Course Information
Course Title Code Semester T + P ECTS
Mathematics II MATH182 2 4 + 0 6

Prerequisites None

Language English
Level Bachelor's Degree
Type Compulsory
Coordinator Assoc.Prof. GÜLNİHAL MERAL
Instructors Assoc.Prof. GÜLNİHAL MERAL, Assoc.Prof. YUSUF KAYA, Assist.Prof. YÜKSEL SOYKAN, Assist.Prof. ZEKERİYA USTAOĞLU
Goals To introduce definite and indefinite integrals, to show fundamental formulas and methods for integration, to apply the integration techniques to science and engineering, to investigate sequence, series and their convergence, to introduce parametric curves and polar coordinates.
Contents Definite Integral, Fundamental Theorem of Calculus, Indefinite integral, Basic Integration Formulas, Integration Techniques, trigonometric Integrals, Improper Integrals, Application of definite Integrals: Area, volume, surface area, length of a curve, Center of Mass,Sequence and Series,Convergence of Sequences and Series, Convergence Tests for Series, Power Series and Radius of Convergence, Taylor Formula, Parametric Curves and Polar coordinates, Area and Length in Polar Coordinates.
Work Placement(s) Absent

Number Learning Outcomes
1 He/she is familiar with the definite and indefinite integral concepts.
2 He/she knows the basic integration rules and methods.
3 He/she can apply the integration techniques that he/she knows to science and engineering.
4 He/she knows sequence and series and can examine their convergence.
5 He/she knows the polar coordinates.

Mode of Delivery Face-to-Face
Planned Learning Activities & Teaching Methods Lecture, question-answer, exercises and applications, problem solving.
Assessment Methods Midterm exam, quiz,final exam



Course Content
Week Topics Study Materials
1 Definite Integral None.
2 Fundamental theorem of Calculus He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
3 Indefinite Integral, Basic Integration Rules He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
4 Techniques of Integration (Change of Variables, Integration by Parts) He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
5 Techniques of Integration (Partial Fractions, Trigonometric transformations) He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
6 Trigonometric integrals He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
7 Improper Integrals of first kind He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
8 Improper Integrals of second kind He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
9 Midterm He/she should revise all previous lectures and solve related exercises.
10 Applications of Definite Integrals(Volume, Surface Area) He/She should solve the questions asked in the midterm once again and try to see his/her mistakes, should read the week's subject from the lecture materials.
11 Applications of Definite Integrals(Length of a curve, Center of Mass, Work) He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
12 Sequences, Series He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
13 Convergence tests for series, power series He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.
14 Parametric curves and Polar Coordinates He/she should revise the previous week, should read the week's subject from the lecture materials, should solve exercises given in the previous week.



Sources
Textbook Thomas GB. Jr. , Weir M. D., Hass J., Calculus 1, (Çeviri: Recep Korkmaz, English edition published by Addison Wesley, 2005) , Beta Basım A.Ş., İstanbul, 2009.
Additional Resources 1. Stewart J., Calculus (Diferensiyel ve İntegral hesap), TÜBA, Ankara, 2007. 2. Balcı, M. Genel Matematik, Balcı Yayınları, Ankara, 2008. 3. Kadıoğlu, E, Kamali, M., Genel Matematik, Erzurum, 2005. 4. Adams R. A., Calculus: a complete course, Addison Wesley Longman, Toronto,2003.



Assessment System Quantity Percentage
In-Term Studies
Mid-terms 1 100
In-Term Total 1 100
Contribution of In-Term Studies to Overall 40
Contribution of Final Exam to Overall 60
Total 100





Course's Contribution to PLO
No Key Learning Outcomes Level
1 2 3 4 5
1 Has the sufficient background on mathematics, science and engineering in his own branch. x
2 Makes use of conceptual and applied knowledge in mathematics, science and in his own area in accordance for engineering solutions. x
3 Determines, defines, formulates and solves problems in engineering; fort his aim selects and applies the appropriate analytical models and modeling techniques. x
4 Analyses a system, system component or process and in order to meet the requirements, designs under realistic conditions; thus applies modern techniques of design. x
5 Selects and uses modern techniques and devices necessary for engineering applications. x
6 Designs and carries out experiments, collects data, analyzes and comments on the findings. x
7 Works effectively and individually on multi disciplinary teams. x
8 Accesses knowledge, and to do this, does research, uses databases and other data sources. x
9 Is aware of the importance of lifelong learning; follows advances in science and technology and updates his knowledge continuously. x
10 Uses communication and information technology at least at advanced level of European Computer Driving License. x
11 Communicates effectively both orally and in writing; uses a foreign language at least at B1 level of European Language Portfolio. x



ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION
Activities Quantity Duration (Hour) Total Work Load (h)
Course Duration 14 4 56
Hours for off-the-classroom study (Pre-study, practice) 14 4 56
Mid-terms 1 25 25
Final examination 1 30 30
Total Work Load (h) 167
Total Work Load / 30 (h) 5.57
ECTS Credit of the Course 6