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) |
Research and Critical Thinking Skills: The ability to access information, evaluate it, record it, apply it, use it to express abstract ideas, evaluate opposing views, and test it with criteria and standards such as reaching well-questioned conclusions |
2 |
2) |
Graphic Expression Skill: Ability to formally express each stage of the programming and design process using a variety of techniques, including two and three-dimensional hand drawings and computer technologies, to make appropriate presentations |
3 |
3) |
Legal Responsibilities, Ethical and Professional Provisions: To understand the legal responsibilities of the architect in matters affecting design such as property rights, zoning and settlement regulations, user rights for public health, safety and welfare |
1 |
4) |
Having Knowledge About World Architectural History: Understanding the rules of world and local architecture in architecture, landscape and urban design, and the climatic, technological, socio-economic, cultural factors and effects of historical heritage that shape and sustain these |
1 |
5) |
Environmental Systems and Sustainable Design: To understand the basic principles in the design of environmental systems and to be able to protect artificial resources and create healthy buildings and settlements in architectural and urban design decisions of sustainability |
1 |
6) |
Formal Composition and Design Skills: Understanding the formation, development and applications of visual perception and arrangement systems in architectural and urban design and the ability to apply basic architectural principles at the level of building, interior and settlement design |
1 |
7) |
Load-bearing Systems: Understanding the principles of behavior of structures standing with vertical and lateral forces and the development and applications of contemporary load-bearing systems |
1 |
8) |
Building Materials and Applications: Understanding the principles and standards regarding the production, use and applications of building materials and components |
1 |
9) |
Construction Management and Application Skills: Understanding the basic principles of office organization, business planning, marketing, financial management, project management, risk reduction and leadership, and the issues of globalization, expanding application area and diversity that affect the profession |
1 |