Calculus II (MATH152) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Calculus II MATH152 4 2 0 5 7
Pre-requisite Course(s)
MATH151 Calculus I
Course Language English
Course Type N/A
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives The course is designed as a continuation of MATH151 Calculus I and aims to give the students the computational skills in series, analytic geometry and multi-variable differential and integral calculus to handle engineering problems.
Course Learning Outcomes The students who succeeded in this course;
  • understand and use sequences, infinite series, power series of functions, Taylor and Maclaurin series,
  • use analytic geometry through vectors and interpret lines, planes and surfaces in 3-dimensional space,
  • understand and use the functions of several variables, partial derivatives, directional derivatives, gradient vectors and tangent planes
  • find local and absolute extrema of multivariable functions, use Lagrange Multipliers and solve optimization problems,
  • understand and use double and triple integrals in different coordinate systems
Course Content Infinite series, vectors in the plane and polar coordinates, vectors and motions in space, multivariable functions and their derivatives, multiple integrals: double integrals, areas, double integrals in polar coordinates, triple integrals in rectangular, cylindrical and spherical coordinates, line integrals, Independence of path,Green's theorem.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 9.1. Sequences and Convergence, 9.2. Infinite Series, pp:495-409
2 9.3. Convergence Tests for Positive Series (The Integral Test, Comparison Tests, The Ratio and Root Tests), 9.4. Absolute and Conditional Convergence, pp:510-526
3 9.5. Power Series, 9.6. Taylor and Maclaurin Series (Convergence of Taylor Series; Error Estimates), pp:526-545
4 9.7. Applications of Taylor and Maclaurin Series, 10.1. Analytic Geometry in Three Dimensions, pp:546-549 pp:562-568
5 10.2. Vectors, 10.3. The Cross Product in 3-Space, pp:568-585
6 10.4. Planes and Lines, 10.5. Quadric Surfaces, pp:585-596
7 Midterm,
8 12.1. Functions of Several Variables, 12.2. Limits and Continuity, pp:669-681
9 12.3. Partial Derivatives, 12.4. Higher Order Derivatives, 12.5. The Chain Rule, pp:681-703
10 12.6. Linear Approximations, Differentiability, and Differentials, 12.7. Gradient and Directional Derivatives, 12.8. Implicit Functions, pp:703-705 pp:706-707 pp:714-726
11 13.1. Extreme Values, 13.2. Extreme Values of Functions Defined on Restricted Domains, pp:743-754
12 13.3. Lagrange Multipliers, 14.1. Double Integrals, pp:756-760 pp:790-796
13 14.2. Iteration of Double Integrals in Cartesian Coordinates, 14.4. Double Integrals in Polar Coordinates, pp:796-802 pp:808-812
14 14.5. Triple Integrals, 14.6. Change of Variables in Triple Integrals (Cylindrical and Spherical Coordinates), pp:818-830
15 14.6. Change of Variables in Triple Integrals (Cylindrical and Spherical Coordinates), pp:824-830
16 Final Exam


Course Book 1. Calculus: A complete Course, R. A. Adams, C. Essex, 7th Edition; Pearson Addison Wesley
Other Sources 2. Thomas’ Calculus Early Transcendentals, 11th Edition.( Revised by M. D. Weir, J.Hass and F. R. Giardano; Pearson , Addison Wesley)
3. Calculus: A new horizon, Anton Howard, 6th Edition; John Wiley & Sons
4. Calculus with Analytic Geometry, C. H. Edwards; Prentice Hall
5. Calculus with Analytic Geometry, R. A. Silverman; Prentice Hall

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 60
Final Exam/Final Jury 1 40
Toplam 3 100
Percentage of Semester Work 60
Percentage of Final Work 40
Total 100

Course Category

Core Courses X
Major Area Courses
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 An ability to apply knowledge of mathematics, science and engineering to Industrial Engineering; an ability to apply theoretical and practical knowledge to model and solve engineering problems. X
2 An ability to identify, formulate and solve complex engineering problems; an ability to select and apply proper analysis and modeling methods. X
3 An ability to design a complex system, process, tool or component to meet desired needs within realistic constraints; an ability to apply modern design.
4 An ability to develop, select and put into practice techniques, skills and modern engineering tools necessary for engineering practice; an ability to use information technology effectively.
5 An ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or disciplinary research topics. X
6 An ability to work individually, on teams, and/or on multidisciplinary teams. X
7 Ability to communicate effectively in Turkish orally and in writing; knowledge of at least one foreign language; effective report writing and understand written reports, preparing design and production reports, making effective presentations, giving and receiving clear and understandable instruction.
8 A recognition of the need for, and an ability to engage in life-long learning; an ability to use information-seeking tools and to follow the improvements in science and technology.
9 An ability to behave according to the ethical principles, an understanding of professional and ethical responsibility. Information on standards used in industrial engineering applications.
10 Knowledge of business applications such as project management, risk management and change management. A recognition of entrepreneurship, innovativeness. Knowledge of sustainable improvement.
11 Information on the effects of industrial engineering practices on health, environment and security in universal and societal dimensions and the information on the problems of the in the field of engineering of the era. Awareness of the legal consequences of engineering solutions.
12 An ability to design, development, implementation and improvement of integrated systems that include human, materials, information, equipment and energy.
13 Knowlede on appropriate analytical, computational and experimental methods to provide system integration.

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 4 64
Application 16 2 32
Special Course Internship
Field Work
Study Hours Out of Class 14 3 42
Presentation/Seminar Prepration
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 2 10 20
Prepration of Final Exams/Final Jury 1 18 18
Total Workload 176