Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
---|---|---|---|---|---|
Mathematıcs I | MAT 111 | 1 | 4 + 0 | 4 | 6 |
Ön Koşul Dersleri | |
Önerilen Seçmeli Dersler | |
Dersin Dili | İngilizce |
Dersin Seviyesi | Lisans |
Dersin Türü | Zorunlu |
Dersin Koordinatörü | Dr.Öğr.Üyesi EMİNE ÇELİK |
Dersi Verenler | Dr.Öğr.Üyesi EMİNE ÇELİK, |
Dersin Yardımcıları | Research Assistants in mathematics department |
Dersin Kategorisi | Diğer |
Dersin Amacı | To give fundamental conceptions of mathematical analysis and limit,continuity, derivative and applications of derivative in single-valued functions |
Dersin İçeriği | Foreknowledge, functions, Limit and continuity, Derivate, Application of derivative |
# | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
---|---|---|---|
1 | He/she defines sets and number set concepts. Explains equality, inequality and equation concepts. | Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, | Testing, Oral Exam, Homework, |
2 | He/she recognizes functions and its properties. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
3 | He/she expresses trigonometric, reverse trigonometric and hyperbolic functions, partial function and special functions ( Absolute value, exact value and sign functions) | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
4 | He/she expresses concept of limit and calculates. Can prove the rules which are used for limit. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
5 | He/she defines right and left approached limit. Knows the undetermined conditions. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
6 | He/she defines the concept of continuity and discontinuity. | Lecture, Drilland Practice, Problem Solving, | Testing, Oral Exam, Homework, |
7 | He/she can explain concept of derivative and calculates derivatives with this definition. Proves the derivative rules with the definition of derivative. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
8 | Can define the derivative of trigonometric, reverse trigonometric functions, Exponential and logarithmic function, hyperbolic and revere hyperbolic functions. | Lecture, Drilland Practice, Problem Solving, | Testing, Homework, |
9 | He/she calculates high order derivatives. Can define the derivatives of given functions and parametric equations. Express the derivative of implicit functions. | Lecture, Drilland Practice, Problem Solving, | Testing, Oral Exam, Homework, |
10 | Defines the increasing and decreasing functions with the help of tangent and normal equations. | Lecture, Question-Answer, Drilland Practice, Demonstration, Motivations to Show, | Testing, Oral Exam, |
11 | Can calculate the limit of undetermined conditions with the help of derivatives. | Lecture, Question-Answer, Problem Solving, | Testing, Oral Exam, |
12 | Can define the maximum, minimum and asymptote of functions. | Lecture, Question-Answer, Drilland Practice, Problem Solving, | Testing, Oral Exam, Homework, |
13 | Expresses the curve plot. | Lecture, Question-Answer, Problem Solving, | Testing, Oral Exam, |
14 | Solves the engineering problems with the help of derivative and approximates with differential approach. | Lecture, Question-Answer, Problem Solving, | Testing, Oral Exam, Homework, |
Hafta | Ders Konuları | Ön Hazırlık |
---|---|---|
1 | Sets. Number sets. Equations. Equality and inequality. | |
2 | Concept of function. Types of functions (Polynomial sets, rational function, exponential and logarithmic functions and the definition set of these functions) | |
3 | Function types (Trigonometric, reverse trigonometric and hyperbolic functions, Partial functions , special defined functions (Absolute value, exact value, sign functions). | |
4 | Concept of limit and limit calculation with the definition of limit. Proof of the rules used for limit rule. Sandwich theorem. Limit of trigonometric functions. | |
5 | Right and left limit. Undetermined conditions (0/0,infinity/infinity, 0.infinity, infinity-infinity,1^infinity) | |
6 | Continuity concept in functions. Types of discontinuity and characteristics of continuous functions (Mid value theorem, absolute maximum and minimum, concept of local maximum and minimum. ) | |
7 | Concept of derivative, and calculation with derivative rule. Proof of derivate with derivative rule. Derivative of reverse function. | |
8 | Derivative of trigonometric and reverse trigonometric functions. Derivative of exponential and logarithmic functions. Derivative of hyperbolic and reverse hyperbolic functions. | |
9 | High order derivatives. Derivatives of functions with parametric equations. Derivative of implicit functions. | |
10 | Equation of tangent and normal. Increasing and decreasing functions. | |
11 | Undetermined conditions ( Analyses of 8 condition with L’hopital Rule ) | |
12 | Maximum, minimum and asymptote of functions. | |
13 | Curve plotting. | |
14 | Engineering problems. Approximation with differential. |
Kaynaklar | |
---|---|
Ders Notu | Lecture Notes |
Ders Kaynakları | [1] Thomas, G.B., Thomas` Calculus, 13e, Pearson Education, 2013. [2] Larson, R., Edwards, B., Calculus, 11e, Cengage Learning, 2018. [3] Stewart, J. Calculus, 8e, Cengage Learning, 2016. |
Değerlendirme Sistemi | |
---|---|
Yarıyıl Çalışmaları | Katkı Oranı |
1. Ara Sınav | 70 |
1. Kısa Sınav | 10 |
2. Kısa Sınav | 10 |
1. Ödev | 10 |
Toplam | 100 |
1. Yıl İçinin Başarıya | 50 |
1. Final | 50 |
Toplam | 100 |
AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
---|---|---|---|
Course Duration (Including the exam week: 16x Total course hours) | 16 | 4 | 64 |
Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
Mid-terms | 1 | 10 | 10 |
Quiz | 1 | 25 | 25 |
Assignment | 1 | 15 | 15 |
Toplam İş Yükü | 162 | ||
Toplam İş Yükü / 25 (Saat) | 6,48 | ||
Dersin AKTS Kredisi | 6 |