Dr. Duong Thanh Pham
A. COURSE OVERVIEW:
1. Course Objectives: To provide the students with the main ideas and techniques of
calculus, concerning limits, continuity, differentiation and integration.
To provide an understanding of the practical meaning, significance and applications
of these ideas and techniques, through practical examples taken from many areas of
engineering, business and the life sciences
To develop skills in mathematical modelling and problem solving, in thinking
logically, and in creatively applying existing knowledge to new situations
To develop confidence and fluency in discussing mathematics in English.
2. Prerequisite: none
3. Main Content: Functions; Limits; Continuity; Derivatives, Differentiation, Derivatives
of Basic Elementary Functions, Differentiation Rules; Applications of Differentiation:
l’Hôpital’s Rule, Optimization, Newton’s Method; Anti-derivatives; Indefinite Integrals,
Definite Integrals, Fundamental Theorem of Calculus; Techniques of Integration;
Improper Integrals; Applications of Integration.
4. Assessment:
Student’s attendances are checked every lectures.
Assignment 20%
Midterm Test: 30%
Final Exam: 50%
In these examinations, students are allowed to bring toonly two sheets of A4 paper
write formulas and important information.
5. Documents:
Main textbook: J. Stewart, ed
Calculus. Concepts and Contexts, 7
th
Other textbooks:
1. J. Rogawski, , W.H. Freeman, 2008.Calculus, Early Transcendentals
2. R.N. Greenwell, N.P. Ritchey, and M.L. Lial, Calculus with Applications for
the Life Sciences, Addition Wesley, 2003.
1
B. A DETAILED OUTLINE:
Chapter Name of
Chapter
Descriptions
01
Functions,
Limits and
Continuity
1.1 What is Calculus?
1.2 Straight Lines. Equations of Lines
1.3 Functions and Graphs
1.4 New Functions from Old Functions. Inverse
Functions
1.5 Parametric Curves
1.6 Definition of a Limit. One-sided Limits
1.7 Laws of Limits. Evaluating Limits. The Squeeze
Theorem
1.8 Continuity
1.9 The Intermediate Value Theorem
1.10 Limits Involving Infinity
Limit: https://hayhochoi.vn/toan-11-gioi-han-cua-ham-
so-cach-tinh-va-bai-tap-ap-dung.html
02
Differentiation
2.1 The Tangent and Velocity Problems. Rates of
Change
2.2 The Derivative. Higher-Order Derivatives
2.3 Rules of Differentiation. Finding Derivatives
using Maple
2.4 Rates of Change in the Natural and Social
Sciences
2.5 Implicit Differentiation
2.6 Differentiation of Inverse Functions
2.7 Linear Approximations. Differentials.
03
Applications
of
Differentiation
3.1 Related Rates
3.2 Maxima and Minima. Critical Points
3.3 The Mean Value Theorem. The First Derivative
Test. Concavity. Shapes of Curves.
3.4 Curve Sketching. Graphing with Calculus and
Computers using Maple
2
3.5 Indeterminate Forms and l’Hôpital’s Rules
3.6 Maxima and Minima Problems
3.7 Newton’s Method
3.8 Anti-derivatives and Indefinite Integrals
04
Integration
4.1 Areas under Curves and Distances
4.2 The Definite Integral
4.3 Properties of the Definite Integral.
4.4 The Fundamental Theorem of Calculus
4.5 Integration by Substitution
4.6 Integration by Parts
4.7 Additional Techniques of Integration. Partial
Fractions
4.8 Integration Using Tables and Computer Algebra
Systems
4.9 Numerical Integration
4.10 Improper Integrals
05
Applications of
Integration
5.1 Areas between Curves
5.2 Areas Enclosed by Parametric Curves
5.3 Volumes
5.4 Arc Length
5.5 Average Value of a Function
5.6 Applications to Engineering, Economics and
Science
------ THE END ------
3
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COURSE OUTLINE for CALCULUS I
Instructor: Assoc. Prof. Dr. Duong Thanh Pham A. COURSE OVERVIEW:
1. Course Objectives:  To provide the students with the main ideas and techniques of
calculus, concerning limits, continuity, differentiation and integration.
