MAT1052 Calculus IIBahçeşehir UniversityDegree Programs CIVIL ENGINEERINGGeneral Information For StudentsDiploma SupplementErasmus Policy StatementNational QualificationsBologna Commission
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 : Dr. Öğr. Üyesi GÜLSEMAY YİĞİT
Course Lecturer(s): Prof. Dr. SÜREYYA AKYÜZ
Dr. Öğr. Üyesi DOĞAN AKCAN
Recommended Optional Program Components: None
Course Objectives: The objective of the course is to give to the students an understanding of the integral and its applications as well as introducing them to sequences and series so as to improve their ability to think critically, and enrich the tools they can use in analyzing and solving problems.

Learning Outcomes

The students who have succeeded in this course;

1) Calculate the approximate area under the curve using the sigma notation and Riemann sums over infinite number of partition
2) Calculate the definite and indefinite integrals using substitution, fractional integral, trigonometric substitution, partial fraction and anti-derivative tables
3) Solve the problems of area finding and volume and arc length using definitions of definite integral
4) Define the irregular integrals and calculate the results of irregular integrals by defining the concepts of limit, convergence and divergence.
5) Determine the convergence or divergence by applying ratio, integral, limit comparison, alternative series and root tests to geometric, alternative, telescopic and power series.
6) Use the Taylor and MacLaurin series to represent functions
7) Find the limit, continuity, partial derivatives, tangent surfaces and normal lines in multivariable functions
8) Calculate the double integrals in multivariable functions, understand the change the integral sequence, find a volume limited to a region determined under a surface

Course Content

Definite integral, fundemantal theorem, indefinite integral and techniques of integration, application of the integral, areas, arc length, volumes and area of surfaces of revolution, numerical integration and improper integrals.

Sequences and series, convergence tests of series, alternating series, power series, Taylon, MacLaurin series and their applications.

Finding limit, continuity, partial derivatives, tangent surfaces and normal lines in multivariable functions.

Calculating double integrals in multivariable functions, changing the integral sequence, finding a volume limited to a region determined under a surface

Weekly Detailed Course Contents

Week Subject Related Preparation
1) Antiderivatives, Estimating areas with finite sums.Riemann sum, upper and lower sums.
2) Definite Integral. The Fundamental Theorem of Calculus. Properties of the definite integral.
3) Indefinite integral, substitution rule. Area Between Curves.
4) Basic Integration Formulas and integration by parts. Integrals of logaritmic and exponential functions. Integration of Rational Functions
5) Trigonometric Integrals,Trigonometric substitution and additional methods of integration. Improper Integrals,
6) Applications of Integrations, Volumes of Solids Revolution.
7) Arc Length and Surface Area, Sequences and Convergence
8) Review for Midterm
9) Infinite Series, Convergence Tests for Positive Series, Integral Test , comparison ratio and root tests.
10) Alternating Series, Absolute and Conditional Convergence, Power Series
11) Taylor and Maclaurin Series, Convergence of Taylor Series; error estimates, applications of power series.
12) Functions of Several Variables, Level Curves, Limits and Continuity, Partial Derivative, Higher Order Derivatives
13) Multiple Integration, Double Integrals, Iteration of Double Integrals in Cartesian Coordinates, Improper Integrals and a Mean Value Theorem
14) Review for Final Exam


Course Notes / Textbooks: Thomas' Calculus International Edition 12th Edition George Thomas, Maurice Weir, Joel Hass, Frank Giordano
References: James Stewart Calculus, 5th Ed. Brooks/Cole Publishing Company

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
Midterms 1 % 40
Final 1 % 60
Total % 100
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 47 1 47
Midterms 1 15 15
Final 1 25 25
Total Workload 157

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.