### Calculus II (MATH 102)

2020 Spring
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
5.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)
English
MATH101
Interactive,Communicative,Discussion based learning,Guided discovery

### CONTENT

Sequences and series. Power series. Taylor polynomials, Taylor series and approximation. Visualizing functions of several variables; graphs and contour diagrams. Vectors. Differentation in several variables; partial and directional derivatives. Linear and quadratic approxiamtion. Classification of local extrema. Optimization, Lagrange Multipliers. Integration in several variables. Iterated integrals. Change of variables; polar, cylindrical and spherical coordinates.

### OBJECTIVE

To introduce series and concepts of multivariable calculus, to relate notions in multivariable calculus to their analogues in single variable.

### LEARNING OUTCOME

Understand the idea of integration over unbounded intervals and compute them
Define the notion of convergence of series and use various tests to determine series convergence
Find Taylor representations of functions and approximate functions via Taylor polynomials
Understand and use the concept of a function of several variables, draw graphs in 3-space
Use the properties of vectors and operations with vectors
Compute partial derivatives, directional derivatives and write equations of tangent planes to surfaces
Apply partial derivatives to find and test local extrema.
Evaluate double integrals in Cartesian and polar coordinates and triple integrals in Cartesian coordinates

### PROGRAMME OUTCOMES

1. Understand the world, their country, their society, as well as themselves and have awareness of ethical problems, social rights, values and responsibility to the self and to others. 1

2. Understand different disciplines from natural and social sciences to mathematics and art, and develop interdisciplinary approaches in thinking and practice. 4

3. Think critically, follow innovations and developments in science and technology, demonstrate personal and organizational entrepreneurship and engage in life-long learning in various subjects. 2

4. Communicate effectively in Turkish and English by oral, written, graphical and technological means. 4

5. Take individual and team responsibility, function effectively and respectively as an individual and a member or a leader of a team; and have the skills to work effectively in multi-disciplinary teams. 1

1. Possess sufficient knowledge of mathematics, science and program-specific engineering topics; use theoretical and applied knowledge of these areas in complex engineering problems. 4

2. Identify, define, formulate and solve complex engineering problems; choose and apply suitable analysis and modeling methods for this purpose. 4

3. Develop, choose and use modern techniques and tools that are needed for analysis and solution of complex problems faced in engineering applications; possess knowledge of standards used in engineering applications; use information technologies effectively. 2

4. Ability to design a complex system, process, instrument or a product under realistic constraints and conditions, with the goal of fulfilling specified needs; apply modern design techniques for this purpose. 2

5. Design and conduct experiments, collect data, analyze and interpret the results to investigate complex engineering problems or program-specific research areas. 1

6. Knowledge of business practices such as project management, risk management and change management; awareness on innovation; knowledge of sustainable development. 1

7. Knowledge of impact of engineering solutions in a global, economic, environmental, health and societal context; knowledge of contemporary issues; awareness on legal outcomes of engineering solutions; understanding of professional and ethical responsibility. 1

1. Develop knowledge of theories, concepts, and research methods in humanities and social sciences. 1

2. Assess how global, national and regional developments affect society. 1

3. Know how to access and evaluate data from various sources of information. 1

1. Demonstrate an understanding of economics, and main functional areas of management. 1

2. Assess the impact of the economic, social, and political environment from a global, national and regional level. 1

### ASSESSMENT METHODS and CRITERIA

 Percentage (%) Final 35 Midterm 30 Exam 15 Assignment 10 Participation 10