 To provide an understanding of the practical meaning, significance and applications
of these ideas and techniques, through practical examples taken from many areas of
engineering, business and the life sciences
 To develop skills in mathematical modelling and problem solving, in thinking
logically, and in creatively applying existing knowledge to new situations
 To develop confidence and fluency in discussing mathematics in English.
2. Prerequisite: none
3. Main Content: Functions; Limits; Continuity; Derivatives, Differentiation, Derivatives
of Basic Elementary Functions, Differentiation Rules; Applications of Differentiation:
l’Hôpital’s Rule, Optimization, Newton’s Method; Anti-derivatives; Indefinite Integrals,
Definite Integrals, Fundamental Theorem of Calculus; Techniques of Integration;
Improper Integrals; Applications of Integration. 4. Assessment:
Student’s attendances are checked every lectures. Assignment 20% Midterm Test: 30% Final Exam: 50%
In these examinations, students are allowed to bring only two sheets of A4 paper to
write formulas and important information. 5. Documents:
Main textbook: J. Stewart, Calculus. Concepts and Contexts, 7th ed Other textbooks:
1. J. Rogawski, Calculus, Early Transcendentals, W.H. Freeman, 2008.
2. R.N. Greenwell, N.P. Ritchey, and M.L. Lial, Calculus with Applications for
the Life Sciences, Addition Wesley, 2003. 1 B. A DETAILED OUTLINE: Chapter Name of Descriptions Chapter 1.1 What is Calculus?
1.2 Straight Lines. Equations of Lines 1.3 Functions and Graphs
1.4 New Functions from Old Functions. Inverse Functions 1.5 Parametric Curves Functions, Limits and
1.6 Definition of a Limit. One-sided Limits 01 Continuity
1.7 Laws of Limits. Evaluating Limits. The Squeeze Theorem 1.8 Continuity
1.9 The Intermediate Value Theorem 1.10 Limits Involving Infinity
Limit: https://hayhochoi.vn/toan-11-gioi-han-cua-ham-
so-cach-tinh-va-bai-tap-ap-dung.html 2.1
The Tangent and Velocity Problems. Rates of Change 2.2
The Derivative. Higher-Order Derivatives 2.3
Rules of Differentiation. Finding Derivatives using Maple Differentiation 02 2.4
Rates of Change in the Natural and Social Sciences 2.5 Implicit Differentiation 2.6
Differentiation of Inverse Functions
2.7 Linear Approximations. Differentials. 03 3.1 Related Rates Applications 3.2
Maxima and Minima. Critical Points of 3.3
The Mean Value Theorem. The First Derivative Differentiation
Test. Concavity. Shapes of Curves. 3.4
Curve Sketching. Graphing with Calculus and Computers using Maple 2 3.5
Indeterminate Forms and l’Hôpital’s Rules 3.6 Maxima and Minima Problems 3.7 Newton’s Method 3.8
Anti-derivatives and Indefinite Integrals 4.1
Areas under Curves and Distances 4.2 The Definite Integral 4.3
Properties of the Definite Integral. 4.4
The Fundamental Theorem of Calculus 4.5 Integration by Substitution 4.6 Integration by Parts 04 Integration
4.7 Additional Techniques of Integration. Partial Fractions
4.8 Integration Using Tables and Computer Algebra Systems 4.9 Numerical Integration 4.10 Improper Integrals 5.1 Areas between Curves
5.2 Areas Enclosed by Parametric Curves Applications of 5.3 Volumes Integration 5.4 Arc Length 05
5.5 Average Value of a Function
5.6 Applications to Engineering, Economics and Science ------ THE END ------ 3