# Mathematics for Chemistry

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Scalars and Vectors: Scalars, Vectors, Vector Products, Vector Spaces, linear independence, basis, curvilinear coordinates, Tensors.Applications: Two body problem, Center of Mass and Relative coordinates – Vector Integration and Differentiation: Gradient, Divergence and Curl, Line Integrals, Surface integrals, volume integrals, Greens theorem, Stokes Theorem.Applications: Force, Work and Potentials. Path integrals – Matrix Algebra: Matrices, Rank, Determinants, Eigenvalues, Eigenvectors, System of Equations. Applications: Slater Determinants, Huckel MO theory – 1st order ODEs: Differential Equations of 1st order. Separation of variables, integrating factor, exact differentials, system of ODEs. Applications: Reaction rates.

2nd order differential equations: 2nd order differential equations with constant coefficients, general solution, particular solution, power series method. Applications: Angular Momentum Eigenfunctions for a single particle – Integral Transforms: Sturm-Liouville problem, basis functions, Fourier and Laplace transforms, dirac-delta functions. Applications: Power spectrum, momentum and position basis – Group Theory Basics: Group, subgroup, group multiplication table, symmetry operations, Great Orthogonality Theorem, Character Tables. Applications: This section is done with illustration of actual calculations – Symmetry adapted linear combinations, molecular motions, selection rules.Applications: This section is done with illustration of actual calculations – Data Analysis, Interpolation, least square fitting, asymptotic analysis, error estimates, random numbers, correlations. Applications: Fluctuations, noise, signal processing, scattering experiments – Numerical Methods: Taylor series, numerical differentiation and integration, matrix diagonalization methods.Applications: Perturbation method for radiation-matter interaction

### Course Curriculum

 Lecture #1 Details 54:37 Lecture #2 Details 52:44 Lecture #3 Details 52:19 Lecture #4 Details 55:4 Lecture #5 Details 27:38 Lecture #6 Details 49:21 Lecture #7 Details 53:34 Lecture #8 Details 58:25 Lecture #9 Details 52:48 Lecture #10 Details 48:42 Lecture #11 Details 52:53 Lecture #12 Details 57:1 Lecture #13 Details 1:3:35 Lecture #14 Details 51:57 Lecture #15 Details 47:45 Lecture #16 Details 55:30 Lecture #17 Details 46:6 Lecture #18 Details 49:4 Lecture #19 Details 44:28 Lecture #20 Details 44:33 Lecture #21 Details 57:21 Lecture #22 Details 1:2:13 Lecture #23 Details 47:46 Lecture #24 Details 47:30 Lecture #25 Details 43:26 Lecture #26 Details 52:36 Lecture #27 Details 50:29 Lecture #28 Details 57:20 Lecture #29 Details 53:14 Lecture #30 Details 41:5 Lecture #31 Details 52:51 Lecture #32 Details 50:33 Lecture #33 Details 51:6 Lecture #34 Details 50:45 Lecture #35 Details 52:6 Lecture #36 Details 56:29 Lecture #37 Details 0:51 Lecture #38 Details 54:7 Lecture #39 Details 1:36 Lecture #40 Details 55:33

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