Application of Math in Chemistry

(in Polish) T

Expository methods:

- conventional-problematic lecture with the use of multimedia presentation

Inquiry methods:

- discussion with students

- classical problems and exchange ideas

- practical exercises

Completion of the seminar: mandatory presence and positive evaluation of two written tests involving solution of problems (E3-E9).

Completion of the lecture: mandatory presence and positive evaluation of one written final test checking students’ knowledge of the theory given in the lectures (E1, E2).

Final evaluation of the course consists of the grade of the final test (50%) and the grade of the seminar (50%).

Learning content:

Lecture and seminar:

Reminder of concepts of scalar and vector operations on vectors, derivatives of single variable functions.

Functions of two and more variables - limits of functions, partial derivatives, Schwarz theorem, derivatives of composite functions – the chain rule.

Differentials of functions of one variable (reminder) and several variables, complete(exact) differential. The use of differentials in chemistry for the estimation of measurement error.

Directional derivatives of functions of two and three variables.

Methods of the search for stationary points and extremes of functions.

The optimization problem in chemistry - methods of optimization.

Reminder of integrals of single variable functions. Special integral functions: gamma function, beta function, Dirac delta etc.

Multiple integrals over a normal or regular. Iterated integrals. Integrals of functions with separated variables.

Conversion of coordinates in the multiple integrals. Application of multiple integrals in chemistry.

Operators. The action of operators on functions. Properties of operators - the additive, homogeneous, linear operators, equality of two operators, commutator. The eigenvalue equation for the operator, degeneration. The hermitian operator.

Elements of the field theory: gradient, potential of the field, divergence, rotation. Nabla and Laplace operator. Examples of the use of operators in physics and chemistry.

Reminder basic types of ordinary differential equations of first and second order.

Special cases of second order differential equations - differential equations of Hermite, Legendre, Laguerre. The use of special differential equations.

Partial Differential Equations of second order. Examples of applications of partial differential equations second order in physics and chemistry – Laplace equation, Poisson equation, Schrödinger equation.

Donald A. McQuarrie, „Mathematical Methods for Scientists and Engineers” University Science Books 2003

Erich Steiner, „The Chemistry Maths Book ” 2nd Ed. Oxford University Press, 2008

W.Krysicki, L. Włodarski, a.J. Zielicki,D. Konstant „Problems and Methods in Analysis”

Additional:

R. Courant, "Differential and integral calculus"

(in Polish) T

Expository methods:

- conventional-problematic lecture with the use of multimedia presentation

Inquiry methods:

- discussion with students

- classical problems and exchange ideas

- practical exercises

Completion of the seminar: mandatory presence and positive evaluation of two written tests involving solution of problems (E3-E9).

Completion of the lecture: mandatory presence and positive evaluation of one written final test checking students’ knowledge of the theory given in the lectures (E1, E2).

Final evaluation of the course consists of the grade of the final test (50%) and the grade of the seminar (50%).

Learning content:

Lecture and seminar:

Reminder of concepts of scalar and vector operations on vectors, derivatives of single variable functions.

Functions of two and more variables - limits of functions, partial derivatives, Schwarz theorem, derivatives of composite functions – the chain rule.

Differentials of functions of one variable (reminder) and several variables, complete(exact) differential. The use of differentials in chemistry for the estimation of measurement error.

Directional derivatives of functions of two and three variables.

Methods of the search for stationary points and extremes of functions.

The optimization problem in chemistry - methods of optimization.

Reminder of integrals of single variable functions. Special integral functions: gamma function, beta function, Dirac delta etc.

Multiple integrals over a normal or regular. Iterated integrals. Integrals of functions with separated variables.

Conversion of coordinates in the multiple integrals. Application of multiple integrals in chemistry.

Operators. The action of operators on functions. Properties of operators - the additive, homogeneous, linear operators, equality of two operators, commutator. The eigenvalue equation for the operator, degeneration. The hermitian operator.

Elements of the field theory: gradient, potential of the field, divergence, rotation. Nabla and Laplace operator. Examples of the use of operators in physics and chemistry.

Reminder basic types of ordinary differential equations of first and second order.

Special cases of second order differential equations - differential equations of Hermite, Legendre, Laguerre. The use of special differential equations.

Partial Differential Equations of second order. Examples of applications of partial differential equations second order in physics and chemistry – Laplace equation, Poisson equation, Schrödinger equation.

Donald A. McQuarrie, „Mathematical Methods for Scientists and Engineers” University Science Books 2003

Erich Steiner, „The Chemistry Maths Book ” 2nd Ed. Oxford University Press, 2008

W.Krysicki, L. Włodarski, a.J. Zielicki,D. Konstant „Problems and Methods in Analysis”

Additional:

R. Courant, "Differential and integral calculus"

(in Polish) T

Expository methods:

- conventional-problematic lecture with the use of multimedia presentation

Inquiry methods:

- discussion with students

- classical problems and exchange ideas

- practical exercises

Completion of the seminar: mandatory presence and positive evaluation of two written tests involving solution of problems (E3-E9).

