The aim of this course is to provide students with an understanding of limits, derivatives and indefinite integrals of functions of one variable and their calculations.
Cartesian Coordinates in the Plane
Graphs of Quadratic Equations
Lecture, problem solving
2. Week
Functions and Their Graphs
Combining Functions to Make New Functions
Lecture, problem solving
3. Week
Polynomials and Rational Functions
The Trigonometric Functions
Lecture, problem solving
4. Week
Limits of Functions
Limits of Infinity and Infinite Limits
Lecture, problem solving
5. Week
Continuity
Tangent Lines and Their Slopes
Lecture, problem solving
6. Week
The Derivative
Differentiation Rules
Lecture, problem solving
7. Week
The Chain Rule
Derivatives of Trigonometric Functions
Lecture, problem solving
8. Week
Higher-Order Derivatives
The Mean-Value Theorem
Lecture, problem solving
9. Week
Implicit Differentiation
Antiderivatives and the Indefinite Integral
Lecture, problem solving
10. Week
Inverse Functions
Exponential and Logarithmic Functions
Lecture, problem solving
11. Week
The Natural Logarithm and Exponential
The Inverse Trigonometric Functions
Lecture, problem solving
12. Week
Hyperbolic Functions
Indeterminate Forms
Lecture, problem solving
13. Week
Extreme Values
Concavity and Inflections
Lecture, problem solving
14. Week
Sketching the Graph of a Function
Lecture, problem solving
15. Week
16. Week
17. Week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Quizzes
10
20
Final Exam
1
40
Program Outcomes
PO-1
Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science.
PO-2
Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science.
PO-3
Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence.
PO-4
Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline.
PO-5
Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science.
PO-6
Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish.
PO-7
Using time effectively in inventing solutions by implementing analytical thinking.
PO-8
Understanding professional ethics and responsibilities.
PO-9
Having the ability to behave independently, to take initiative, and to be creative.
PO-10
Understanding the importance of lifelong learning and developing professional skills continuously.
PO-11
Using professional knowledge for the benefit of the society.
Learning Outcomes
LO-1
Discuss and explain the real numbers and the real line, Cartesian coordinates in the plane, graphs of quadratic equations
LO-2
Identify functions and their graphs to combine functions to make new functions, polynomials and rational functions
LO-3
Describe the trigonometric functions, inverse functions, the inverse trigonometric functions
LO-4
Explain exponential and logarithmic functions, the natural logarithm and exponential
LO-5
Identify limits of functions, limits at infinity and infinite limits
LO-6
Express the role continuity
LO-7
Use tangent lines and their slopes, the derivative and the differentiation rules
LO-8
Explain the importance of the Chain Rule; identify the derivatives of trigonometric functions, inverse functions, exponential and logarithmic functions, the Inverse Trigonometric Functions; use the higher-order derivatives
LO-9
Analyse the Mean Value Theorem and use implicit differentiation
LO-10
Identify the indeterminate forms and resolve them using l'Hopital's Rule
LO-11
Identify extreme values and solve the extreme-value problems
LO-12
Identify concavity and inflections
LO-13
Explain and discuss sketching the graph of a function
