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

Sources

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 Adequate knowledge in mathematics, science and subjects specific to the Materials Engineering; the ability to apply theoretical and practical knowledge of these areas to solve complex engineering problems and to model and solve of materials systems X
2 Understanding of science and engineering principles related to the structures, properties, processing and performance of Materials systems
3 Ability to identify, define, formulate and solve complex engineering problems; selecting and applying proper analysis and modeling techniques for this purpose X
4 Ability to design and choose proper materials for a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design and materials selection methods for this purpose X
5 Ability to develop, select and utilize modern techniques and tools essential for the analysis and solution of complex problems in Materails Engineering applications; the ability to utilize information technologies effectively X
6 Ability to design and conduct experiments, collect data, analyse and interpret results using statistical and computational methods for complex engineering problems or research topics specific to Materials Engineering X
7 Ability to work effectively in inter/inner disciplinary teams; ability to work individually
8 Effective oral and written communication skills in Turkish; knowlegde of at least one foreign language; the ability to write effective reports and comprehend written reports, to prepare design and production reports, to make effective presentations, to give and receive clear and understandable instructions
9 Recognition of the need for lifelong learning; the ability to access information; follow recent developments in science and technology with continuous self-development
10 Ability to behave according to ethical principles, awareness of professional and ethical responsibility; knowledge of standards used in engineering applications
11 Knowledge on business practices such as project management, risk management and change management; awareness in entrepreneurship and innovativeness; knowledge of sustainable development
12 Knowledge of the effects of Materials Engineering applications on the universal and social dimensions of health, environment and safety, knowledge of modern age problems reflected on engineering; awareness of legal consequences of engineering solutions

ECTS/Workload Table

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
Total Workload 176