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ISTANBUL GELİŞİM UNIVERSITY INFORMATION SYSTEM

ADVANCED MATHEMATICS COURSE IDENTIFICATION AND APPLICATION INFORMATION

Code Name of the Course Unit Semester In-Class Hours (T+P) Credit ECTS Credit
MAT451 ADVANCED MATHEMATICS 7 5 5 6

WEEKLY COURSE CONTENTS AND STUDY MATERIALS FOR PRELIMINARY & FURTHER STUDY
Week Preparatory Topics(Subjects) Method
1 - Multivariable Functions: Limit, Continuity, Partial Derivatives -
2 - Chain Rule, Directional Derivative, Gradient Vector -
3 - Tangent Plane and Normal Line Equations, Linearization, and Differentiability -
4 - Maximum and Minimum in Multivariable Functions -
5 - Lagrange Multiplier Method, Taylor’s Formula for Multivariable Functions -
6 - Double Integrals, Area, and Moment -
7 - Double Integrals in Polar Coordinates / Midterm I Triple Integrals, Cylindrical and Spherical Coordinates -
8 - Change of Variables and Applications of Triple Integrals, Generalized Multivariable Integrals -
9 - Line Integrals, Vector Fields, Path Independence -
10 - MID-TERM EXAM -
11 - Potential Function, Fundamental Theorems of Line Integrals -
12 - Green’s Theorem in the Plane -
13 - Surface Area and Surface Integrals -
14 - Stokes' and Divergence (Gauss) Theorems -
15 - Stokes' and Divergence (Gauss) Theorems -
16 - FINAL EXAM -
17 - FINAL EXAM -