# 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 N/A Bachelor’s Degree (First Cycle) Face To Face Lecture, Question and Answer, Problem Solving. 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. 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 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

### Sources

Course Book 1. Calculus: A complete Course, R. A. Adams, C. Essex, 7th Edition; Pearson Addison Wesley 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

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 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 Adequate knowledge of subjects related to mathematics, natural sciences, and Electrical and Electronics Engineering discipline; ability to apply theoretical and applied knowledge in those fields to the solution of complex engineering problems. X
2 An ability to identify, formulate, and solve complex engineering problems, ability to choose and apply appropriate models and analysis methods for this. X
3 An ability to design a system, component, or process under realistic constraints to meet desired needs, and ability to apply modern design approaches for this. X
4 The ability to select and use the necessary modern techniques and tools for the analysis and solution of complex problems encountered in engineering applications; the ability to use information technologies effectively
5 Ability to design and conduct experiments, collect data, analyze and interpret results for investigating complex engineering problems or discipline-specific research topics. X
6 An ability to function on multi-disciplinary teams, and ability of individual working.
7 Ability to communicate effectively orally and in writing; knowledge of at least one foreign language; active report writing and understanding written reports, preparing design and production reports, the ability to make effective presentation the ability to give and receive clear and understandable instructions. X
8 Awareness of the necessity of lifelong learning; the ability to access knowledge, follow the developments in science and technology and continuously stay updated.
9 Acting compliant with ethical principles, professional and ethical responsibility, and knowledge of standards used in engineering applications.
10 Knowledge about professional activities in business, such as project management, risk management, and change management awareness of entrepreneurship and innovation; knowledge about sustainable development.
11 Knowledge about the impacts of engineering practices in universal and societal dimensions on health, environment, and safety. the problems of the current age reflected in the field of engineering; awareness of the legal consequences of engineering solutions.

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