COURSE INTRODUCTION AND APPLICATION INFORMATION


Course Name
Advanced Calculus II
Code
Semester
Theory
(hour/week)
Application/Lab
(hour/week)
Local Credits
ECTS
MATH 202
Spring
2
2
3
5
Prerequisites
 MATH 201To attend the classes (To enrol for the course and get a grade other than NA or W)
Course Language
English
Course Type
Required
Course Level
First Cycle
Mode of Delivery -
Teaching Methods and Techniques of the Course
Course Coordinator -
Course Lecturer(s)
Assistant(s)
Course Objectives The main objective of this course is to introduce the fundamental concepts of multivariable calculus and vector analysis. Advanced Calculus is one of the most useful of all mathematical tools, and this quarter we develop one of the basic concepts, the double integrals, and discuss its applications and consequences. The course begins with an introduction of double integrals, vector fields, line integrals. At the last stage of the course, some applications of flux integral and the triple integrals will be addressed. This course will conclude with an introduction to vector fields in 3D and surface integrals. The concept of line integrals in space and Stokes' theorem is an essential part of advanced calculus and mathematics in general.
Learning Outcomes The students who succeeded in this course;
  • will be able to calculate line integrals.
  • will be able to calculate line integrals of vector fields.
  • will be able to calculate surface and flux integrals
  • will be able to use Green's theorem.
  • will be able to use Divergence theorem
  • will be able to use Stoke’s theorem
  • will be able to solve physical applications of vector calculus
Course Description In this course vector fields and vector calculus will be discussed. Line integrals, surface integrals, flux integrals will be calculated. Green's theorem, divergence theorem and Stokes' theorem will be discussed and some physical applications will be solved.

 



Course Category

Core Courses
X
Major Area Courses
Supportive Courses
Media and Managment Skills Courses
Transferable Skill Courses

 

WEEKLY SUBJECTS AND RELATED PREPARATION STUDIES

Week Subjects Required Materials
1 Triple Integrals. Application of Triple Integrals "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 14.5
2 Curves and Parametrizations "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 11.3
3 Vector and Scalar fields: Field Lines "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.1
4 Line Integrals "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.3
5 Line Integrals of Vector Fields "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.4
6 Surface and Surface Integrals "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.5
7 Oriented Surfaces and Flux Integrals "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 15.6
8 Gradient, Divergent, and Curl "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.1
9 Green’s Theorem in the Plane "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.3
10 Review and Midterm Exam -
11 The Divergence Theorem in 3-Space "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.4
12 The Stoke’s Theorem "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.5
13 Some Physical Applications of Vector Calculus: Fluid Dynamics, Electromagnetism "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.6
14 Electrostatics, Magnetostatics, Maxwell’s Equations "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.6
15 Orthogonal Curvilinear Coordinates "Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman. Section 16.7
16 Review of the semester
Course Notes/Textbooks

Calculus. A Complete Course (eight edition)", by Robert A. Adams. Addison Wesley Longman.

Suggested Readings/Materials None

 

EVALUATION SYSTEM

Semester Activities Number Weigthing
Participation
Laboratory / Application
Field Work
Quizzes / Studio Critiques
4
20
Portfolio
Homework / Assignments
1
10
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterm
1
30
Final Exam
1
40
Total

Weighting of Semester Activities on the Final Grade
6
60
Weighting of End-of-Semester Activities on the Final Grade
1
40
Total

ECTS / WORKLOAD TABLE

Semester Activities Number Duration (Hours) Workload
Course Hours
(Including exam week: 16 x total hours)
16
4
64
Laboratory / Application Hours
(Including exam week: 16 x total hours)
16
Study Hours Out of Class
15
3
Field Work
Quizzes / Studio Critiques
2
4
Portfolio
Homework / Assignments
1
1
Presentation / Jury
Project
Seminar / Workshop
Oral Exam
Midterms
1
15
Final Exams
1
15
    Total
148

 

COURSE LEARNING OUTCOMES AND PROGRAM QUALIFICATIONS RELATIONSHIP

#
Program Competencies/Outcomes
* Contribution Level
1
2
3
4
5
1 To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics. X
2 To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics, X
3 To be able to define and analyze problems and to find solutions based on scientific methods, X
4 To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials, X
5 To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself, X
6 To be able to criticize and renew her/his own models and solutions, X
7 To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way, X
8

To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge up-to-date, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,

X
9

To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,

10

To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,

X
11 To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense, X
12

By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,

X
13

To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,

14

To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,

15

To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively.

*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest

 

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