| 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) |
Ability to utilize advanced theoretical and applied knowledge in the field. |
1 |
| 2) |
Using the advanced knowledge and skills acquired in the field, being able to interpret and evaluate data, identify problems, analyze them, and develop solution proposals based on research and evidence. |
3 |
| 3) |
Being able to organize and implement projects and activities for the social environment in which one lives with a sense of social responsibility. |
1 |
| 4) |
Being able to follow information in one foreign language at least at the European Language Portfolio B1 General Level and communicate with colleagues in the field. |
1 |
| 5) |
Ability to use information and communication technologies together with at least European Computer Driving License Advanced Level computer software, as required by the field. |
1 |
| 6) |
Being able to evaluate advanced knowledge and skills in the field critically. |
1 |
| 7) |
Identifying learning needs and being able to direct learning. |
2 |
| 8) |
Developing a positive attitude towards lifelong learning. |
1 |
| 9) |
Acting in accordance with social, scientific, cultural, and ethical values in the stages of collecting, interpreting, applying, and announcing the results related to the field. |
1 |
| 10) |
Having sufficient awareness about the universality of social rights, social justice, quality culture, preservation of cultural values, as well as environmental protection, occupational health, and safety. |
1 |
| 11) |
Being able to conduct an advanced study independently in the field. |
2 |
| 12) |
To take responsibility individually and as a team member to solve complex problems encountered in the field of application, which are unforeseen. |
2 |
| 13) |
Being able to plan and manage activities for the development of those under their responsibility within the framework of a project. |
2 |
| 14) |
Possess advanced level theoretical and practical knowledge supported by textbooks with updated information, practice equipments and other resources. |
1 |
| 15) |
Being able to inform relevant individuals and institutions about the field; expressing their thoughts and solution proposals for problems both in written and verbal form. |
1 |
| 16) |
Being able to share your thoughts and solutions regarding subjects related to the field with both experts and non-experts, supported by quantitative and qualitative data. |
1 |
Istanbul Health and Technology University INFORMATION PACKAGE / COURSE CATALOGUE