# Extended Calculus II (MATH158) Ders Detayları

Course Name Corse Code Dönemi Lecture Hours Uygulama Saati Lab Hours Credit ECTS
Extended Calculus II MATH158 2. Semester 4 2 0 5 7.5
Pre-requisite Course(s)
Math 157 Extended Calculus I
Course Language İngilizce Service Courses Taken From Other Departments Lisans Face To Face Lecture, Question and Answer, Problem Solving. The course is designed as a continuation of Math 157 Extended Calculus I and aims to give the students the computational skills in series, analytic geometry and multi-variable differential and integral calculus and line integrals 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, chain rule, directional derivatives, gradient vectors and tangent planes, find local and absolute extrema of multivariable functions and use the Lagrange Multipliers understand and use double and triple integrals in different coordinate systems, understand line integral understand and apply the Green’s Theorem in plane 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 9.2 Infinite Series, 9.3 Convergence Tests for Positive Series (The Integral Test,Comparison Tests, The Ratio and Root Tests) pp:503-519
2 9.4 Absolute and Conditional Convergence, 9.5 Power Series pp:520-536
3 9.6 Taylor and Maclaurin Series (Convergence of Taylor Series; Error Estimates) 9.7 Applications of Taylor and Maclaurin Series, pp:536-549
4 10.1 Analytic Geometry in Three Dimensions, 10.2 Vectors, 10.3 The Cross Product in 3-Space, pp:562-585
5 10.4 Planes and Lines, 10.5 Quadric Surfaces, pp:585-596
6 12.1 Functions of Several Variables, 12.2 Limits and Continuity pp:669-681
7 Midterm
8 12.3 Partial Derivatives, 12.4 Higher Order Derivatives, pp:681-693
9 12.5 The Chain Rule, 12.6 Linear Approximations, Differentiability, and Differentials, pp:693-705 pp:706-707
10 12.7 Gradient and Directional Derivatives, 12.8 Implicit Functions, pp:714-726
11 13.1 Extreme Values, 13.2 Extreme Values of Functions Defined on Restricted Domains, 13.3 Lagrange Multipliers, pp:743-754 pp:756-760
12 14.1 Double Integrals, 14.2 Iteration of Double Integrals in Cartesian Coordinates, pp:790-802
13 14.4 Double Integrals in Polar Coordinates, 14.5 Triple Integrals pp:808-812 pp:818-824
14 14.6 Change of Variables in Triple Integrals (Cylindrical and Spherical Coordinates) 15.1 Vector and Scalar Fields, 15.2 Conservative Fields pp:824-830 pp:842-857
15 15.3 Line Integrals, 15.4 Line Integrals of Vector Fields, 16.3 Green’s Theorem in the Plane, pp:858-869 pp:903-906
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

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Accumulated knowledge on mathematics, science and mechatronics engineering; an ability to apply the theoretical and applied knowledge of mathematics, science and mechatronics engineering to model and analyze mechatronics engineering problems. X
2 An ability to differentiate, identify, formulate, and solve complex engineering problems; an ability to select and implement proper analysis, modeling and implementation techniques for the identified engineering problems. X
3 An ability to design a complex system, product, component or process to meet the requirements under realistic constraints and conditions; an ability to apply contemporary design methodologies; an ability to implement effective engineering creativity techniques in mechatronics engineering. (Realistic constraints and conditions may include economics, environment, sustainability, producibility, ethics, human health, social and political problems.) X
4 An ability to develop, select and use modern techniques, skills and tools for application of mechatronics engineering and robot technologies; an ability to use information and communications technologies effectively.
5 An ability to design experiments, perform experiments, collect and analyze data and assess the results for investigated problems on mechatronics engineering and robot technologies. X
6 An ability to work effectively on single disciplinary and multi-disciplinary teams; an ability for individual work; ability to communicate and collaborate/cooperate effectively with other disciplines and scientific/engineering domains or working areas, ability to work with other disciplines.
7 An ability to express creative and original concepts and ideas effectively in Turkish and English language, oral and written, and technical drawings.
8 An ability to reach information on different subjects required by the wide spectrum of applications of mechatronics engineering, criticize, assess and improve the knowledge-base; consciousness on the necessity of improvement and sustainability as a result of life-long learning; monitoring the developments on science and technology; awareness on entrepreneurship, innovative and sustainable development and ability for continuous renovation.
9 Consciousness on professional and ethical responsibility, competency on improving professional consciousness and contributing to the improvement of profession itself.
10 A knowledge on the applications at business life such as project management, risk management and change management and competency on planning, managing and leadership activities on the development of capabilities of workers who are under his/her responsibility working around a project.
11 Knowledge about the global, societal and individual effects of mechatronics engineering applications on the human health, environment and security and cultural values and problems of the era; consciousness on these issues; awareness of legal results of engineering solutions.
12 Competency on defining, analyzing and surveying databases and other sources, proposing solutions based on research work and scientific results and communicate and publish numerical and conceptual solutions.
13 Consciousness on the environment and social responsibility, competencies on observation, improvement and modify and implementation of projects for the society and social relations and be an individual within the society in such a way that planing, improving or changing the norms with a criticism.

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 4 56
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury
Prepration of Final Exams/Final Jury 1 16 16