Faculty of Engineering and Natural Sciences · Food Engineering (English 30%) · Undergraduate
ECTS: 6 T+P+L: 4+0+0 Compulsory
Coordinator: Dr. Öğr. Üyesi Sümeyra BEDİR
Prerequisites: MAT 115 - Mathematics I
Course Objective
The aim of this course is to provide a mathematical foundation for students studying in engineering program.
Course Content
It includes integration techniques, generalized integral, arrays, infinite series, power series, parametric curves, polar coordinates and integration in polar coordinates.
Required Resources
Calculus, Early Transcendentals, 7th Edition, by J. Stewart, 2008, Brook/Cole
Recommended Resources
Genel Matematik 1, Mustafa Balci, Balci yayinlari
Course Learning Outcomes
- Using appropriate integral techniques including methods such as integration with simple fractions, trigonometric transformation, partial integration to integrate algebraic, logarithmic, exponential, trigonometric, and resultant functions.
- Calculate generalized integrals and apply tests for convergence.
- Calculation of the arc length, the surface area formed by the rotation of the graphs and parametric curves.
- Draw the polar curves, find the arc length and the surrounding area.
- Application of theorems about the limits of arrays.
- Using different tests to determine the convergence of series.
- Take power series and use them to represent functions.
- To determine the Taylor series of functions, to prove the convergence of functions and to find the range of convergence.
- Applying Taylor series to approach problems.
Core Area Distribution
(46) Mathematics and Statistics%100
Teaching Methods
ExpressionDiscussionExercise and PracticePresentationGuided PracticeBrain StormingSelf studyProblem Solving
Assessment & Evaluation
HomeworkOral ExamTesting (Essay / Tests: True-Falls, multiple-choice, short answer, matching)
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 14 | 4 | 56 |
| Out of Class Study Period | 20 | 3 | 60 |
| Midterm | 2 | 2 | 4 |
| Quiz | 10 | 1 | 10 |
| Assignment | 6 | 1 | 6 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 2 | 2 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | • 7.1: Integration by Parts • 7.2: Trigonometric Integrals | • 5: Review of Formulas and Integration Techniques |
| 2 | • 7.3: Trigonometric Substitution • 7.4: Integration of Rational Functions by Partial Fractions | Integration of Rational Functions by Partial Fractions |
| 3 | • 7.5: Strategy for Integration • 7.8: Improper Integrals | Improper Integrals |
| 4 | • 8.1: Arc Length • 8.2: Area of a Surface of Revolution | Arc Length, Area of a Surface of Revolution |
| 5 | • 10.1: Parametric Equations • 10.2: Calculus with Parametric Curves | Calculus with Parametric Curves |
| 6 | • 10.3: Polar Coordinates • 10.4: Area and Length in Polar Coordinates | Polar Coordinates |
| 7 | Review for Midterm Exam 1 | Review for Midterm Exam 1 |
| 8 | Ara Sınav | Ara Sınav |
| 9 | • 11.1: Sequences of Real Numbers | Sequences of Real Numbers |
| 10 | • 11.2 Infinite Series • 11.3: Integral Test and Estimates of Sums | Infinite Series |
| 11 | • 11.4: Comparison Tests • 11.5: Alternating Series | Comparison Tests |
| 12 | • 11.6: Absolute Convergence and the Ratio and Root Tests | Absolute Convergence and the Ratio and Root Tests |
| 13 | • 11.8: Power Series | • 11.8: Power Series |
| 14 | • 11.9: Representation of Functions as Power Series • 11.10: Taylor and Maclaurin Series | Representation of Functions as Power Series |
| 15 | • Final Exam Review | Final Exam Review |
| 16 | Final Sınavı | Final Sınavı |