### Calculus II (MATH 102)

2015 Fall
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)
Kağan Kurşungöz kursungoz@sabanciuniv.edu,
English
MATH101
Formal lecture,Recitation

### 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

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 solve optimization problems
Evaluate double integrals in Cartesian and polar coordinates and triple integrals in Cartesian, cylindrical and spherical 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. 5

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. 3

4. Communicate effectively by oral, written, graphical and technological means and have competency in English. 3

5. Take individual and team responsibility, function effectively and respectively as an individual and a member or a leader of a team. 1

1. Develop a thorough knowledge of theories, concepts, and research methods in the field and apply them in research design and data analysis. 1

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

3. Know how to access written and visual, primary and secondary sources of information, interpret concepts and data from a variety of sources in developing disciplinary and interdisciplinary analyses. 1

1. Possess and apply knowledge of mathematics, science, and engineering. 5

2. Design and conduct research, do experiments, as well as analyze and interpret data. 1

3. Identify, formulate, and solve engineering problems. 2

4. Use the techniques, skills, and modern engineering tools necessary for engineering practice. 1

5. Analyze, design and model engineering systems, components and processes. 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 25 Midterm 50 Exam 17 Homework 10 Other 8