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.

### 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,

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English

Undergraduate

MATH102

Formal lecture,Interactive lecture

Interactive,Other

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__here__to view.Programs\Type | Required | Core Elective | Area Elective |

BA- Political Science | |||

BA-Cultural Studies | |||

BA-Cultural Studies | |||

BA-Economics | |||

BA-Economics | |||

BA-International Studies | |||

BA-International Studies | |||

BA-Management | |||

BA-Management | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Political Sci.&Inter.Relat. | |||

BA-Social & Political Sciences | |||

BA-Visual Arts&Visual Com.Des. | |||

BA-Visual Arts&Visual Com.Des. | |||

BS-Biological Sci.&Bioeng. | * | ||

BS-Computer Science & Eng. | * | ||

BS-Computer Science & Eng. | * | ||

BS-Electronics Engineering | * | ||

BS-Electronics Engineering | * | ||

BS-Industrial Engineering | * | ||

BS-Manufacturing Systems Eng. | * | ||

BS-Materials Sci. & Nano Eng. | * | ||

BS-Materials Science & Eng. | * | ||

BS-Mechatronics | * | ||

BS-Mechatronics | * | ||

BS-Microelectronics | |||

BS-Molecular Bio.Gen.&Bioeng | * | ||

BS-Telecommunications | * | ||

Mathematics |

### CONTENT

### 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,

### Update Date:

### ASSESSMENT METHODS and CRITERIA

Percentage (%) | |

Final | 30 |

Midterm | 30 |

Homework | 40 |

### RECOMENDED or REQUIRED READINGS

Textbook |
Calculus Early Transcendentals 2nd Edition (Global Edition), Briggs, Cochran & Gillett. |