# 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

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 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 An ability to apply knowledge in mathematics and basic sciences and computational skills to solve manufacturing engineering problems
2 An ability to define and analyze issues related with manufacturing technologies
3 An ability to develop a solution based approach and a model for an engineering problem and design and manage an experiment
4 An ability to design a comprehensive manufacturing system based on creative utilization of fundamental engineering principles while fulfilling sustainability in environment and manufacturability and economic constraints
5 An ability to chose and use modern technologies and engineering tools for manufacturing engineering applications
6 An ability to utilize information technologies efficiently to acquire datum and analyze critically, articulate the outcome and make decision accordingly
7 An ability to attain self-confidence and necessary organizational work skills to participate in multi-diciplinary and interdiciplinary teams as well as act individually
8 An ability to attain efficient communication skills in Turkish and English both verbally and orally
9 An ability to reach knowledge and to attain life-long learning and self-improvement skills, to follow recent advances in science and technology
10 An awareness and responsibility about professional, legal, ethical and social issues in manufacturing engineering
11 An awareness about solution focused project and risk management, enterpreneurship, innovative and sustainable development
12 An understanding on the effects of engineering applications on health, social and legal aspects at universal and local level during decision making process

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