Completion of the lecture: mandatory presence and positive evaluation of one written final test checking students’ knowledge of the theory given in the lectures (E1, E2).

Final evaluation of the course consists of the grade of the final test (50%) and the grade of the seminar (50%).

Learning content:

Lecture and seminar:

Reminder of concepts of scalar and vector operations on vectors, derivatives of single variable functions.

Functions of two and more variables - limits of functions, partial derivatives, Schwarz theorem, derivatives of composite functions – the chain rule.

Differentials of functions of one variable (reminder) and several variables, complete(exact) differential. The use of differentials in chemistry for the estimation of measurement error.

Directional derivatives of functions of two and three variables.

Methods of the search for stationary points and extremes of functions.

The optimization problem in chemistry - methods of optimization.

Reminder of integrals of single variable functions. Special integral functions: gamma function, beta function, Dirac delta etc.

Multiple integrals over a normal or regular. Iterated integrals. Integrals of functions with separated variables.

Conversion of coordinates in the multiple integrals. Application of multiple integrals in chemistry.

Operators. The action of operators on functions. Properties of operators - the additive, homogeneous, linear operators, equality of two operators, commutator. The eigenvalue equation for the operator, degeneration. The hermitian operator.

Elements of the field theory: gradient, potential of the field, divergence, rotation. Nabla and Laplace operator. Examples of the use of operators in physics and chemistry.

Reminder basic types of ordinary differential equations of first and second order.

Special cases of second order differential equations - differential equations of Hermite, Legendre, Laguerre. The use of special differential equations.

Partial Differential Equations of second order. Examples of applications of partial differential equations second order in physics and chemistry – Laplace equation, Poisson equation, Schrödinger equation.

Donald A. McQuarrie, „Mathematical Methods for Scientists and Engineers” University Science Books 2003

Erich Steiner, „The Chemistry Maths Book ” 2nd Ed. Oxford University Press, 2008

W.Krysicki, L. Włodarski, a.J. Zielicki,D. Konstant „Problems and Methods in Analysis”

Additional:

R. Courant, "Differential and integral calculus"

(in Polish) T

Expository methods:

- conventional-problematic lecture with the use of multimedia presentation

Inquiry methods:

- discussion with students

- classical problems and exchange ideas

- practical exercises

Completion of the seminar: mandatory presence and positive evaluation of two written tests involving solution of problems (E3-E9).

Completion of the lecture: mandatory presence and positive evaluation of one written final test checking students’ knowledge of the theory given in the lectures (E1, E2).

Final evaluation of the course consists of the grade of the final test (50%) and the grade of the seminar (50%).

Learning content:

Lecture and seminar:

Reminder of concepts of scalar and vector operations on vectors, derivatives of single variable functions.

Functions of two and more variables - limits of functions, partial derivatives, Schwarz theorem, derivatives of composite functions – the chain rule.

Differentials of functions of one variable (reminder) and several variables, complete(exact) differential. The use of differentials in chemistry for the estimation of measurement error.

Directional derivatives of functions of two and three variables.

Methods of the search for stationary points and extremes of functions.

The optimization problem in chemistry - methods of optimization.

Reminder of integrals of single variable functions. Special integral functions: gamma function, beta function, Dirac delta etc.

Multiple integrals over a normal or regular. Iterated integrals. Integrals of functions with separated variables.

Conversion of coordinates in the multiple integrals. Application of multiple integrals in chemistry.

Operators. The action of operators on functions. Properties of operators - the additive, homogeneous, linear operators, equality of two operators, commutator. The eigenvalue equation for the operator, degeneration. The hermitian operator.

Elements of the field theory: gradient, potential of the field, divergence, rotation. Nabla and Laplace operator. Examples of the use of operators in physics and chemistry.

Reminder basic types of ordinary differential equations of first and second order.

Special cases of second order differential equations - differential equations of Hermite, Legendre, Laguerre. The use of special differential equations.

Partial Differential Equations of second order. Examples of applications of partial differential equations second order in physics and chemistry – Laplace equation, Poisson equation, Schrödinger equation.

