THAI NGUYEN UNIVERSITY

UNIVERSITY OF INFORMATION AND COMMUNICATION TECHNOLOGY

SOCIALIST REPUBLIC OF VIET NAM

Independence - Freedom - Happiness

Subject Code

Subject Title

CALCULUS

Credit Value

 Total: 4 (60 periods);            Theory:            45                    Practice: 15

Level

2

Pre-requisite

No

Co-requisite/ Exclusion

 No

Description

Theory: The course consists of 10 chapters with the following contents: Functions, limits and continuity, derivatives, integrals and applications, transcendental functions, series theory, differential equations of first order.

 Practice: Do exercises from basic to advanced. Practice, understand some applications in science and technology through projects.

Objectives

In this course, students are provided with knowledge of analysis and applications in engineering science. Thereby students can solve the exercises and master the tools to apply them in real problems.

Intended Learning Outcomes

Upon completion of the subject, students will be able to:

Knowledge:

(a)       have a basic understanding of functions, limits, continuity of functions and applications.

(b)       have a basic understanding of Derivatives and applications

(c)       have a basic understanding of integrals and applications

(d)       Have a basic understanding of series theory, series of functions and applications.

(e) Have a basic understanding of differential equations and their applications.

Subject Synopsis/ Indicative Syllabus

Chapter 1(6 periods): Functions - Functions are fundamental to the study of calculus. In this chapter we review what functions are and how they are visualized as graphs, how they are combined and transformed, and ways they can be classified.

Chapter 2(6 periods): Limits and Continuity - In this chapter we develop the concept of a limit, first intuitively and then formally. We use limits to describe the way a function varies. Some functions vary continuously; small changes in x produce only small changes in ƒ(x). Other functions can have values that jump, vary erratically, or tend to increase or decrease without bound. The notion of limit gives a precise way to distinguish among these behaviors.

Chapter 3(6 periods): Derivatives - The derivative is used to study a wide range of problems in mathematics, science, economics, and medicine.

Chapter 4(6 periods): Applications of Derivatives - In this chapter we apply derivatives to find extreme values of functions, to determine

and analyze the shapes of graphs, and to solve equations numerically. We also introduce the idea of recovering a function from its derivative. The key to many of these applications is the Mean Value Theorem, which connects the derivative and the average change of a function.

Chapter 5 (6 periods): Integrals

Chapter 6 (6 periods): Applications of Definite Integrals

Chapter 7 (6 periods): Transcendental Functions

Chapter 8 (6 periods): Techniques of Integration

Chapter 9 (6 periods): First-Order Differential Equations

Chapter 10 (6 periods): Infinite Sequences and Series

Teaching/Learning Methodology

 Lectures: focuses on developing conceptual understanding of the underlying mathematical ideas. Intuitive and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets.

Self-Study

Student Study Effort Expected

Class contact:

•  Lectures 45 Prs

• Tutorials 15 prs

Other student study effort:

• Self-Study 120 Prs

Total student study effort 180 Prs

Specific assessment methods/tasks

Weighting

%

Intended subject learning outcomes to be assessed (Please tick as appropriate)

a

b

c

d

e

1.Attendance

10%

2.Written assessment I

10%

x

x

 x

3.Written assessment II

10%

x

x

x

4.Written assignment III

10%

x

x

x

5. End of subject exam

60%

x

x

x

x

x

Total

100 %

Score Structure

+ Attendance: (a)

+ Test 1: (b)

+ Test 2: (c)

+ Test 3 (d)

+ Middle score: (e)

(e) = (a + b+c+d)/4

+ Final Score: (f)