| 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) |
Having advanced theoretical and practical knowledge supported by textbooks, application tools and other resources containing current information in the field. |
|
| 2) |
Ability to use advanced theoretical and practical knowledge acquired in the field. |
|
| 3) |
Ability to interpret and evaluate data, identify and analyze problems, and develop solution suggestions based on research and evidence, using the advanced knowledge and skills acquired in the field. |
|
| 4) |
To be able to inform relevant people and institutions on issues related to the field; Ability to convey thoughts and solution suggestions to problems in written and oral form. |
|
| 5) |
Ability to share one's thoughts on issues related to one's field and solutions to problems, supported by quantitative and qualitative data, with experts and non-experts. |
|
| 6) |
Ability to organize and implement projects and events for the social environment in which one lives with awareness of social responsibility. |
|
| 7) |
Ability to monitor knowledge in the field and communicate with colleagues by using a foreign language at least at the European Language Portfolio B1 General Level. |
|
| 8) |
Ability to use information and communication technologies along with computer software at least at the Advanced Level of the European Computer Usage License required by the field. |
|
| 9) |
Acting in accordance with social, scientific, cultural and ethical values during the collection, interpretation, application and announcement of the results of data related to the field. |
|
| 10) |
Having sufficient awareness about the universality of social rights, social justice, quality culture and protection of cultural values, environmental protection, occupational health and safety. |
|
| 11) |
Ability to evaluate the advanced knowledge and skills acquired in the field with a critical approach. |
|
| 12) |
Ability to identify learning needs and direct learning |
|
| 13) |
Being able to develop a positive attitude towards lifelong learning. |
|
| 14) |
Ability to independently carry out an advanced study related to the field. |
|
| 15) |
Ability to take responsibility individually and as a team member to solve unforeseen complex problems encountered in field-related applications. |
|
| 16) |
Ability to plan and manage activities aimed at the development of the employees under his/her responsibility within the framework of a project. |
|
Istanbul Health and Technology University INFORMATION PACKAGE / COURSE CATALOGUE