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 related engineering discipline; ability to use theoretical and practical knowledge in these areas in complex engineering problems. |
3 |
2) |
An ability to detect, identify, formulate, and solve complex engineering problems; the ability to select and apply appropriate analysis and modelling methods for this purpose. |
3 |
3) |
An ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions; the ability to apply modern design methods for this purpose. |
2 |
4) |
An ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems in engineering applications. |
2 |
5) |
An ability to use information technologies effectively. |
2 |
6) |
Ability to design, conduct experiments, collect data, analyse, and interpret results to investigate complex engineering problems or discipline-specific research topics. |
2 |
7) |
Ability to work effectively in disciplinary and multidisciplinary teams; ability to work individually. |
3 |
8) |
Ability to communicate effectively in oral and written Turkish. |
1 |
9) |
Knowledge of at least one foreign language. |
1 |
10) |
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. |
1 |
11) |
Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology and ability to renew themselves. |
2 |