The objective of this course is to give students an understanding of basic calculus as well as to enable them to approach problems from a mathematical perspective.
teacher profile teaching materials
Cartesian coordinates in the plane. Distance between points on the line, in the plane. Equation of a circle. Absolute value as distance from the origin of a point on the real line.
Linear algebra (in 2 and 3 dimensions): points and vectors; slope of a segment; sum and difference of vectors, product by a scalar, parallelism conditions; scalar product, orthogonality conditions; vector product, equivalence of the geometric and coordinate formulation for both products.
Introduction to the functions of a variable, relationships between quantities. Graph of a function. Algebra of graphs.
Examples and definition of limit: to infinity, and then to a point. Operations with limits, Squeeze theorem. Limits of quotients of polynomials. Asymptotes. Some important limits.
Continuous functions; continuity at a point and an interval. Theorems on continuous functions: existence of the maximum and minimum, intermediate values. Discontinuity.
Exponential and logarithm functions.
Derivatives: geometric meaning, definition. Operations with derivatives: sum, product, quotient, multiplication by a constant. Derivation techniques, derivatives of the main functions. Derivation of composite functions and the inverse of a function. Equation of the tangent line at a point on the graph. Stationary points.
Fermat's theorem. Rolle and the mean value or Lagrange theorems. Monotonicity and sign of the first derivative. Linear approximation, or first-order Taylor formula. Second derivatives, concavities, inflections. Graph sketching. Related changes, growth rates.
Introduction to integrals: indefinite and definite integrals, their meaning. The problem of calculating the area of a region in the plane. The mean value theorem. The fundamental theorem of integral calculus. Integration for parts and replacement.
Introduction to Differential Equations: growth models, logistic equation. Separation of variables method; Cauchy problems. Exponential growth and decay.
Dario Benedetto, Mirko Degli Esposti, Carlotta Maffei Matematica per le scienze della vita, Terza edizione, Casa Editrice Ambrosiana. Zanichelli, 2015
Giorgio Israel, La Matematica e la realtà. Capire il mondo con i numeri. Carocci, 2015.
Mutuazione: 20440014 ISTITUZIONI DI MATEMATICHE in Scienze geologiche L-34 R A - E MAGRONE PAOLA
Programme
Quantifiers. Numbers: natural, integer, rational, real. Axioms of real numbers; density of Q in R. Irrationality of 2.Cartesian coordinates in the plane. Distance between points on the line, in the plane. Equation of a circle. Absolute value as distance from the origin of a point on the real line.
Linear algebra (in 2 and 3 dimensions): points and vectors; slope of a segment; sum and difference of vectors, product by a scalar, parallelism conditions; scalar product, orthogonality conditions; vector product, equivalence of the geometric and coordinate formulation for both products.
Introduction to the functions of a variable, relationships between quantities. Graph of a function. Algebra of graphs.
Examples and definition of limit: to infinity, and then to a point. Operations with limits, Squeeze theorem. Limits of quotients of polynomials. Asymptotes. Some important limits.
Continuous functions; continuity at a point and an interval. Theorems on continuous functions: existence of the maximum and minimum, intermediate values. Discontinuity.
Exponential and logarithm functions.
Derivatives: geometric meaning, definition. Operations with derivatives: sum, product, quotient, multiplication by a constant. Derivation techniques, derivatives of the main functions. Derivation of composite functions and the inverse of a function. Equation of the tangent line at a point on the graph. Stationary points.
Fermat's theorem. Rolle and the mean value or Lagrange theorems. Monotonicity and sign of the first derivative. Linear approximation, or first-order Taylor formula. Second derivatives, concavities, inflections. Graph sketching. Related changes, growth rates.
Introduction to integrals: indefinite and definite integrals, their meaning. The problem of calculating the area of a region in the plane. The mean value theorem. The fundamental theorem of integral calculus. Integration for parts and replacement.
Introduction to Differential Equations: growth models, logistic equation. Separation of variables method; Cauchy problems. Exponential growth and decay.
Core Documentation
James Stewart, Calcolo. Funzioni di una variabile. Apogeo Education - Maggioli Editore (più i capitoli del secondo volume, sull’algebra lineare e sulle equazioni differenziali, che verranno forniti in pdf)Dario Benedetto, Mirko Degli Esposti, Carlotta Maffei Matematica per le scienze della vita, Terza edizione, Casa Editrice Ambrosiana. Zanichelli, 2015
Giorgio Israel, La Matematica e la realtà. Capire il mondo con i numeri. Carocci, 2015.
