100 $ MIA

Content to tensor calculus 1

lec 3 continued fraction: Euler continued fraction,e and π form of continued fraction

lec 5 Quantum mechanics 1: commutation relation and commutator

lec 1.1 Tensor analysis 1: Einstein summation conversation solved problems

lec 2 continued fraction: continued roots and Some Ramanujan's results

lec 1 continued fraction:A overview of the course content

lec 39 Jacobi theta function: explicit value for theta 3 at e^(-9π)

lec 41 Jacobi theta function: Values of psi version of theta function

lec 40 Jacobi theta function: Values of version 4 of theta function

lec 4 Quantum mechanics 1: bra ket notation ( Dirac notation )

lec 38 explicit value for theta 3 at e^(-8π)

lec 37 explicit value for theta 3 at e^(-6π) and e^(-3/2π)

lec 36 explicit values for theta 3 at e^(-3π) and e^(-4π)

lec 35 lec 34 Values a P-Q at q^5 by h_5,9

lec 34 Values a P-Q at q^5 by h_n,k

lec 33 P-Q at q^5

lec 4 Tensor analysis: Metric matrix and Jacobian

lec 3 Quantum mechanics 1: Schrödinger's equation

lec 2 Quantum mechanics 1: Double slit experiment under uncertainty principle

lec 1 Quantum mechanics 1: ultraviolet catastrophe and Planck quantization law

lec 32 P-Q at q^3

lec 31 P-Q at q^2

lec 30 P-Q at q^2

lec 28 relation between h_n,n & h‘_n,n & r_n,n & r‘_n,k and Ramanujan G _n

lec 27 relation between h_n,k & h‘_n,k & r_n,k & r‘_n,k and Ramanujan G _n and g_n part 5

lec 29 relation between h_n,n & h‘_n,n & r_n,n & r‘_n,k and Ramanujan G _n

lec 26 relation between h_n,k & h‘_n,k & r_n,k & r‘_n,k and Ramanujan G _n and g_n part 4

lec 8 Relation between ellabtic integral and hypergeometric function

lec 25 relation between h_n,k & h‘_n,k & r_n,k & r‘_n,k and Ramanujan G _n and g_n part 3