Prerequisite: ICNS 102
Techniques of integration, improper integrals, applications of integration, analytical geometry, infinite series, polar coordinates, parametric equations, vectors in the plane. ICMA 212 General Mathematics II
Prerequisite: ICMA 211
Three-dimensional space; rectangular, spherical and cylindrical coordinates; functions of several variables; partial derivatives; multiple integrals; vector calculus; line and surface integrals of vector functions; Green’s theorem; the divergence theorem; Stoke’s theorem. ICMA 214 Ordinary Differential Equations
First order differential equations and their applications, fundamental solutions of the homogeneous second order equation, linear independence, higher order linear equations. ICMA 215 Calculus
Prerequisites: ICNS 102 or equivalent
Limits, continuity, derivatives, techniques of differentiation, application of derivatives, antiderivatives, techniques of integration, improper integrals and application of integration. ICMA 222 Introduction to Pascal
Introduction to Pascal programming language; basic programming techniques on how to program to solve mathematics problems. ICMA 321 Linear Algebra
Vector spaces, linear transformations, rank and nullity, isomorphisms, eigen vectors, canonical forms. ICMA 322 Advanced Calculus>
Functions, continuity, integration, convergence, differentiability. ICMA 323 Partial Differential Equations
The potential, diffusion and wave operators, existence, uniqueness, stability, regularity, boundary conditions, solution methods and mathematical tools. ICMA 324 Real Analysis
Measurable functions, measures, the integrable functions, the Lebesque space, modes of convergence. ICMA 331 Special Functions
Bessel functions, Gamma functions, Hermites functions, Laguerre functions, Legendre functions, Zeta functions. ICMA 333 Boundary Value Problems
Linear homogenous and Sturm-Liouville boundary value problems, solution of non-homogeneous problems; Green’s function and generalized Green’s function. ICMA 335 Theory of Complex Numbers
Complex numbers, elementary functions of a complex variable, analyticity, Cauchy-Rieman equations, Cauchy’s integral theorem, classification of singularities, residues, evaluation of integrals, conformal mappings. ICMA 336 Numerical Analysis
Error analysis, numerical solution of nonlinear equations, Interpolation theory, approximation of functions, numerical differentiation and integration, numerical solution of ordinary and partial differential equations. ICMA 341 Fluid Dynamics
Review of fluid mechanics, including one dimensional flow, two dimensional motion, Eulerian methods and momentum, the pressure equation, general equation of motion, irrotational motion, viscous fluid, stream functions, complex potential, method of images, and basic singularities. ICMA 423 Set Theory
Inclusion, partially ordered sets and lattices, function, relations, countable sets, cardinal number, Zorn’s lemma, ordinal numbers, the axiom of choice, basic properties of metric spaces. ICMA 424 Abstract Algebra
Group theory, preliminary ideas of ring and field, integral domain, polynomial ring, irreducible polynomials. ICMA 425 Introduction to Topology
Closed and open sets, open covers, convergence, completeness and compactness, separability, metric spaces, topological spaces, connectedness. ICMA 441 Viscous Fluid
Concept of continuity; voracity, continuity equation, equations of motions; exact solutions; low Reynolds number flows; boundary layer analysis; inner and outer expansions. ICMA 442 Discrete Mathematics
Mathematical induction, equivalence relations and partitions, Counting Recurrence relations, trees, graphs. ICMA 444 Research Project in Applied Mathematics (6-cr.)
Small research project in Mathematics or related fields under the supervision of an advisor. ICMA 445 Seminar in Applied Mathematics (2-cr.)
Staff seminar; student presentations and discussions of research; review of topics.