Type of delivery of the course
The course is organized in lectures and exercise class. Lectures on different subjects starts with several examples then general cases followed by definitions, theorems and proofs. The subject is presented from a geometrical and analytical point of view with a modeling description. Part of the lectures is on exercises made by singular students or divided in small groups. During exercise classes we give some exercises and problems, let the students try to solve them then we discuss the solution and, if necessary, we give the full solution at the blackboard. Some of the exercise classes are dedicated to hands-on activities with the use of paper and other materials or a computer for visualization.Attendance
The teaching regulations of the Course are followed; in any case, attendance is highly recommended.Type of evaluation
Written test and oral test. Mid term tests teacher profile teaching materials
Cartesian coordinates in the plane. Distance between points on the line, in the plane. Equation of a circle. Absolute value as distance from the origin of a point on the real line.
Linear algebra (in 2 and 3 dimensions): points and vectors; slope of a segment; sum and difference of vectors, product by a scalar, parallelism conditions; scalar product, orthogonality conditions; vector product, equivalence of the geometric and coordinate formulation for both products.
Introduction to the functions of a variable, relationships between quantities. Graph of a function. Algebra of graphs.
Examples and definition of limit: to infinity, and then to a point. Operations with limits, Squeeze theorem. Limits of quotients of polynomials. Asymptotes. Some important limits.
Continuous functions; continuity at a point and an interval. Theorems on continuous functions: existence of the maximum and minimum, intermediate values. Discontinuity.
Exponential and logarithm functions.
Derivatives: geometric meaning, definition. Operations with derivatives: sum, product, quotient, multiplication by a constant. Derivation techniques, derivatives of the main functions. Derivation of composite functions and the inverse of a function. Equation of the tangent line at a point on the graph. Stationary points.
Fermat's theorem. Rolle and the mean value or Lagrange theorems. Monotonicity and sign of the first derivative. Linear approximation, or first-order Taylor formula. Second derivatives, concavities, inflections. Graph sketching. Related changes, growth rates.
Introduction to integrals: indefinite and definite integrals, their meaning. The problem of calculating the area of a region in the plane. The mean value theorem. The fundamental theorem of integral calculus. Integration for parts and replacement.
Introduction to Differential Equations: growth models, logistic equation. Separation of variables method; Cauchy problems. Exponential growth and decay.
Dario Benedetto, Mirko Degli Esposti, Carlotta Maffei Matematica per le scienze della vita, Terza edizione, Casa Editrice Ambrosiana. Zanichelli, 2015
Giorgio Israel, La Matematica e la realtà. Capire il mondo con i numeri. Carocci, 2015.
Mutuazione: 20440014 ISTITUZIONI DI MATEMATICHE in Scienze geologiche L-34 R F - Q BARBIERI MARCO
Programme
Quantifiers. Numbers: natural, integer, rational, real. Axioms of real numbers; density of Q in R. Irrationality of 2.Cartesian coordinates in the plane. Distance between points on the line, in the plane. Equation of a circle. Absolute value as distance from the origin of a point on the real line.
Linear algebra (in 2 and 3 dimensions): points and vectors; slope of a segment; sum and difference of vectors, product by a scalar, parallelism conditions; scalar product, orthogonality conditions; vector product, equivalence of the geometric and coordinate formulation for both products.
Introduction to the functions of a variable, relationships between quantities. Graph of a function. Algebra of graphs.
Examples and definition of limit: to infinity, and then to a point. Operations with limits, Squeeze theorem. Limits of quotients of polynomials. Asymptotes. Some important limits.
Continuous functions; continuity at a point and an interval. Theorems on continuous functions: existence of the maximum and minimum, intermediate values. Discontinuity.
Exponential and logarithm functions.
Derivatives: geometric meaning, definition. Operations with derivatives: sum, product, quotient, multiplication by a constant. Derivation techniques, derivatives of the main functions. Derivation of composite functions and the inverse of a function. Equation of the tangent line at a point on the graph. Stationary points.
Fermat's theorem. Rolle and the mean value or Lagrange theorems. Monotonicity and sign of the first derivative. Linear approximation, or first-order Taylor formula. Second derivatives, concavities, inflections. Graph sketching. Related changes, growth rates.
Introduction to integrals: indefinite and definite integrals, their meaning. The problem of calculating the area of a region in the plane. The mean value theorem. The fundamental theorem of integral calculus. Integration for parts and replacement.
Introduction to Differential Equations: growth models, logistic equation. Separation of variables method; Cauchy problems. Exponential growth and decay.
