### Calculus II (MATH 102)

2021 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)
Nilay Duruk Mutlubaş -nilaydm@sabanciuniv.edu, Matteo Paganin -paganin@sabanciuniv.edu,
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

### ASSESSMENT METHODS and CRITERIA

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