CIVIL ENGINEERING
Bachelor	TR-NQF-HE: Level 6	QF-EHEA: First Cycle	EQF-LLL: Level 6

Course Introduction and Application Information

Course Code	Course Name	Semester	Theoretical	Practical	Credit	ECTS
MAT1052	Calculus II	Spring	3	2	4	7

Basic information

Language of instruction:	English
Type of course:	Must Course
Course Level:	Bachelor’s Degree (First Cycle)
Mode of Delivery:	Face to face
Course Coordinator :	Assist. Prof. TÜRKAN YELİZ GÖKÇER ELLİDOKUZ
Course Lecturer(s):	Prof. Dr. SÜREYYA AKYÜZ Prof. Dr. İRİNİ DİMİTRİYADİS Prof. Dr. ENGİN HALİLOĞLU Assist. Prof. DUYGU ÜÇÜNCÜ Assist. Prof. LAVDİE RADA ÜLGEN RA AYSUN SOYSAL Assist. Prof. MÜRÜVVET ASLI AYDIN Prof. Dr. HALE GONCE KÖÇKEN Prof. Dr. MURAT SARI Assoc. Prof. DOĞAN AKCAN
Recommended Optional Program Components:	None
Course Objectives:	Gain proficiency in multivariable calculus to formulate and solve problems, and to communicate solutions to others. The course will provide students with a thorough understanding of the improper integral, sequences and series, functions of several variables, differentiation of functions of several variables, optimizing functions of several variables, integrating functions of several variables, and the polar coordinate system.

Learning Outcomes

The students who have succeeded in this course;
1) Determine the convergence and divergence of an improper integral
2) Define and determine the convergence/divergence of a sequence and use appropriate convergence tests to determine the convergence/divergence of a series
3) Find power series representations of functions, and approximate functions via Taylor polynomials
4) Find the domain and range of a function of several variables, and draw graphs of functions of several variables
5) Define vectors and operations on vectors
6) Compute partial derivatives, directional derivatives, and write equations of tangent planes to surfaces
7) Find and classify critical points of functions, and optimize functions in several variables
8) Evaluate double integrals in Cartesian and polar coordinates

Course Content

The teaching methods of the course are in the form of exposition and problem-solving. The topics covered in the course can be listed as follows: L'Hôpital's Rule and improper integrals. Sequences, infinite series, divergence and integral tests, ratio, root, comparison and alternating series tests. Power series, Taylor series. Vectors, dot product, cross product, planes and surfaces. Functions of several variables, partial derivatives, chain rule, directional derivatives, gradient, tangent planes. Maximum and minimum values problems, Lagrange multipliers. Double Integrals in Cartesian and polar coordinates.

Weekly Detailed Course Contents

Week	Subject	Related Preparation
1)	L'Hôpital's Rule, Improper Integrals
2)	Sequences, Infinite Series
3)	Geometric Series, Divergence and Integral Tests
4)	Ratio Test, Root Test, Comparison Test, Alternating Series Test
5)	Power Series, Taylor Series
6)	Taylor Series, Vectors, Dot Product
7)	Cross Products, Planes and Surfaces
8)	Planes and Surfaces, Level Curves, Functions in Several Variables
9)	Partial Derivatives, Chain Rule
10)	Directional Derivatives, Gradient, Tangent Planes
11)	Maximum and Minimum Problems
12)	Maximum and Minimum Problems, Lagrange Multipliers
13)	Double Integrals Over Rectangular and General Regions
14)	Double Integrals in Polar Coordinates

Sources

Course Notes / Textbooks:	Thomas' Calculus International Edition 12th Edition George Thomas, Maurice Weir, Joel Hass, Frank Giordano
References:	Calculus, Early Transcendentals, Metric Version, 8th Edition, by James Stewart, Cengage Learning. 2015 C.H. Edwards, Jr. David E. Penney, Calculus with Analytic Geometry Richard Silverman, Calculus with Analytic Geometry, Prentice Hall

Evaluation System

Semester Requirements	Number of Activities	Level of Contribution
Quizzes	4	% 24
Midterms	1	% 36
Final	1	% 40
Total		% 100
PERCENTAGE OF SEMESTER WORK		% 60
PERCENTAGE OF FINAL WORK		% 40
Total		% 100

ECTS / Workload Table

Activities	Number of Activities	Duration (Hours)	Workload
Course Hours	14	3	42
Application	14	2	28
Study Hours Out of Class	14	4	56
Quizzes	4	2	8
Midterms	1	17	17
Final	1	22	22
Total Workload			173

Contribution of Learning Outcomes to Programme Outcomes

No Effect	1 Lowest	2 Low	3 Average	4 High	5 Highest

	Program Outcomes	Level of Contribution
1)	Adequate knowledge in mathematics, science and civil engineering; the ability to use theoretical and practical knowledge in these areas in complex engineering problems.	5
2)	Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.	2
3)	Ability to design a complex system, process, structural and/or structural members to meet specific requirements under realistic constraints and conditions; ability to apply modern design methods for this purpose.
4)	Ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in civil engineering applications; ability to use civil engineering technologies effectively.
5)	Ability to design, conduct experiments, collect data, analyze and interpret results for the study of complex engineering problems or civil engineering research topics.	3
6)	Ability to work effectively within and multi-disciplinary teams; individual study skills.
7)	Ability to communicate effectively in English and Turkish (if he/she is a Turkish citizen), both orally and in writing.
8)	Awareness of the necessity of lifelong learning; ability to access information to follow developments in civil engineering technology.
9)	To act in accordance with ethical principles, professional and ethical responsibility; having awareness of the importance of employee workplace health and safety.
10)	Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
11)	Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of civil engineering solutions.