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)
Math 251 Advanced Calculus I
Course Language English
Course Type Compulsory Departmental Courses
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Discussion, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives 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.
Course Learning Outcomes 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
Course Content 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


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

Evaluation System

Requirements Number Percentage of Grade
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
Percentage of Final Work 40
Total 100

Course Category

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

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

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Application 16 2 32
Special Course Internship
Field Work
Study Hours Out of Class 16 4 64
Presentation/Seminar Prepration
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
Total Workload 161