Donald A. McQuarrie, „Mathematical Methods for Scientists and Engineers” University Science Books 2003

Erich Steiner, „The Chemistry Maths Book ” 2nd Ed. Oxford University Press, 2008

W.Krysicki, L. Włodarski, a.J. Zielicki,D. Konstant „Problems and Methods in Analysis”

Additional:

R. Courant, "Differential and integral calculus"

(in Polish) T

Expository methods:

- conventional-problematic lecture with the use of multimedia presentation

Inquiry methods:

- discussion with students

- classical problems and exchange ideas

- practical exercises

Completion of the seminar: mandatory presence and positive evaluation of two written tests verifying the knowledge of theory and ability to solve tasks (E1-E9). To obtain the positive grade from the test the student must obtain at least 56% of the maximum number of points.

Completion of the lecture: activity on the lectures.

The grade for the seminar is also the final grade for the course.

Learning content:

Lecture and seminar:

Reminder of concepts of scalar and vector operations on vectors, derivatives of single variable functions.

Functions of two and more variables - limits of functions, partial derivatives, Schwarz theorem, derivatives of composite functions – the chain rule.

Differentials of functions of one variable (reminder) and several variables, complete(exact) differential. The use of differentials in chemistry for the estimation of measurement error.

Directional derivatives of functions of two and three variables.

Methods of the search for stationary points and extremes of functions.

The optimization problem in chemistry - methods of optimization.

Reminder of integrals of single variable functions. Special integral functions: gamma function, beta function, Dirac delta etc.

Multiple integrals over a normal or regular. Iterated integrals. Integrals of functions with separated variables.

Conversion of coordinates in the multiple integrals. Application of multiple integrals in chemistry.

Operators. The action of operators on functions. Properties of operators - the additive, homogeneous, linear operators, equality of two operators, commutator. The eigenvalue equation for the operator, degeneration. The hermitian operator.

Elements of the field theory: gradient, potential of the field, divergence, rotation. Nabla and Laplace operator. Examples of the use of operators in physics and chemistry.

Reminder basic types of ordinary differential equations of first and second order.

Special cases of second order differential equations - differential equations of Hermite, Legendre, Laguerre. The use of special differential equations.

Partial Differential Equations of second order. Examples of applications of partial differential equations second order in physics and chemistry – Laplace equation, Poisson equation, Schrödinger equation.

Donald A. McQuarrie, „Mathematical Methods for Scientists and Engineers” University Science Books 2003

Erich Steiner, „The Chemistry Maths Book ” 2nd Ed. Oxford University Press, 2008

W.Krysicki, L. Włodarski, a.J. Zielicki,D. Konstant „Problems and Methods in Analysis”

Additional:

R. Courant, "Differential and integral calculus"

(in Polish) T

Expository methods:

- conventional-problematic lecture with the use of multimedia presentation

Inquiry methods:

- discussion with students

- classical problems and exchange ideas

- practical exercises

Completion of the seminar: mandatory presence and positive evaluation of two written tests verifying the knowledge of theory and ability to solve tasks (E1-E9). To obtain the positive grade from the test the student must obtain at least 56% of the maximum number of points.

Completion of the lecture: activity on the lectures.

The grade for the seminar is also the final grade for the course.

Learning content:

Lecture and seminar:

Reminder of concepts of scalar and vector operations on vectors, derivatives of single variable functions.

Functions of two and more variables - limits of functions, partial derivatives, Schwarz theorem, derivatives of composite functions – the chain rule.

Differentials of functions of one variable (reminder) and several variables, complete(exact) differential. The use of differentials in chemistry for the estimation of measurement error.

Directional derivatives of functions of two and three variables.

Methods of the search for stationary points and extremes of functions.

The optimization problem in chemistry - methods of optimization.

Reminder of integrals of single variable functions. Special integral functions: gamma function, beta function, Dirac delta etc.

Multiple integrals over a normal or regular. Iterated integrals. Integrals of functions with separated variables.

Conversion of coordinates in the multiple integrals. Application of multiple integrals in chemistry.

Operators. The action of operators on functions. Properties of operators - the additive, homogeneous, linear operators, equality of two operators, commutator. The eigenvalue equation for the operator, degeneration. The hermitian operator.

Elements of the field theory: gradient, potential of the field, divergence, rotation. Nabla and Laplace operator. Examples of the use of operators in physics and chemistry.

Reminder basic types of ordinary differential equations of first and second order.

Special cases of second order differential equations - differential equations of Hermite, Legendre, Laguerre. The use of special differential equations.

Partial Differential Equations of second order. Examples of applications of partial differential equations second order in physics and chemistry – Laplace equation, Poisson equation, Schrödinger equation.