Core Documentation
James Stewart, Calcolo. Funzioni di una variabile. Apogeo Education - Maggioli Editore (più i capitoli del secondo volume, sull’algebra lineare e sulle equazioni differenziali, che verranno forniti in pdf)Dario Benedetto, Mirko Degli Esposti, Carlotta Maffei Matematica per le scienze della vita, Terza edizione, Casa Editrice Ambrosiana. Zanichelli, 2015
Giorgio Israel, La Matematica e la realtà. Capire il mondo con i numeri. Carocci, 2015.
Attendance
The teaching regulations of the Course are followed; in any case, attendance is highly recommended.Type of evaluation
Written test and oral test. Mid term tests teacher profile teaching materials
Cartesian coordinates in the plane. Distance between points on the line, in the plane. Equation of a circle. Absolute value as distance from the origin of a point on the real line.
Linear algebra (in 2 and 3 dimensions): points and vectors; slope of a segment; sum and difference of vectors, product by a scalar, parallelism conditions; scalar product, orthogonality conditions; vector product, equivalence of the geometric and coordinate formulation for both products.
Introduction to the functions of a variable, relationships between quantities. Graph of a function. Algebra of graphs.
Examples and definition of limit: to infinity, and then to a point. Operations with limits, Squeeze theorem. Limits of quotients of polynomials. Asymptotes. Some important limits.
Continuous functions; continuity at a point and an interval. Theorems on continuous functions: existence of the maximum and minimum, intermediate values. Discontinuity.
Exponential and logarithm functions.
Derivatives: geometric meaning, definition. Operations with derivatives: sum, product, quotient, multiplication by a constant. Derivation techniques, derivatives of the main functions. Derivation of composite functions and the inverse of a function. Equation of the tangent line at a point on the graph. Stationary points.
Fermat's theorem. Rolle and the mean value or Lagrange theorems. Monotonicity and sign of the first derivative. Linear approximation, or first-order Taylor formula. Second derivatives, concavities, inflections. Graph sketching. Related changes, growth rates.
Introduction to integrals: indefinite and definite integrals, their meaning. The problem of calculating the area of a region in the plane. The mean value theorem. The fundamental theorem of integral calculus. Integration for parts and replacement.
Introduction to Differential Equations: growth models, logistic equation. Separation of variables method; Cauchy problems. Exponential growth and decay.
Mutuazione: 20440014 ISTITUZIONI DI MATEMATICHE in Scienze geologiche L-34 R R - Z REUVERS ROBIN JOHANNES PETRUS, DE SETA MONICA
Programme
Quantifiers. Numbers: natural, integer, rational, real. Axioms of real numbers; density of Q in R. Irrationality of 2.Cartesian coordinates in the plane. Distance between points on the line, in the plane. Equation of a circle. Absolute value as distance from the origin of a point on the real line.
Linear algebra (in 2 and 3 dimensions): points and vectors; slope of a segment; sum and difference of vectors, product by a scalar, parallelism conditions; scalar product, orthogonality conditions; vector product, equivalence of the geometric and coordinate formulation for both products.
Introduction to the functions of a variable, relationships between quantities. Graph of a function. Algebra of graphs.
Examples and definition of limit: to infinity, and then to a point. Operations with limits, Squeeze theorem. Limits of quotients of polynomials. Asymptotes. Some important limits.
Continuous functions; continuity at a point and an interval. Theorems on continuous functions: existence of the maximum and minimum, intermediate values. Discontinuity.
Exponential and logarithm functions.
Derivatives: geometric meaning, definition. Operations with derivatives: sum, product, quotient, multiplication by a constant. Derivation techniques, derivatives of the main functions. Derivation of composite functions and the inverse of a function. Equation of the tangent line at a point on the graph. Stationary points.
Fermat's theorem. Rolle and the mean value or Lagrange theorems. Monotonicity and sign of the first derivative. Linear approximation, or first-order Taylor formula. Second derivatives, concavities, inflections. Graph sketching. Related changes, growth rates.
Introduction to integrals: indefinite and definite integrals, their meaning. The problem of calculating the area of a region in the plane. The mean value theorem. The fundamental theorem of integral calculus. Integration for parts and replacement.
Introduction to Differential Equations: growth models, logistic equation. Separation of variables method; Cauchy problems. Exponential growth and decay.
Attendance
The teaching regulations of the Course are followed; in any case, attendance is highly recommended.Type of evaluation
Written test and oral test. Mid term tests teacher profile teaching materials
Mutuazione: 20440014 ISTITUZIONI DI MATEMATICHE in Scienze geologiche L-34 R R - Z REUVERS ROBIN JOHANNES PETRUS, DE SETA MONICA