Faculty of Engineering and Natural Sciences · Industrial Engineering (English 30%) · Undergraduate
Course Objective
This course is designed to help the students to
1. Develop the mathematical concepts of limits, derivatives and integrals, and interpret them graphically and physically in the context of real-world problems.
2. Apply differentiation and integration formulas, and implement the limit and derivative concepts and techniques to analyze functions.
3. Apply the ideas and techniques of differentiation and integration to a variety of applications such as extreme values, rates of change, optimization, areas, and volumes.
4. Describe the basic ideas of differential calculus in algebraic, geometric, and numeric terms, and utilize graphs to estimate relative rates, extreme values, limits, and derivatives.
5. Employ numerical methods to evaluate limits, derivatives, and integrals and utilize the Computer Algebra System Maple, in the computer-based laboratory, efficiently as a tool.
Course Content
The course includes functions of one variable; limits and continuity, derivative and differantiation; chain rule, implicit differentiation. Applications of derivative; maxima and minima, the mean value theorem. L'Hospital rule. Integration; indefinite integrals, integral rules, definite integrals, the fundamental and the mean value theorems of integral calculus. Applications of definite integrals; length of curves, area, volumes of revolution.
Required Resources
Calculus, Early Transcendentals, 7th Edition, by J. Stewart, 2008, Brook/Cole Matematik 1, Mustafa Balci, Balci yayinları
Recommended Resources
Calculus, Early Transcendentals, 7th Edition, by J. Stewart, 2008, Brook/Cole
Matematik 1, Mustafa Balci, Balci yayinları
Course Learning Outcomes
- Evaluate limits graphically and numerically. Determine if a limit exists and evaluate limits analytically.
- 2 Use the concepts of the continuity, determine the continuity regions and the discontinuity types of functions.
- State the definition of derivative and give its geometrical interpretation.
- Use the derivative to find the equation of the tangent line at a point.
- Find the first and higher-order derivatives of a function by applying basic differentiation rules and find the rate of change using implicit derivatives.
- Use derivatives to approximate complicated functions and compute differentials.
- Evaluate the value of the limit using L’Hôpital’s rule.
- Apply Rolle’s, the Intermediate Value, and the Mean Value theorems.
- Set up related rates, optimization problems and use differentiation to solve them.
- Apply the extreme value theorem to determine extrema on a closed interval.
- Utilize the first and second derivative tests to find relative extrema, intervals for which the function is increasing or decreasing, concavity, and points of inflection
- Perform curve sketching (derivatives and curve shape, graphing).
- Compute the definite integral of any polynomial or root function, and integrate using the substitution technique
- Find upper, lower and middle sums for a region. Define the definite integral as a limit of Riemann sum approximations
- Evaluate definite integrals by using the Fundamental Theorem of Calculus and apply integration to compute areas between curves and volumes of solids of revolution.
Core Area Distribution
Teaching Methods
Assessment & Evaluation
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 | Limit Kavramı, Limitlerin Hesabı | Limit |
| 2 | Süreklilik ve Sonuçları | Süreklilik ve Sonuçları |
| 3 | Sonsuzluk İçeren Limitler | Sonsuzluk İçeren Limitler |
| 4 | Teğet Doğrular ve Hız, Türev | Teğet |
| 5 | Türev Hesabı: Kuvvet Kuralı, Çarpım ve Bölüm Kuralları | Türev Hesabı |
| 6 | Zincir Kuralı | Zincir Kuralı |
| 7 | Trigonometrik Fonksiyonların Türevleri, Üstel ve Logaritmik Fonksiyonların Türevleri | Trigonometrik Fonksiyonların Türevleri, Üstel ve Logaritmik Fonksiyonların Türevleri |
| 8 | Ara Sınav | Ara Sınav |
| 9 | Kapalı Türetme ve Ters Trigonometrik Fonksiyonlar, Ortalama Değer Teoremi | Ortalama Değer Teoremi |
| 10 | Lineer Yaklaşımlar ve and Newton Yöntemi | Lineer Yaklaşımlar ve and Newton Yöntemi |
| 11 | Belirsiz Şekiller ve L’Hôpital Kuralı, Maximum ve Minimum Değerler, Artan ve Azalan Fonksiyonlar | L’Hôpital Kuralı |
| 12 | Konkavlık ve İkinci Türev Testi, Eğri Çizimi | Eğri Çizimi |
| 13 | Optimizasyon, İlişkili Oranlar | Optimizasyon |
| 14 | Ters Türevler, Toplam Notasyonu ve Sonlu Toplamlar, Alan | Ters Türevler |
| 15 | Belirli İntegral, Analizin Temel Teoremi, Yerine Koyma Yöntemi ile İntegrasyon | Belirli İntegral |
| 16 | Final Sınavı | Final Sınavı |