| 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) |
Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems. |
3 |
| 2) |
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose. |
3 |
| 3) |
Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. |
2 |
| 4) |
Ability to devise, select, and use modern techniques and tools needed for analysing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. |
2 |
| 5) |
Ability to design and conduct experiments, gather data, analyse and interpret results for investigating complex engineering problems or discipline specific research questions. |
2 |
| 6) |
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. |
3 |
| 7) |
Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. |
1 |
| 8) |
Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. |
3 |
| 9) |
Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice. |
1 |
| 10) |
Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. |
1 |
| 11) |
Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions |
1 |
Istanbul Health and Technology University INFORMATION PACKAGE / COURSE CATALOGUE