Course Language:
English
Course Objectives:
The aim of this course is to provide students with an understanding of differentiation and integration of multivariable functions and their calculations.
Course Content:
Vector functions; space curves, derivatives and integrals, arc length, motion in space, parametric surfaces. Multiple integrals and applications. Vector calculus; vector fields, line integrals, Green’s theorem, curl and divergence, surface integrals, Stokes’ theorem, the divergence theorem.
Course Methodology:
1: Lecture, 2: Problem Solving
Course Evaluation Methods:
A: Written examination, B: Homework
Vertical Tabs
Course Learning Outcomes
| Learning Outcomes | Program Learning Outcomes | Teaching Methods | Assessment Methods |
| 1) Evaluates the arclength of space curves. | 1,2,7 | 1,2 | A |
| 2) Evaluates double and triple integrals. | 1,2,4,7 | 1,2 | A |
| 3) Changes variables in double and triple integrals. | 1,2,4,7 | 1,2 | A |
| 4) Evaluates line integrals and surface integrals. | 1,2,4,7 | 1,2 | A |
| 5) Expresses the concepts of circulation, work and flux using line and surface integrals. | 1,2,3,4,7 | 1,2 | A |
| 6) Uses Green's, Stokes' and the divergence theorems. | 1,2,3,4,7 | 1,2 | A |
Course Flow
| COURSE CONTENT | ||
| Week | Topics | Study Materials |
| 1 | Functions of Several Variables, Limits, Continuity, | Textbook |
| 2 | Partial Derivatives and Higher Order Derivatives | Textbook |
| 3 | Chain Rule, Gradient, Directional Derivatives,Extreme Values, Lagrange Multipliers | Textbook |
| 4 | Vector-Valued Functions : Arc Length, Vector Fields, Divergence and Curl | Textbook |
| 5 | Double and Triple Integrals : The Double Integral Over a Rectangle, The Double Integral Over More General Regions | Textbook |
| 6 | Changing the Order of Integration, The Triple Integral | Textbook |
| 7 | The Change of Variables Formula and Applications of Integration: The Geometry of Maps from R2 to R2, The Change of Variables Theorem | Textbook |
| 8 | Applications of Double and Triple Integrals, Improper Integrals | Textbook |
| 9 | Integrals: The Path Integral, Line Integrals | Textbook |
| 10 | Parametrized Surfaces, Area of a Surface | Textbook |
| 11 | Integrals of Scalar Functions Over Surfaces, Surface Integrals of Vector Functions | Textbook |
| 12 | The Integral Theorems of Vector Analysis: Green's Theorem | Textbook |
| 13 | Stokes' Theorem, Conservative Fields, | Textbook |
| 14 | Gauss' Theorem | Textbook |
Recommended Sources
| Textbook | “Vector Calculus”, 6th Edition, by J. Marsden and A. Tromba |
| Additional Resources |
Material Sharing
| Documents | |
| Assignments | |
| Exams |
Assessment
| IN-TERM STUDIES | NUMBER | PERCENTAGE |
| Mid-terms | 2 | 100 |
| Quizzes | ||
| Assignments | ||
| Total | 100 | |
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | 60 | |
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | 40 | |
| Total | 100 |
| COURSE CATEGORY | Core Courses |
Course’s Contribution to Program
| No | Program Learning Outcomes | Contribution | ||||
| 1 | 2 | 3 | 4 | 5 | ||
| 1 | The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) | X | ||||
| 2 | Acquiring fundamental knowledge on fundamental research fields in mathematics | X | ||||
| 3 | Ability form and interpret the relations between research topics in mathematics | X | ||||
| 4 | Ability to define, formulate and solve mathematical problems | X | ||||
| 5 | Consciousness of professional ethics and responsibilty | X | ||||
| 6 | Ability to communicate actively | X | ||||
| 7 | Ability of self-development in fields of interest | X | ||||
| 8 | Ability to learn, choose and use necessary information technologies | |||||
| 9 | Lifelong education | |||||
ECTS
| ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION | |||
| Activities | Quantity |
Duration (Hour) |
Total Workload (Hour) |
| Course Duration (14x Total course hours) | 14 | 5 | 70 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 5 | 70 |
| Mid-terms (Including self study) | 2 | 10 | 20 |
| Quizzes | - | - | - |
| Assignments | - | - | - |
| Final examination (Including self study) | 1 | 15 | 15 |
| Total Work Load | 175 | ||
| Total Work Load / 25 (h) | 7 | ||
| ECTS Credit of the Course | 7 | ||