# Advanced Calculus II (MATH252) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Advanced Calculus II MATH252 4. Semester 3 2 0 4 8
Pre-requisite Course(s)
Course Language English Compulsory Departmental Courses Bachelor’s Degree (First Cycle) Face To Face Lecture, Discussion, Problem Solving. The course is designed as a continuation of Math 251 Advenced Calculus I and aims to introduce students higher-level aspects of the calculus through a rigorous development of the fundamental ideas in the topic and to achieve a further development of the math student's ability to deal with abstract mathematics and proofs. The students who succeeded in this course; Comprehend and use vector and scalar fields, the gradient field and the curl of a vector field, Comprehend and use multiple integrals in different coordinate systems, Know and use the line and surface integrals together with their applications, Apply Green’s and Stoke’s theorems Vector and scalar fields. Double integrals. Triple integrals. Integral of vector functions. Improper İntegrals. Line İntegrals. Green?s theorem. Surface integrals. The divergence Theorem. Stoke?s Theorem

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Vectors and scalar fields, The gradient field, The curl of a vector field. pp. 179-186
2 Combined operations. Double Integrals. pp. 187-190, 228-233
3 Triple Integrals. pp. 234-235
4 Multiple integrals, Integrals of vector functions. pp. 236-237
5 Change of variables in integrals, Arc length and surface area. pp. 238-250
6 Improper multiple integrals, Integrals depending on a parameter (Leibnitz's rule). pp. 251-260
7 Midterm
8 Line integrals in the plane, Integrals with respect to arc length, Properties of line integrals, pp. 271-283
9 Line integrals as integrals of vectors, Green's theorem, pp. 284-290
10 Independence of path in simply connected domains, Extension of the Results to Multiply Connected Domains. pp. 291-307
11 Line integrals in space, Surfaces in space. pp. 308-309
12 Surface integrals, The divergence theorem. pp. 313-325
13 Stoke's theorem, Integrals independent of path. pp. 326-335
14 Change of variables in a multiple integral. pp. 336-343
15 Review.
16 Final

### Sources

Course Book 1. W. Kaplan, Advanced Calculus. Addison-Wesley, 1993 2. H. Helson. Honors Calculus 3. B. Demidovich. Problem book in mathematical analysis

### Evaluation System

Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 5 10
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 50
Final Exam/Final Jury 1 40
Toplam 8 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Has the ability to apply scientific knowledge gained in the undergraduate education and to expand and extend knowledge in the same or in a different area X
2 Can apply gained knowledge and problem solving abilities in inter-disciplinary research X
3 Has the ability to work independently within research area, to state the problem, to develop solution techniques, to solve the problem, to evaluate the obtained results and to apply them when necessary X
4 Takes responsibility individually and as a team member to improve systematic approaches to produce solutions in unexpected complicated situations related to the area of study X
5 Can develop strategies, implement plans and principles on the area of study and can evaluate obtained results within the framework X
6 Can develop and extend the knowledge in the area and to use them with scientific, social and ethical responsibility X
7 Has the ability to follow recent developments within the area of research, to support research with scientific arguments and data, to communicate the information on the area of expertise in a systematically by means of written report and oral/visual presentation X
8 To have an oral and written communication ability in at least one of the common foreign languages ("European Language Portfolio Global Scale", Level B2) X
9 Has software and hardware knowledge in the area of expertise, and has proficient information and communication technology knowledge X
10 Follows scientific, cultural, and ethical criteria in collecting, interpreting and announcing data in the research area and has the ability to teach. X
11 Has professional ethical consciousness and responsibility which takes into account the universal and social dimensions in the process of data collection, interpretation, implementation and declaration of results in mathematics and its applications. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application 16 2 32
Special Course Internship
Field Work
Study Hours Out of Class 16 4 64
Presentation/Seminar Prepration
Project
Report
Homework Assignments 5 5 25
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 20 20