Roots of polynomials • 10`2 Method of Durand-Kerner

 Graphing • 10`6 Bivariate function surface (as grid) • 10`6 Multivariate function (as slices)

 Numerical integration • 08`a Trapezoidal, Simpson rule (single equation) • 09`c.~Trapezoidal-Simpson
• 10`4.~Trap-S. Gaussian integral; 10`5.~more general • 15`3.~From uploaded file

 Eigenanalysis • Proper values & vectors: 10`2.Danilevskii

 Catenary • 16`2.Catenary & parabola

 ODE (n ordinary differential equations) — by Runge-Kutta, 4.th order (RK4), typically
n = 1 — 09`4.~Single ([Rieder & Busby] Exa. 5.3) & Mathematica • 15`8.~Pendulum (damped) • 15`c.~Falling body
n = 2 — [Smith] 09`4.~Typical problem (paradigm, Case study 8, p 122); 04`4.~Surge tank (C. study 9, p 123)
n = ... — Isomerization (4): 10`2.~numerical method, § (= under construction) 10`2.~analytical method
• 14`4.~Template; 16`b.~ver. 2
• 10`2.~Post-buckling {n = 4} • Catenary: 10`4.~via Newton-Raphson {12}, 10`4.~via Nelder-Mead {4}; 10`5.~with loads {4} 24`1.~Catenary (new) with loads
BVP via shooting • 10`8.~2.nd order problem, "Dirichlet conditions" (y_i & y_f)

 ODE numerical experiments • 18`8.~Morken 14,39 (Mørken, Univ. of Oslo) • 18`9.~2.nd order prototype
• 20`3.~Detail: RK4 ODE, 1.st • 20`3.~Detail: RK4 ODE, higher

 Chemical kinetics • 03`5.~Tubular reactor ([Robinson] 3 ODE's, Euler, Fortran 90 sample)
• 05`5.~Cooled reactor ([Lemos et al.] 3 ODE's, Pr. C.1.3) • 17`9.~Iodine clock reaction • 18`b.~CSTR 3 components (Helmy)
• [Nauman] 05`5.~Batch consecutive reactions (4 ODE's, Exa. 2.2); effect of temperature
• 09`4.~Oscillating reactions (2 ODE's) • Finding § (under observation) 14`9.~decomposition kinetics
 • Determining 'iodine clock' kinetics: 17`a.~data insertion; 17`a.~upload
 19`c.~Chemical reaction and optimization (Winkel) (F90 & upload: paradigm) (19`b.~former)

 Properties • 13`7.~C_p vs. T

 Bibliography

• Atkinson, Kendall, 1985, "Elementary numerical analysis", John Wiley & Sons, New York, NY (USA). ISBN 0-471-82983-8.

• Conte, Samuel D., and Carl de Boor, 1980 (1987), "Elementary numerical analysis", McGraw-Hill, Singapore. ISBN 0-07-066228-2.

• Greenspan, Donald, Vincenzo Casulli, 1988, "Numerical analysis for applied mathematics, science, and engineering", Addison-Wesley, Redwood City, CA (USA). ISBN 0-201-09286-7 (QA297.G725).

• Smith, I. M., 2001 (1995), "Programming in Fortran 90: a first course for engineers and scientists", ed. Wiley, New York, NY (USA) (ISBN 0-471-94185-9).

• Robinson, E. R., 1975, "Time Dependent Chemical Processes", Applied Science Publishers, London. (ISBN 0-85334-608-9)

• Nauman, E. B., 1987, "Chemical reactor design", John Wiley & Sons, Inc., New York, NY (ISBN 0-471-84580-9).

• Lemos, Francisco, José M. Lopes, Fernando Ramôa Ribeiro, 2002, «Reactores Químicos» (Chemical reactors), IST Press, Lisboa (Pt) (ISBN ¬ 9728469098).

• Rieder, William G., and Henry R. Busby, 1986, "Introductory engineering modeling emphasizing differential models and computer simulations", ed. John Wiley & Sons, Inc., New York, NY (USA) (ISBN 0-471-89537-7).

• Chapra, Stephen C., and Raymond P. Canale, 1998, "Numerical methods for engineers: with programming and software applications", 3.rd ed. (4.th ed., 2002), ed. WCB/McGraw-Hill, New York, NY (USA) (ISBN 0-07-010938-9).

• Alexiades, Vasilios: Numerical Algorithms (The Univ. of Tennessee).

• Unicode Entity Codes for Math — ∂/∫/″/‴ — ⋄/≃/∥/∎/∘/∙/≐/≟/⊲/⊳ — ∜/⁵/⅓/ᵢ/x̄/X̄/X̄/ (Penn State).

• Ordinary differential equations (Wikipedia).

• Google search: "ordinary differential equations".