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Academic staff member responsible for the design of the course syllabus
(name, surname, academic title/scientific degree, email address and signature)
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NA
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Lecturer (name, surname, academic title/scientific degree, email address
and signature) and Office Hours:
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Shkëlqim Hajrulla
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Second Lecturer(s) (name, surname, academic title/scientific degree, email
address and signature) and Office Hours:
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NA
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| Teaching Assistant(s) and Office Hours: |
NA
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| Language: |
English
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| Compulsory/Elective: |
Compulsory
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| Classroom and Meeting Time: |
A131 Tuesday 08:45
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| Course Description: |
Each topic is considered in a way that assumes in the student average knowledge of the program of the high school. The theory is introduced in every topic as an essential definition, formulas, theorems, laws, and procedures. The practice problems and exercises are introduced as a correct application of the mathematical truths. Real architectural problems are presented as mathematical problems, aiming to improve the students’ ability to solve and to optimize them.
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| Course Objectives: |
The course aims to further improve the students’ knowledge on the covered topics in high school in mathematics. This course will improve the students’ ability to utilize the mathematical knowledge in problem understanding, synthesis, and solution.
|
| Week |
Topics |
| 1 |
General overview on functions and their properties. |
| 2 |
New functions from old ones. One-to-one and onto functions. Bijections. |
| 3 |
The concept of the limit, precise definition. One-sided limits. |
| 4 |
Indeterminate forms. Limits at infinity. Linear asymptotes. |
| 5 |
The squeeze theorem. Continuity. |
| 6 |
Derivatives. Formal definition. Differentiation rules. |
| 7 |
Applications of derivatives: tangent and normal lines, monotony. |
| 8 |
Midterm exam. |
| 9 |
Applications of derivatives: concavity, the L'Hospital's rule. |
| 10 |
Applications of derivatives: optimization problems. |
| 11 |
Applications of derivatives: related rate problems. |
| 12 |
Introduction to integrals.The fundamental theorem of calculus. |
| 13 |
Integration techniques: integration by substitution. |
| 14 |
Integration techniques: integration by parts. |
| 1 |
Compute limits of algebraic functions graphically, numerically, and algebraically. |
| 2 |
Compute the derivative of basic algebraic, exponential, and logarithmic functions using derivative rules and implicit differentiation. |
| 3 |
Interpret the derivative graphically and as a rate of change in applications. |
| 4 |
Apply derivatives in optimization problems. |
| 5 |
Compute indefinite and definite integrals of functions using anti-derivative rules and the Fundamental Theorem of Calculus. |
| 6 |
Represent area as a definite integral and interpret the result in applications. |
| No |
Program Competencies |
Cont. |
| Integrated second cycle study program in Architecture (5 years) Program |
| 1 |
Speaking and Writing Skills Ability to read, write, listen, and speak effectively |
4 |
| 2 |
Critical Thinking Skills Ability to raise clear and precise questions, use abstract ideas to interpret information, consider diverse points of view, reach well-reasoned conclusions, and test them against relevant criteria and standards |
5 |
| 3 |
Graphics Skills Ability to use appropriate representational media, including freehand drawing and computer technology, to convey essential formal elements at each stage of the programming and design process |
3 |
| 4 |
Research Skills Ability to gather, assess, record, and apply relevant information in architectural course work |
3 |
| 5 |
Formal Ordering Systems Understanding of the fundamentals of visual perception and the principles and systems of order that inform two- and three-dimensional design, architectural composition, and urban design |
3 |
| 6 |
Fundamental Design Skills Ability to use basic architectural principles in the design of buildings, interior spaces, and sites |
3 |
| 7 |
Collaborative Skills Ability to recognize the varied talent found in interdisciplinary design project teams in professional practice and work in collaboration with other students as members of a design team |
3 |
| 8 |
International Traditions Understanding of the International architectural canons and traditions in architecture, landscape and urban design, as well as the climatic, technological, culture-economic, and other cultural factors that have shaped and sustained them |
1 |
| 9 |
National and Regional Traditions Understanding of national traditions and the local regional heritage in architecture, landscape design and urban design, including the vernacular tradition |
1 |
| 10 |
Use of Precedents Ability to incorporate relevant precedents into architecture and urban design projects |
1 |
| 11 |
Conservation and Restoration of Historical Districts Knowledge on historical districts and the gain of conservation consciousness documentation of historical buildings and the understanding the techniques which are needed to prepare restoration projects. |
1 |
| 12 |
Human Behavior Understanding of the theories and methods of inquiry that seek to clarify the relationship between human behavior and the physical environment |
1 |
| 13 |
Human Diversity Understanding of the diverse needs, values, behavioral norms, physical ability, and social and spatial patterns that characterize different cultures and individuals and the implication of this diversity for the societal roles and responsibilities of architects |
1 |
