


Politecnico di Torino  
Academic Year 2013/14  
01OHTLU Calculus 

1st degree and Bachelorlevel of the Bologna process in Architecture  Torino 





Subject fundamentals
The main purpose of this course is to provide to all students, coming from different experiences, the knowledge of the main basic mathematical concepts. In particular, the course will provide the main tools useful in subsequent courses, like other mathematical or statistical courses, building physics, statics, town planning or financial evaluation of projects. All the mathematical concepts and tools are explained in a basic and simple way, with the aim to provide knowledge about that more than to provide the ability to solve hard mathematical problems; in fact, the purpose is to let the students able to understand and describe problems and solutions in future activities.

Expected learning outcomes
The knowledge obtained through this course consists on the essential mathematical tools to understand and to face with problems of differential calculus (initially in one real variable and later in more variables), integral calculus, linear algebra and descriptive statistics. The skills consist on the ability to recognize the mathematical instruments to solve simple mathematical problems or useful in different subjects of planning, structural and physical methodologies , and to understand and formulate simple models to describe such problems.

Prerequisites / Assumed knowledge
Standard high school mathematics is the only prerequisite.

Contents
Linear algebra and geometry: Matrices, vectors, straight lines and planes, systems of linear equations, eigenvalues and eigenvectors, conic sections.
Differential calculus: functions and their graphs (rational and irrational functions, exponential, logarithm, trigonometric functions, hyperbolic functions), limits, continuity of fucntions, derivation, De L'Hopital rule, monotonicity, concavity and convexity, extrema of domains, qualitative graph of functions. Integral calculus: definite integrals and areas, indefinite integral and primitives. Functions of two variables, critical points, tangent plane. Differential equations. Elementary statistics: numerical and graphical representations; correlations. 
Delivery modes
The course includes theoretical lectures and classes devoted to solving excercises. Theoretical lectures take 60% of the total time in class.

Texts, readings, handouts and other learning resources
Suitable textbooks are the following:
R. A. Adams: Calculus, a complete course, Pearson Canada Murray R. Spiegel, John J. Schiller, R. AluSrinivasan, Schaum's Outline of Probability and Statistics, McGrawHill 
Assessment and grading criteria
The exam consists of a two hours long written test, including excercises on linear algebra, on functions of one real variable, on integrals and areas, and differential equations. The exam is to be taken after classes have been attended. The results of the written test are then made part of an oral discussion. If the oral part is satisfactory, the final grade is the one obtained in the the written part. If the oral part is not satisfactory, the student is invited to repeat the exam.

