CALCULUS-II

Course Description

This course provides the methods of differential and integral calculus with applications in geometry, physics and engineering. Topics included are as follows: Sequences and infinite series, properties of sequences, test for convergence, tests for series with both positive and nonpositive series, absolutely convergence and conditionally convergence . Power series, Taylor and Maclourin series, radius of convergence. Parametric equations and Polar coordinates, graph of polar equations, area in polar coordinates, arc length, speed on a curve and derivative of polar equations. Vectors and vector valued functions, dot product and cross product of two vectors. Lines and Planes. Functions of several variables, their domain, limit and partial derivatives and definite integral of a function over a region.

CALCULUS-II

Evaluation Tools (Active Term)

Course outcomes

1. 01 1. Identify the series and sequences
2. 02 2. decide the convergences of series and sequences.
3. 03 3. analyze the convergence criterion of power series
4. 04 5. Find parametric and polar equations
5. 05 analyze the several variable functions

Course Syllabus

Reference Books & Course Materials

1. 01 Thomas’ Calculus Early Transcendentals, M.D. Weir, J. Hass, F.R. Giordano, 12th Edition, Pearson, ISBN-13: 978-0321888549 ISBN-10: 0321888545
2. 02 Calculus, Larson Edwards, 9th Edition, Brooks/Cole . ISBN-13: 978-1285057095 ISBN-10: 1285057090
3. 03 Calculus, Complete Course, Roberts A. Adams, Eleventh Edition. ISBN-13: 978-0321549280 ISBN-10: 0321549287

Learning Outcomes

1. L01 1. Identify the series and sequences
2. L02 2. decide the convergences of series and sequences.
3. L03 3. analyze the convergence criterion of power series
4. L04 4. Apply multiple integrals
5. L05 5. Find parametric equations and find Taylor series of functions.

Program Outcomes

1. P01 Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems.
2. P02 Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
3. P03 Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose.
4. P04 Ability to devise, select, and use modern techniques and tools needed for analysing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively
5. P05 Ability to design and conduct experiments, gather data, analyse and interpret results for investigating complex engineering problems or discipline specific research questions
6. P06 Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
7. P07 Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions.
8. P08 Recognition of the need for lifelong learning ; ability to access information, to follow developments in science and technology, and to continue to educate him/herself
9. P09 Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice.
10. P10 Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
11. P11 Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.

Po-Lo Matrix