| Course Contents |
| Coordinate systems. Functions and graphs. Logarithms and their properties. Differential calculus : Functions of single and several variables. Integral calculus : proper and improper integrals; general methods of integration; applications of proper integrals; multiple integrals. Infinite series; scalars and vectors. Determinants and their properties. Matrices : matrix algebra; eigen values and eigen vectors. Differential equations : ordinary differential equations and their solutions. Numerical methods : Newton-Raphson method; numerical integration. Basic statistics and error analysis : probability, experimental errors; propagation of errors; least square method and curve fitting.
|
| Weekly Course Content |
| Week |
Subject |
Learning Activities and Teaching Methods |
| 1 |
Coordinate systems. Cartesian, plane polar and spherical polar coordinates. Complex numbers and its usage in chemistry. Complex plane |
solution of the relevant question |
| 2 |
Functions and graphs. Graphical representation of functions. Roots to polynomial equations. |
solution of the relevant question |
| 3 |
Logarithms. General properties of logarithms. Common logarithms, natural logarithms. |
solution of the relevant question |
| 4 |
Differential calculus : Functions of single variables. Functions of several variables. Partial derivatives, total differential, exact differential. Geometric properties of derivatives. Constrained maxima and minima. |
solution of the relevant question |
| 5 |
Integral calculus : proper and improper integral; general methods of integration; applications of proper integrals; multiple integrals. |
solution of the relevant question |
| 6 |
Differential equations : classifications of ordinary differential equations and their solutions; partial differential equations; wave equation; Schrödinger’s equation; special polynomial solutions : Hermite equation; Laguerre equation; Lege |
solution of the relevant question |
| 7 |
Infinite series : Tests for convergence and divergence; power series; Taylor ve Maclaurin series; Binomial series; Fourier series and Fourier transformations. |
solution of the relevant question |
| 8 |
mid-term exam |
|
| 9 |
Scalars and vectors : Scalars; vectors; summation of vectors; multiplications of vectors. Vector applications. |
solution of the relevant question |
| 10 |
Matrices and determinants : Square matrices and determinants; matrix algebra; solution of systems of linear equations; eigen values and eigen vectors. |
solution of the relevant question |
| 11 |
Matrices and determinants : Square matrices and determinants; matrix algebra; solution of systems of linear equations; eigen values and eigen vectors. |
solution of the relevant question |
| 12 |
Operators : vector operators; eigen values and eigen functions; Hamiltonian operators; Hermitian operators; rotational operators; transformation of coordinate systems. |
solution of the relevant question |
| 13 |
Numerical analysis; Numerical methods : Newton-Raphson method; numerical integration. Basic statistics and error analysis : probability, experimental errors; propagation of errors; least square method and curve fitting. |
solution of the relevant question |
| 14 |
Mathematica® Applications in Chemistry |
solution of the relevant question |
| 15 |
Mathematica® Applications in Chemistry |
solution of the relevant question |
| 16 |
final exam |
|
| Recommend Course Book / Supplementary Book/Reading |
| 1 |
[Hirst, D.M., Mathematics for Chemists, MacMillan, London, 1976. |
| Required Course instruments and materials |
| projection |