Donald A. McQuarrie, „Mathematical Methods for Scientists and Engineers” University Science Books 2003

Erich Steiner, „The Chemistry Maths Book ” 2nd Ed. Oxford University Press, 2008

W.Krysicki, L. Włodarski, a.J. Zielicki,D. Konstant „Problems and Methods in Analysis”

Additional:

R. Courant, "Differential and integral calculus"

(in Polish) T

Expository methods:

- conventional-problematic lecture with the use of multimedia presentation

Inquiry methods:

- discussion with students

- classical problems and exchange ideas

- practical exercises

Completion of the seminar: mandatory presence and positive evaluation of two written tests verifying the knowledge of theory and ability to solve tasks (E1-E9). To obtain the positive grade from the test the student must obtain at least 56% of the maximum number of points.

Completion of the lecture: activity on the lectures.

The grade for the seminar is also the final grade for the course.

Learning content:

Lecture and seminar:

Reminder of concepts of scalar and vector operations on vectors, derivatives of single variable functions.

Functions of two and more variables - limits of functions, partial derivatives, Schwarz theorem, derivatives of composite functions – the chain rule.

Differentials of functions of one variable (reminder) and several variables, complete(exact) differential. The use of differentials in chemistry for the estimation of measurement error.

Directional derivatives of functions of two and three variables.

Methods of the search for stationary points and extremes of functions.

The optimization problem in chemistry - methods of optimization.

Reminder of integrals of single variable functions. Special integral functions: gamma function, beta function, Dirac delta etc.

Multiple integrals over a normal or regular. Iterated integrals. Integrals of functions with separated variables.

Conversion of coordinates in the multiple integrals. Application of multiple integrals in chemistry.

Operators. The action of operators on functions. Properties of operators - the additive, homogeneous, linear operators, equality of two operators, commutator. The eigenvalue equation for the operator, degeneration. The hermitian operator.

Elements of the field theory: gradient, potential of the field, divergence, rotation. Nabla and Laplace operator. Examples of the use of operators in physics and chemistry.

Reminder basic types of ordinary differential equations of first and second order.

Special cases of second order differential equations - differential equations of Hermite, Legendre, Laguerre. The use of special differential equations.

Partial Differential Equations of second order. Examples of applications of partial differential equations second order in physics and chemistry – Laplace equation, Poisson equation, Schrödinger equation.

Donald A. McQuarrie, „Mathematical Methods for Scientists and Engineers” University Science Books 2003

Erich Steiner, „The Chemistry Maths Book ” 2nd Ed. Oxford University Press, 2008

W.Krysicki, L. Włodarski, a.J. Zielicki,D. Konstant „Problems and Methods in Analysis”

Additional:

R. Courant, "Differential and integral calculus"

(in Polish) T

Expository methods:

- conventional-problematic lecture with the use of multimedia presentation

Inquiry methods:

- discussion with students

- classical problems and exchange ideas

- practical exercises

Completion of the seminar: mandatory presence and positive evaluation of two written tests involving solution of problems (E3-E9).

Completion of the lecture: mandatory presence and positive evaluation of one written final test checking students’ knowledge of the theory given in the lectures (E1, E2).

Final evaluation of the course consists of the grade of the final test (50%) and the grade of the seminar (50%).

Learning content:

Lecture and seminar:

Reminder of concepts of scalar and vector operations on vectors, derivatives of single variable functions.

Functions of two and more variables - limits of functions, partial derivatives, Schwarz theorem, derivatives of composite functions – the chain rule.

Differentials of functions of one variable (reminder) and several variables, complete(exact) differential. The use of differentials in chemistry for the estimation of measurement error.

Directional derivatives of functions of two and three variables.

Methods of the search for stationary points and extremes of functions.

The optimization problem in chemistry - methods of optimization.

Reminder of integrals of single variable functions. Special integral functions: gamma function, beta function, Dirac delta etc.

Multiple integrals over a normal or regular. Iterated integrals. Integrals of functions with separated variables.

Conversion of coordinates in the multiple integrals. Application of multiple integrals in chemistry.

Operators. The action of operators on functions. Properties of operators - the additive, homogeneous, linear operators, equality of two operators, commutator. The eigenvalue equation for the operator, degeneration. The hermitian operator.

Elements of the field theory: gradient, potential of the field, divergence, rotation. Nabla and Laplace operator. Examples of the use of operators in physics and chemistry.

Reminder basic types of ordinary differential equations of first and second order.

Special cases of second order differential equations - differential equations of Hermite, Legendre, Laguerre. The use of special differential equations.

Partial Differential Equations of second order. Examples of applications of partial differential equations second order in physics and chemistry – Laplace equation, Poisson equation, Schrödinger equation.

Donald A. McQuarrie, „Mathematical Methods for Scientists and Engineers” University Science Books 2003

Erich Steiner, „The Chemistry Maths Book ” 2nd Ed. Oxford University Press, 2008

W.Krysicki, L. Włodarski, a.J. Zielicki,D. Konstant „Problems and Methods in Analysis”

Additional:

R. Courant, "Differential and integral calculus"