Faculty of Engineering and Natural Sciences · Electrical & Electronics Engineering (English 30%) · Undergraduate
ECTS: 5 T+P+L: 3+0+0 Compulsory
Coordinator: Doç. Dr. Sinem GÜLER
Instructors: Prof. Dr. KENZU ABDELLA
Prerequisites: MAT 116 - Mathematics II
Course Objective
students should develope a clear understanding of the fundamental concepts of single variable calculus and a range of skills allowing them to work effectively with the concepts.
Course Content
Covers calculus of functions of several variables, vectors and analytic geometry of three-dimensional space, partial derivatives, gradients, directional derivatives, maxima and minima, multiple integrals, line and surface integrals, Green’s theorem, divergence theorem and Stokes’ theorem.
Course Learning Outcomes
- Compute and interpret derivatives of vector functions, partial derivatives and gradients, and use them in applications including optimization
- Construct, evaluate and interpret multiple integrals in rectangular, polar, and cylindrical coordinates.
- Construct, evaluate, and interpret line and surface integrals using vector calculus techniques.
- Use vector methods to analyze curves and surfaces in 3-dimensional space
Core Area Distribution
(46) Mathematics and Statistics%60 (52) Engineering and Engineering Trades%40
Teaching Methods
ExpressionQuestion-AnswerDiscussionSelf studyProblem Solving
Assessment & Evaluation
HomeworkTesting (Essay / Tests: True-Falls, multiple-choice, short answer, matching)
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 16 | 3 | 48 |
| Out of Class Study Period | 16 | 3 | 48 |
| Midterm | 2 | 2 | 4 |
| Quiz | 10 | 1 | 10 |
| Assignment | 3 | 5 | 15 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 2 | 2 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | 12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product | MAT 116 |
| 2 | 12.4 The Cross Product 12.5 Equations of Lines and Planes 12.6 Cylinders and Quadric Surfaces | MAT 116 |
| 3 | 13.1 Vector Functions and Space Curves 13.2 Derivatives and Integrals of Vector Functions 13.3 Arc Length (curvature will not be examined) | MAT 116 |
| 4 | 13.4 Motion in Space: Velocity and Acceleration 14.1 Functions of Several Variables 14.2 Limits and Continuity | MAT 116 ve FİZ I |
| 5 | 14.3 Partial Derivatives 14.4 Tangent Planes and Linear Approximations | MAT 116 |
| 6 | 14.5 The Chain Rule 14.6 Directional Derivatives and the Gradient Vector | MAT 116 |
| 7 | 14.7 Maximum and Minimum Values 14.8 Lagrange Multipliers | MAT 116 |
| 8 | 15.1 Double Integrals over rectangles 15.2 Double Integrals over General Regions | MAT 116 |
| 9 | 15.3 Double Integrals in Polar Coordinates 15.4 Applications of Double Integrals 15.5 Surface Area | MAT 116 |
| 10 | 15.6 Triple Integrals 15.7 Triple Integrals in Cylindrical Coordinates | MAT 116 |
| 11 | 15.8 Triple Integrals in Spherical Coordinates 16.1 Vector Field | FIZ I |
| 12 | 16.2 Line Integrals 16.3 The Fundamental Theorem for Line Integrals | MAT 116 |
| 13 | 16.4 Green’s Theorem 16.5 Curl and Divergence | MAT 116 |
| 14 | 16.6 Parameterized Surfaces and Their Areas 16.7 Surface Integrals 16.8 Stokes’ Theorem | MAT 116 |
| 15 | 16.9 The Divergence Theorem | MAT 116 |
| 16 | Final | Bütün dönem |