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 Acquires sufficient knowledge in mathematics, natural sciences, and related engineering disciplines; gains the ability to use theoretical and applied knowledge in these fields in solving complex engineering problems. X
2 Gains the ability to identify, define, formulate, and solve complex engineering problems; acquires the skill to select and apply appropriate analysis and modeling methods for this purpose. X
3 Gains the ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions, and applies modern design methods for this purpose.
4 Develops the skills to develop, select, and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in industrial engineering applications; gains the ability to effectively use information technologies.
5 Gains the ability to design experiments, conduct experiments, collect data, analyze and interpret results for the investigation of complex engineering problems or discipline-specific research topics. X
6 Acquires the ability to work effectively in intra-disciplinary and multidisciplinary teams, as well as individual work skills. X
7 Acquires effective oral and written communication skills in Turkish; at least one foreign language proficiency; gains the ability to write effective reports, understand written reports, prepare design and production reports, make effective presentations, and give and receive clear instructions.
8 Develops awareness of the necessity of lifelong learning; gains the ability to access information, follow developments in science and technology, and continuously renew oneself.
9 Acquires the consciousness of adhering to ethical principles, and gains professional and ethical responsibility awareness. Gains knowledge about the standards used in industrial engineering applications.
10 Gains knowledge about practices in the business life such as project management, risk management, and change management. Develops awareness about entrepreneurship and innovation. Gains knowledge about sustainable development.
11 Gains knowledge about the universal and social dimensions of the impacts of industrial engineering applications on health, environment, and safety, as well as the problems reflected in the engineering field of the era. Gains awareness of the legal consequences of engineering solutions.
12 Gains skills in the design, development, implementation, and improvement of integrated systems involving human, material, information, equipment, and energy.
13 Gains knowledge about appropriate analytical and experimental methods, as well as computational methods, for ensuring 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