| 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) |
Sufficient knowledge in mathematics, science and software engineering discipline-specific topics; the theoretical and practical knowledge in these areas, the ability to use in complex engineering problems. |
3 |
| 2) |
The ability to identify, formulate, and solve complex engineering problems; selecting and applying appropriate analysis and modelling methods for this purpose. |
3 |
| 3) |
The ability to design a complex system, process, device or product under realistic constraints and conditions to meet specific requirements; the ability to apply modern design methods for this purpose. |
3 |
| 4) |
Ability to develop, select and use modern techniques and tools necessary for analysis and solution of complex problems in engineering applications; ability to use information technologies effectively. |
2 |
| 5) |
Ability to design experiments, conduct experiments, collect data, analyse and interpret the results of complex engineering problems or discipline-specific research topics. |
2 |
| 6) |
Disiplin içi ve çok disiplinli takımlarda etkin biçimde çalışabilme becerisi; bireysel çalışma becerisi. |
3 |
| 7) |
Awareness of the need for lifelong learning; access to knowledge, ability to follow developments in science and technology, and constant self-renewal. |
2 |
| 8) |
Effective communication skills in Turkish oral and written communication; at least one foreign language knowledge; ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give clear and understandable instructions and to receive. |
1 |
| 9) |
Conformity to ethical principles, professional and ethical responsibility; Information on standards used in engineering applications. |
2 |
| 10) |
Information on practices in business, such as project management, risk management and change management; awareness about entrepreneurship, innovation; information on sustainable development. |
1 |
| 11) |
Information on the effects of engineering applications on health, environment, and safety in universal and social dimensions, and on the problems of the modern age in engineering; awareness of the legal consequences of engineering solutions. |
1 |
| 12) |
Adequate skills in the analysis, design, verification, evaluation, implementation, implementation, and maintenance of software systems |
1 |
Istanbul Health and Technology University INFORMATION PACKAGE / COURSE CATALOGUE