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Langmuir model with transport In this worksheet I am working on the identifiability of the parameters of a model of antibody binding. usefull lists and sets In this worksheet we shall obtain results and look at the case where the inlet concentration, is known or alternately unknown set up equations B equations y equations C equations eliminate B1 substitute the above into some equations create an equation to later get rid of C_ij or B_2 obtain y and derivatives multinomial Create further derivatives second derivative create a list of things to substitute into them because we can no longer simplify y2 third derivative the following is horrible deal with quotients at I_i=0 at I_i=C_T C_T known C_T unknown look at products we know that if at I_i=0 at I_i=C_T*d_i known unknown look at coefficients at I_i=0 at I_i=C_t*d_i known C_T unknown C_T Create sets of equations for known and unknown C_T for the known case for the unknown case solve Solve the system of equations from the coefficients where C_T is known (this command causes problems it may be better to look at the solution for unknown and make appropriate substitutions) Solve the system of equations from the coefficients whilst I_i=C_T, where C_T is unknown (8.1)