Course Information
SemesterCourse Unit CodeCourse Unit TitleT+P+LCreditNumber of ECTS CreditsLast Updated Date
2MTHM112Calculus II4+2+05621.10.2025

 
Course Details
Language of Instruction English
Level of Course Unit Bachelor's Degree
Department / Program Mechanical Engineering (English)
Type of Program Formal Education
Type of Course Unit Compulsory
Course Delivery Method Face To Face
Objectives of the Course 1.To provide the concepts and applications of the convergence of improper integrals, sequences and infinite series.
2.To provide the knowledge of applications of partial differentiation and multiple integrals.
3.To give an ability to apply knowledge of mathematics on engineering problems.
Course Content Improper integrals, Infinite sequences and series, Vectors in Space,Vector-Valued Functions, Multivariable Functions and Partial Derivatives , Multiple Integrals.
Course Methods and Techniques Lecture
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Asist Prof. Güler KARAPINAR
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources G.B Thomas, R. L. Finney, M.D.Weir, F.R.Giordano., 2005, Thomas Calculus, 10th Edition., Addison Wesley, ISBN:0201441411.
Course Notes 1:Lecture, 4:Homework, 10:Uygulama
Exams 1 Final Sınavı, 1 Ara Sınav, 1 Kısa Sınav

Course Category
Mathematics and Basic Sciences %50
Engineering %25
Engineering Design %25

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Mid-terms 1 % 30
Final examination 1 % 50
Total
2
% 80

 
ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Course Duration 14 6 84
Hours for off-the-c.r.stud 14 5 70
Mid-terms 1 2 2
Final examination 1 2 2
Total Work Load   Number of ECTS Credits 6 158

 
Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 Compute limits of sequences and series; determine the convergence of the series and the radius of convergence of power series
2 Represent a known function as a Taylor series; approximate a known function with a Taylor polynomial and determine the error involved.
3 Compute the standard representation of a vector in 3-space, compute the dot product and cross product of vectors; write equations of lines, planes and quadric surfaces in 3-space.
4 Use the concepts of continuity, differentiation, and integration of vector-valued functions.
5 Understand the multivariable functions, analyze limits, determine continuity, and compute partial derivatives of them; find tangent planes, directional derivatives.
6 Apply the second partials test, and Lagrange multipliers to approximate and solve optimization problems.
7 Compute multiple integrals and apply them in problem situations involving area and volume.

 
Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Improper Integrals
2 Sequences
3 Infinite Series
4 Infinite Series
5 Infinite Series
6 Infinite Series
7 Vectors in Space and Polar Coordinates
8 Vector-Valued Functions
9 MIDTERM EXAM
10 Multivariable Functions and Partial Derivatives
11 Multivariable Functions and Partial Derivatives
12 Multivariable Functions and Partial Derivatives
13 Multivariable Functions and Partial Derivatives
14 Multiple Integrals
15 Multiple Integrals
16 FINAL EXAM

 
Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12
All 5 5
C1 5 5
C2 5 5
C3 5 5
C4 5 5
C5 5 5
C6 5 5
C7 5 5

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