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Description of Individual Course Units
| Course Unit Code | Course Unit Title | Type of Course Unit | Year of Study | Semester | Number of ECTS Credits |
|---|---|---|---|---|---|
| 1989001042010 | MATHEMATICS-II | 1 | 2 | 3,00 |
Level of Course Unit
Önlisans
Language of Instruction
Turkish
Objectives of the Course
The aim of the course is to teach students the concepts of limit, partial derivative, multiple integral in functions of several variables and important theorems of vector analysis and to gain application skills in engineering.
Name of Lecturer(s)
Learning Outcomes
| 1 | Ability to calculate the derivatives of functions of several variables. |
| 2 | Ability to perform optimization applications by finding the maximum and minimum values of multivariable functions. |
| 3 | Ability to calculate multiple integrals in cartesian, polar, cylindrical, and spherical coordinates. |
| 4 | Ability to perform applications of the line integral. |
| 5 | Ability to comprehend the concepts and applications of Gradient, Divergence, and Curl. |
| 6 | Ability to comprehend the Green theorem and to perform physical applications of vector calculus. |
Mode of Delivery
Face to Face
Prerequisities and Co-Requisities
None
Recommended Optional Programme Components
None
Content of the Course
Functions of several variables. Limits and continuity. Partial Derivatives. Tangent planes and normal lines. Gradients and directional derivatives. Jacobian determinant. Extreme values of functions of several variables. Lagrange multipliers. Double integral in Cartesian and Polar coorsinates. Triple integrals. Cylindrical coordinates. Spherical coordinates. Vector and scalar fields. Line integral. Gradient, Divergence, and Curl. Green’s theorem. Physical applications of Vector calculus.
Weekly Detailed Course Contents
| Week | Subjects (Theoretical) | Teaching Methods | Preparatory |
|---|---|---|---|
| 1 | Functions of several variables. Limits and continuity. | ||
| 2 | Functions of several variables. Partial Derivatives. | ||
| 3 | Higher-order derivatives. Chain rule. Gradient and directional derivatives. | ||
| 4 | Tangent planes and normal lines of surfaces. Linear approximation. Taylor series for functions of two variables. | ||
| 5 | Extreme values of functions of several variables. Extreme values of functions defined on restricted domains. | ||
| 6 | Lagrange multipliers. Optimization applications for functions of several variables. | ||
| 7 | Multiple integral. Iteration of double integrals in Cartesian coordinates. Double integrals in Polar coordinates. | ||
| 8 | Midterm Exam | ||
| 9 | Triple integrals. Cylindrical coordinates. Spherical coordinates. | ||
| 10 | Applications of multiple integrals. | ||
| 11 | Vector and scalar fields. | ||
| 12 | Line integral and its applications. | ||
| 13 | Gradient, Divergence, and Curl. | ||
| 14 | Green’s theorem and its applications. | ||
| 15 | Some physical applications of Vector calculus. | ||
| 16 | Final Exam |
Text Book / Material / Recommended Resources
1) Adams R., Essex C. "Calculus: A Complete Course", Eighth Edition, Pearson, 2014. 2) Briggs W., Cochran L., Gillett B. "Calculus for Scientists and Engineers: Early Transcendentals", Pearson, 2013. 3) Thomas G.B. "Thomas' Calculus: Early Transcendentals", Pearson, 2013. 4) James G. "Modern Engineering Mathematics", Pearson, 2010. 5) Stein S.K. , Barcellos A. “Calculus and Analytic Geometry”, McGraw-Hill, 1992.
Planned Learning Activities and Teaching Methods
Assessment Methods and Criteria
| Term (or Year) Learning Activities | Quantity | Weight |
|---|---|---|
| Midterm Examination | 1 | 100 |
| Total | 100 | |
| End Of Term (or Year) Learning Activities | Quantity | Weight |
| Final Examination | 1 | 100 |
| Total | 100 | |
| Term (or Year) Learning Activities | 40 | |
| End Of Term (or Year) Learning Activities | 60 | |
Work Pacement(s)
None
Workload Calculation
| Activities | Number | Time (hours) | Total Work Load (hours) |
|---|---|---|---|
| Midterm Examination | 1 | 1 | 1 |
| Final Examination | 1 | 1 | 1 |
| Attending Lectures | 14 | 2 | 28 |
| Team/Group Work | 14 | 1 | 14 |
| Report Preparation | 14 | 1 | 14 |
| Self Study | 14 | 3 | 42 |
| Total Work Load (hours) | 100 | ||
Contribution of Learning Outcomes to Programme Outcomes
| PO 1 | PO 2 | PO 3 | PO 4 | PO 5 | PO 6 | PO 7 | PO 8 | PO 9 | PO 10 | PO 11 | PO 12 | PO 13 | |
| LO 1 | 3 | 4 | 3 | ||||||||||
| LO 2 | 3 | 4 | 3 | ||||||||||
| LO 3 | 3 | 4 | 3 | ||||||||||
| LO 4 | 3 | 4 | 3 | ||||||||||
| LO 5 | 3 | 4 | 3 | ||||||||||
| LO 6 | 3 | 4 | 3 |
* Contribution Level: 1 Very low 2 Low 3 Medium 4 High 5 Very High