Mathematical Methodsin Chemical & Biomolecular Engineering IIFall 2020, TT 12:00-13:15Instructor: Prof. Jinhoon ChoiPhone: 705-8917E-mail: [email protected]: E. Kreyszig, ”Advanced Engineering Mathematics”, 10th Ed.,John Wiley & Sons, 2011.References:• P. V. O’neil, ”Advanced Engineering Mathematics”, 4th Ed., PWSPublishing Co., 1995.• R. G. Rice and D. D. Do, ”Applied Mathematics and Modeling forChemical Engineers”, John Wiley, 1995.• R. Courant and F. John, ”Introduction to Calculus and Analysis, Vol-ume II”, Springer-Verlag, 1989.• R. C. Buck, ”Advanced Calculus”, 3rd Ed., McGraw-Hill, 1978.• S. J. Farlow, ”Partial Differential Equations for Scientists and Engi-neers”, Dover, 1993.• D. L. Powers, ”Boundary Value Problems”, 3rd Ed., Harcourt BraceJovanovich, 1987.• A. Constantinides and N. Mostoufi, ”Numerical Methods for ChemicalEngineers with MATLAB Applications”, Prentice-Hall, 1999.• J. C. Strikwerda, ”Finite Difference Schemes and Partial DifferentialEquations”, Wadworth Brooks/Cole, 1989.• R. V. Churchill and J. W. Brown, ”Complex Variables and Applica-tions”, 6th Ed., McGraw-Hill, 1995.• L. V. Ahlfors, ”Complex Analysis”, 3rd Ed., McGraw-Hill, 1979.1Grading:Midterm: 50%Final: 50%Outline• Vector Calculus– Vectors: Scalars and vectors, Inner product, Outer product, Tripleproduct– Vector Differential Calculus : Derivatives of vector functions,Derivatives of scalar fields, Derivatives of vector fields, Deriva-tives in orthogonal curvilinear coordinates– Vector Integral Calculus: Line integrals, Green’s theorem in theplane, Surface integral, Gauss’ Divergence theorem, Stokes’ the-orem• Fourier Analysis and Partial Differential Equations– Fourier Series and Transform: Infinite dimensional linear spaces,Periodic functions and trigonometric series, Fourier series, Evenand odd functions, Half-range expansion, Complex form of Fourierseries, Fourier transform, Eigenfunction expansion– Linear Partial Differential Equations: Classifications of partialdifferential equations, Derivations of partial differential equations,Solution methods for one dimensional hyperbolic PDE’s, Solutionmethods for one dimensional parabolic PDE’s, Solution methodsfor two dimensional elliptic PDE’s, Solution methods for two di-mensional parabolic PDE’s– Numerical Solutions of PDE’s: Finite difference methods for parabolicequations, Finite difference methods for hyperbolic equations, Fi-nite difference methods for eliiptic equations, Finite volume meth-ods for parabolic equations• Complex Analysis:– Complex Analysis: Complex variables, Elementary functions ofcomplex variables, Multivalued functions, Analyticity, Integra-tion: Cauchy theorem, Residue