### Vector Calculus (MATH 206)

2021 Spring
Faculty of Engineering and Natural Sciences
Mathematics(MATH)
3
6.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)
Kağan Kurşungöz kursungoz@sabanciuniv.edu,
English
MATH102
Formal lecture,Interactive lecture
Interactive,Other

### CONTENT

Multiple integrals. Change of variables formula. Curvilinear coordinates. Inverse and implicit function theorems. Parameterization: Curves, vector fields, surfaces. Line integrals. Gradient fields. Green's theorem. Surface integrals. Calculus of vector fields: Curl, divergence.Stokes' and Gauss' theorems. Applications.

### OBJECTIVE

To introduce vector calculus that is usually skipped in basic freshmen
calculus courses and to relate these concepts to applications from a wide variety of areas.

### LEARNING OUTCOME

Upon completion of the course, student should be able to

use the change of coordinates in multiple integrals

parametrize basic curves and surfaces
evaluate line and surface integrals
understand the basic theorems of vector calculus; Green's, Stokes and the Divergence Theorem.
apply ideas from vector calculus to modeling and solve concrete problems.
follow related derivations in science and engineering with a better understanding,

### ASSESSMENT METHODS and CRITERIA

 Percentage (%) Final 30 Midterm 30 Homework 40