Fișa disciplinei:

BP1-16 A Matematica.pdf

Department:

Basics of Architectural Design

Course Leader:

conf.dr.arh. Anca Vitcu

Teaching language:

Romanian

Learning outcomes:

General Objective
Acquiring basic knowledge and skills in:
- mathematical modeling of the behaviour of civil constructions under the action of various physical phenomena.
Specific Objectives
O1. Knowing some basic math concepts and how are used when performing the calculation in the statics of the rigid solid, statics of rigid body systems, wire statics,...;
O2. Knowledge of basic mathematical concepts, methods and techniques associate to dynamic analysis of structures in various contexts;
O3. Knowledge of basic mathematical concepts associated with some computations and analyzes specific to the architectural design.

Content:

Course
1. Elements of trigonometry (trigonometric functions, graphing trigonometric functions, equations and trigonometric inequalities, inverse trigonometric functions, solving the triangle with trigonometric functions)
2. General notions of matrix calculus
3. Vector calculus (composition and decomposition of forces concurrent in plan, composition and decomposition of forces concurrent in space, equilibrium of a material point, moments)
4. Vector calculus (composition and decomposition of forces parallel forces, centres of gravity - their determination, applications and properties)
5. Vector calculus (reduction of forces applied to a non-deformable solid, the equilibrium of a non-deformable solid, the equilibrium of a system of non-deformable solids)
6. General elements of differential calculus
7. General elements of integral calculus

Seminar
1. Elements of trigonometry - applications in
Statics and Architectural Design
2. General notions of matrix calculus -
Applications in Construction Engineering and Architectural Design
3. Vector calculus - applications in Statics, Kinematics and Dynamics
4. Vector calculus - applications in Statics, Kinematics and Dynamics
5. Vector calculus - applications in Statics, Kinematics and Dynamics
6. General elements of differential calculus - applications in Statics, Kinematics and Dynamics
7. General elements of integral calculus – applications in Statics, Kinematics and Dynamics

Teaching Method:

Course: Lecture accompanied by exercises and debate
Seminar: Exercises – applications in architectural design and technical disciplines associated to the development of architectural projects

Assessment:

Evaluation during the semester

The evaluation of theoretical knowledge is done through the problems proposed to be solved at the seminar. (colloquium) (30%)
Solving the problems proposed at the seminar. (colloquium) (70%)

Minimal performance standards
To understand fundamental mathematical concepts in the context of their correct application in the field of structural engineering and architectural design.

Bibliography:

BIBLIOGRAPHY:
Beer P. Ferdinand (2013) - Vector Mechanics for Engineers: Statics and Dynamics, McGraw-Hill
Brent J. Lewis (2022) – Advanced Mathematics for Engineering Students: The Essential Toolbox, Elsevier
Choubey K. R. (2011) – Course in Mathematics: Trigonometry, Pearson
Hibbler R. C. (2015) - Engineering Mechanics: Statics, Pearson
Høgsberg Jan, Krenk Steen (2013) – Statics and Mechanics of Structures, Springer
Meriam J. L., Kraige L. G. (2012) – Engineering Mechanics (vol. I): Statics, Wiley
Meriam J. L., Kraige L. G. (2018) - Engineering Mechanics (vol. II): Dynamics, Wiley
Roberts A. P. (2003) - Statics and Dynamics with Background Mathematics, Cambridge
Vitcu Anca – Course notes

Selective Bibliography (seminar):
Hibbler R. C. (2015) - Engineering Mechanics: Statics, Pearson
Meriam J. L., Kraige L. G. (2012) – Engineering Mechanics (vol. I): Statics, Wiley
Onouye Barry (2011) - Statics and Strength of Materials for Architecture and Building Construction, Pearson
Powers Gary (2013) - Trigonometry for Engineering Technology: With Mechanical, Civil, and Architectural Applications, Industrial Press
Vitcu Anca – Worksheets (problem selections)