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B011280 - MATHEMATICS AND STATISTICS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Teaching Methods
Type of Assessment
Course program
Academic Year 2016-17
Coorte 2016 - 3-years First Cycle Degree (DM 270/04) in APPLIED PHARMACEUTICAL SCIENCES- QUALITY CONTROL AND ASSURANCE
Course year
First year - First Semester
Belonging Department
Neurosciences, Psychology, Drug Research and Child Health (NEUROFARBA)
Course Type
Single education field course
Scientific Area
MAT/03 - GEOMETRY
Credits
6
Teaching Hours
48
Teaching Term
26/09/2016 ⇒ 30/04/2018
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Course program
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Lectureship
Teaching Language
Italian
Course Content
Basic elements of descriptive statistics, probability theory, differential and integral calculus.
Suggested readings (Search our library's catalogue)
Analisi Matematica 1 e 2 di Giuseppe Anichini e di Giuseppe Conti. Notes taken at lesson.
Learning Objectives
Knowledge and understanding
- Understanding the concept of function of function, in particular continuous, and the concept of asymptotic behavior and limit.
- Knowledge of the definition of a derivative and integral.
- Knowledge of the basic concepts of probability and statistics.
- Basic knowledge of some programs for the study of functions and for data analysis.
Applying knowledge and understanding
- Ability to describe the qualitative behavior of elementary functions and calculate derivative and integral.
- Knowing how to analyze a statistical population, for example by calculating the mean and standard deviation.
- Understanding the concept of function of function, in particular continuous, and the concept of asymptotic behavior and limit.
- Knowledge of the definition of a derivative and integral.
- Knowledge of the basic concepts of probability and statistics.
- Basic knowledge of some programs for the study of functions and for data analysis.
Applying knowledge and understanding
- Ability to describe the qualitative behavior of elementary functions and calculate derivative and integral.
- Knowing how to analyze a statistical population, for example by calculating the mean and standard deviation.
Teaching Methods
Lectures
Type of Assessment
The final exam consists of a written examination in order to check the knowledge of the matter. There are 2 written tests that replace the final written in such a case, the final exam grade will be an arithmetic average of the marks obtained to the three intermediate tests.
The intermediate tests consist of open-response tests (with reasoned replies), consisting of 5 questions in 2 hours. Intermediate tests will take place in November and in December. At January there are the written esam.
The oral examination is mandatory for every student.
The intermediate tests consist of open-response tests (with reasoned replies), consisting of 5 questions in 2 hours. Intermediate tests will take place in November and in December. At January there are the written esam.
The oral examination is mandatory for every student.
Course program
intuitive set theory. Introduction to discrete probability: events. distributions
probability. Relative frequencies. Axiomatic definition of probability. Probability of the union of events, complementary event probabilities. independent events. Extraction with or without replacement. Conditional probability. basic principle of combinatorics. Provisions with or without repetition. Means.
Permutations. Factorial of a number. Combinations with or without repetition. Coefficient binomiale. Binomio Newton. Permutations with repetition. binomial distribution.
Functions. Domain and range. Image and inverse image. identity function,
constant function. injective, surjective and bijective. Restriction of a function. Function
reverse. Composition of functions. monotone functions. Even and odd functions. central indexes and dispersion indices. Linear functions, and quadratic functions.
The rational functions. irrational functions, exponential and logarithmic. periodic functions. Radiant definition. Sine and cosine of an angle: properties.
Tangent and cotangent. Trigonometric formulas. trigonometric functions reverse. Elementary trigonometric equations and inequalities. The absolute value of a number. Equations and inequalities with absolute value. Triangular inequality.
Internal and border of a set. Accumulation points and isolated points. closed sets and open. Around circular. Around left and right. Limit formal definition. right limit and left limit. Theorem of the sign and the reverse theorem stay. the existence of a limit theorem for monotone functions. Calculating limits and indeterminate forms. significant limitations. Infinite and infinitesimal and principle
substitution.
The problem of the tangent. The quotient. The derivative. Differentiability implies
continuity but not worth the back (with proof). Derived left and right. Derivatives of
elementary functions. Derivative of the sum, product, quotient of differentiable functions. Derivative of composite and inverse function.
tangent line at an punto. Asintoti oblique. Derivatives of inverse trigonometric functions. non-differentiable points. theorem
Rolle, Lagrange and Cauchy . Teorema de l'Hospital. Maximum and minimum relative and absolute, concavity and convexity. inflection points. Study of function.
Primitive of a function and their characterization. Indefinite Integral. Function integrated into a range: continuous functions can be integrated (no dim). immediate and almost immediate integrals. Integration of rational functions.
Integration by parts. Integration of square root and function trigonometric. Problem areas. Partition of an interval. Plurirettangoli. Amounts less and
higher sums. Integrable function in a range and definition of definite integral. Property. Integration by substitution. Integrability of monotone functions. Theorem of the integral average. fundamental theorem of calculus. (All with dim.)
Differential equations of 1° and 2° order or variables separables.
probability. Relative frequencies. Axiomatic definition of probability. Probability of the union of events, complementary event probabilities. independent events. Extraction with or without replacement. Conditional probability. basic principle of combinatorics. Provisions with or without repetition. Means.
Permutations. Factorial of a number. Combinations with or without repetition. Coefficient binomiale. Binomio Newton. Permutations with repetition. binomial distribution.
Functions. Domain and range. Image and inverse image. identity function,
constant function. injective, surjective and bijective. Restriction of a function. Function
reverse. Composition of functions. monotone functions. Even and odd functions. central indexes and dispersion indices. Linear functions, and quadratic functions.
The rational functions. irrational functions, exponential and logarithmic. periodic functions. Radiant definition. Sine and cosine of an angle: properties.
Tangent and cotangent. Trigonometric formulas. trigonometric functions reverse. Elementary trigonometric equations and inequalities. The absolute value of a number. Equations and inequalities with absolute value. Triangular inequality.
Internal and border of a set. Accumulation points and isolated points. closed sets and open. Around circular. Around left and right. Limit formal definition. right limit and left limit. Theorem of the sign and the reverse theorem stay. the existence of a limit theorem for monotone functions. Calculating limits and indeterminate forms. significant limitations. Infinite and infinitesimal and principle
substitution.
The problem of the tangent. The quotient. The derivative. Differentiability implies
continuity but not worth the back (with proof). Derived left and right. Derivatives of
elementary functions. Derivative of the sum, product, quotient of differentiable functions. Derivative of composite and inverse function.
tangent line at an punto. Asintoti oblique. Derivatives of inverse trigonometric functions. non-differentiable points. theorem
Rolle, Lagrange and Cauchy . Teorema de l'Hospital. Maximum and minimum relative and absolute, concavity and convexity. inflection points. Study of function.
Primitive of a function and their characterization. Indefinite Integral. Function integrated into a range: continuous functions can be integrated (no dim). immediate and almost immediate integrals. Integration of rational functions.
Integration by parts. Integration of square root and function trigonometric. Problem areas. Partition of an interval. Plurirettangoli. Amounts less and
higher sums. Integrable function in a range and definition of definite integral. Property. Integration by substitution. Integrability of monotone functions. Theorem of the integral average. fundamental theorem of calculus. (All with dim.)
Differential equations of 1° and 2° order or variables separables.