Faculty of Education · Secondary School Mathematics Education · Undergraduate
Course Objective
To learn basic definitions and theorems of analysis, to learn the methodology of constructing a scientific structure by proving the theories and their properties by using the definitions and axioms, to assimilate basic mathematical knowledge, advanced analysis, functional analysis and use in all mathematics fields and to construct an infrastructure for this purpose, to learn analytical thinking and analysis.
Course Content
Sets, Induction Method, Real Number Series, Limits and Convergence in Sequences, Real Valuable Functions and Types, Limit and Continuity, Derivative and Derivative Rules, Rolle-Mean Value Theorems, Indeterminate Shapes, L'Hospital Rule, Exponential, Logarithmic, Trigonometric, Hyperbolic Functions in Cartesian Coordinates, Parametric and Polar Diagram Drawing.
Course Learning Outcomes
- Learns to prove by inductive method.
- Learns the limit in single variable functions and apply them to problems.
- Learns the derivatives in single variable functions and can apply them to problems.
- Develops analytical thinking and analysis skills.
- Builds mathematical models using mathematical knowledge.
- Mathematical thinking, identification and analysis.
Core Area Distribution
Teaching Methods
Assessment & Evaluation
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 16 | 2 | 32 |
| Out of Class Study Period | 10 | 2 | 20 |
| Midterm | 1 | 8 | 8 |
| Quiz | 0 | 0 | 0 |
| Assignment | 0 | 0 | 0 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 15 | 15 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | Set theory | Essential source 1 |
| 2 | Numbers: Real Numbers, Induction Method, Sum and Product Symbol | Essential source 1 |
| 3 | Relation, Cartesian Product | Essential source 1 |
| 4 | Functions and some special functions | Essential source 1 |
| 5 | Partial functions and polynomial functions | Essential source 1 |
| 6 | Trigonometric functions | Essentiail source 1 |
| 7 | Exponential and logarithmic functions | Essential Sources 1-2-3 |
| 8 | Midterm | Midterm |
| 9 | Sequences and limit of sequences | essential source 1-2-3 |
| 10 | Limit of functions | Essential source 1-2-3 |
| 11 | Continuity, discontinuity and discontinuity types | essential source 1-2-3 |
| 12 | Definition and properties of derivative | essential source 1-2-3 |
| 13 | Geometric Interpretation of Derivative | essential sources 1-2-3 |
| 14 | Applications of derivative | essential sources 1-2-3 |
| 15 | L’hospital | Essential sources 1-2-3 |
| 16 |