Week |
Subject |
Related Preparation |
1) |
Functions: Domain, Functions and Their Graphs, Even-odd Functions, Symmetry, Operations on Functions, Piecewise Functions, Polynomials and Rational Functions, Trigonometric Functions. |
|
2) |
Limit and Continuity: Limit of a Function and Limit Rules, Sandwich Theorem, Exact Definition of Limit, One-Sided Limits, Limits Including Infinity, Infinite Limits. |
|
3) |
Continuity: Continuity at a Point, Continuous Functions, Intermediate Value Theorem, Types of Discontinuity. Derivative: Tangent and Normal Lines, Derivative at a Point, Derivative as a Function, One-Sided Differentiation. |
|
4) |
Derivative on an Interval, Derivative Rules, Higher Order Derivatives, Derivatives of Trigonometric Functions, Chain Rule, Derivative in Implicit Functions, Linearization and Differentials, Increasing-Decreasing Functions. |
|
5) |
Transcendent Functions: Inverse Functions and Derivatives, Properties and Derivatives of Exponential and Logarithmic Functions, Inverse Trigonometric Functions and Derivatives, Hyperbolic and Inverse Hyperbolic Functions and Derivatives. |
|
6) |
Indeterminate forms and L'Hopital's Rule, Extremum values of functions, Critical points. |
|
7) |
Rolle's Theorem, Mean Value Theorem, First Derivative Test for Local Extrema, Concavity, Second Derivative Test for Concavity, Inflection Points, Second Derivative Test for Local Extrema. |
|
8) |
Sketch graph. |
|
9) |
Indefinite Integral, Integration Table Integral: Estimating with Area and Finite Sums, Sigma Notation and Limits of Finite Sums, Riemann Sums, Definite Integral, Properties of the Definite Integral, Area Under the Graph of a Non-Negative Function, Average Value of a Continuous Function. |
|
10) |
Mean Value Theorem for Definite Integrals, Fundamental Theorem of Calculus: Fundamental Theorem Part 1, Fundamental Theorem Part 2.
|
|
11) |
Integration Techniques: Substitution Technique (Variable Substitution), Partial Integration, Trigonometric Integrals, Reduction Formulas. |
|
12) |
Applications of Definite Integral: Calculation of Areas of Plane Regions, Area Between Two Curves, Calculation of Volumes of Rotational Objects (Disk Method, Washer Method, Cylindrical Shell Method), Arc Length, Areas of Rotational Surfaces. |
|
13) |
Improper Integrals. |
|
14) |
Example Solutions |
|
Course Notes / Textbooks: |
Thomas Calculus Cilt I, George B. Thomas, Maurice D. Weir, Joel R. Hass, Frank Giordano, Beta Yayınları, 2009. |
References: |
Thomas Calculus Cilt I, George B. Thomas, Maurice D. Weir, Joel R. Hass, Frank Giordano, Beta Yayınları, 2009. |
|
Program Outcomes |
Level of Contribution |
1) |
To be able to use advanced theoretical and practical knowledge acquired in the field |
2 |
2) |
To be able to interpret and evaluate data using advanced knowledge and skills acquired in the field, to be able to identify and analyze problems, to be able to develop solutions based on research and evidence. |
3 |
3) |
To be able to plan and manage activities for the development of employees under his/her responsibility within the framework of a project. |
2 |
4) |
To act in accordance with social, scientific, cultural and ethical values in the stages of collecting, interpreting, applying and announcing the results of data related to the field. |
1 |
5) |
To be able to carry out an advanced level study related to the field independently. |
2 |
6) |
To be able to take responsibility individually and as a team member to solve complex and unforeseen problems encountered in applications related to the field. |
2 |
7) |
To have advanced theoretical and practical knowledge supported by textbooks, application tools and other resources containing up-to-date information in the field. |
2 |
8) |
To have sufficient awareness of the universality of social rights, social justice, quality culture and protection of cultural values, environmental protection, occupational health and safety. |
1 |
9) |
To be able to inform the relevant people and institutions about the issues related to the field; to be able to convey his / her thoughts and suggestions for solutions to problems in written and orally. |
1 |
10) |
To be able to share his/her thoughts and suggestions for solutions to problems related to his/her field with experts and non-experts by supporting them with quantitative and qualitative data. |
1 |
11) |
To be able to organize and implement projects and activities for the social environment in which he/she lives with a sense of social responsibility |
1 |
12) |
To be able to evaluate the advanced knowledge and skills acquired in the field with a critical approach |
1 |
13) |
To be able to identify their learning needs and direct their learning |
1 |