Course Language:
İngilizce
Course Objectives:
The aim of this course is to provide students with an understanding of limits, derivatives and integrals of functions of one variable and their calculations.
Course Content:
Functions. Limits and continuity. Derivatives. Rules of differentiation. Applications of derivatives; extreme values, sketching graphs of functions. Definite Integrals, the fundamental theorems of calculus. Methods of integration, areas of plane regions.
Course Methodology:
1: Lecture, 2: Problem Solving
Course Evaluation Methods:
A: Written examination
Vertical Tabs
Course Learning Outcomes
| Learning Outcomes | Teaching Methods | Assessment Methods |
| 1) Knows the concepts of limits and continuity of functions of a single variable and performs related calculations. | 1,2 | A |
| 2) Knows the concept of derivative and some of its applications and performs related calculations. | 1,2 | A |
| 3) Knows the concepts of definite, indefinite and improper integrals and some of their applications and performs related calculations. | 1,2 | A |
Course Flow
| COURSE CONTENT | ||
| Week | Topics | Study Materials |
| 1 | Limits of functions, Limits at infinity and infinite limits | (From textbook) 1.2,1.3 |
| 2 | Continuity, The formal definition of limit, Tangent lines and their slopes, | 1.4,1.5,2.1 |
| 3 | The derivative , Differentiation rules, The chain rule, | 2.2,2.3,2.4 |
| 4 | Derivatives of trigonometric functions, Higher order derivatives, The Mean-Value Theorem, | 2.5,2.6,2.8 |
| 5 | Implicit differentiation, Antiderivatives and Initial-Value Problems, Inverse functions, Exponential and logarithmic functions, | 2.9,2.10,3.1,3.2 |
| 6 | The natural logarithm and exponential, The inverse trigonometric functions, | 3.3,3.5 |
| 7 | Related rates , Indeterminate forms, | 4.1,4.3 |
| 8 | Extreme values, Concavity and inflections | 4.4,4.5 |
| 9 | Sketching the graph of a function, Extreme-value problems, | 4.6,4.8 |
| 10 | Linear approximations , Sums and sigma notation, Areas as limits of sums, The definite integral, | 4.9,5.1,5.2,5.3 |
| 11 | Properties of the definite integral, The Fundamental Theorem of Calculus | 5.4,5.5 |
| 12 | The method of substitution, Areas of plane regions | 5.6,5.7 |
| 13 | Integration by parts, Integrals of rational functions | 6.1,6.2 |
| 14 | Inverse substitutions, Improper integrals | 6.3,6.5 |
Recommended Sources
| Textbook | R. A. Adams and C. Essex, Calculus, 8th Ed., Pearson (2013) |
| Additional Resources |
Material Sharing
| MATERIAL SHARING | |
| Documents | |
| Assignments | |
| Exams | |
Assessment
| IN-TERM STUDIES | NUMBER | PERCENTAGE |
| Mid-terms | 1 | 80 |
| Quizzes | 0 | 0 |
| Assignments | 6 | 20 |
| Total | 100 | |
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | 1 | 50 |
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | 50 | |
| Total | 100 |
Course’s Contribution to Program
| COURSE'S CONTRIBUTION TO PROGRAM | |||||||
| No | Program Learning Outcomes | Contribution | |||||
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry) | X | |||||
| 2 | Acquiring fundamental knowledge on fundamental research fields in mathematics | X | |||||
| 3 | Ability form and interpret the relations between research topics in mathematics | X | |||||
| 4 | Ability to define, formulate and solve mathmatical problems | X | |||||
| 5 | Consciousness of professional ethics and responsibilty | X | |||||
| 6 | Ability to communicate actively | ||||||
| 7 | Ability of self-development in fields of interest | X | |||||
| 8 | Ability to learn, choose and use necessary information technologies | ||||||
| 9 | Lifelong education | ||||||
ECTS
| Activities | Quantity | Duration (Hour) |
Total Workload (Hour) |
| Course Duration (14x Total course hours) | 14 | 5 | 70 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 3 | 42 |
| Mid-terms (Including self study) | 2 | 4 | 8 |
| Quizzes | |||
| Assignments | 2 | 4 | 8 |
| Final examination (Including self study) | 1 | 12 | 12 |
| Total Work Load | 140 | ||
| Total Work Load / 25 (h) | 5.6 | ||
| ECTS Credit of the Course | 6 |