|Course Code||Course Name||Credit|
|MATH 101||Calculus I (Diferansiyel ve İntegral Hesap I)||(3+0+2) 4|
|Functions, graphs, limits and continuity. Derivatives, derivative rules, chain rule, implicit differentiation. Applications of derivatives. Indefinite integrals, integration by substitution, definite integrals. Applications of integrals. Transcendental functions.|
|MATH 102||Calculus II (Diferansiyel ve İntegral Hesap II)||(3+0+2) 4|
|Integration techniques; improper integrals. Infinite series, positive and alternating series, power series, Taylor and Maclaurin series. Polar coordinates. Vectors and motion in space, vector valued functions.
Prerequisite: MATH 101
|MATH 103||Mathematics I (Matematik I)||(3+0+0) 3|
|Functions, exponential and logarithmic functions. Limits and continuity, differentiation. Applications of derivatives to economics. Curve sketching.|
|MATH 104||Mathematics II (Matematik II)||(3+0+0) 3|
|Indefinite integrals, definite integral and its applications. Functions of several variables, partial derivative and its applications. Matrix algebra, systems of linear equations.
Prerequisite: MATH 103
|MATH 142||Discrete Mathematics (Ayrık Matematik)||(3+1+0) 3|
|Logic and sets, functions. Mathematical reasoning, counting, relations, graphs, trees, algebraic structures, Boolean algebra. Modelling computation.|
|MATH 200||Linear Algebra (Doğrusal Cebir)||(3+0+0) 3|
|Matrix algebra, determinants, Cramer's rule, systems of linear equations. Vectors, vector spaces, sub-spaces, linear dependence and bases, dot and cross products. Linear transformations, eigenvalues, eigenvectors and diagonalization.|
|MATH 201||Calculus III (Diferansiyel ve İntegral Hesap III)||(3+0+2) 4|
|Functions of several variables, limits and continuity. Partial derivatives, directional derivatives, Lagrange multipliers, Taylor's formula. Double integrals in cartesian and polar coordinates, triple integrals in cartesian, cylindrical and spherical coordinates, line integrals, Green's theorem, surface integrals, Stokes' theorem, divergence theorem.
Prerequisite: MATH 101
|MATH 203||Multivariable Calculus and Differential Equations (Çok değişkenli İntegral ve Diferansiyel Hesap ve Diferansiyel Denklemler)||(4+1+0) 4|
|Multivariable functions, partial derivatives, directional derivatives. Lagrange multipliers.
Double integrals, triple integrals, line integrals. Green's theorem. Surface integrals, Stokes' theorem.
Gauss theorem. First order differential equations. Second and higher order linear equations with constant coefficients. Reduction of order. Nonhomogeneous equations. The Laplace transform, initial value problems. Systems of first order linear equations with constant coefficients.
Prerequisite: MATH 102
|MATH 212||Complex Analysis I (Karmaşık Analiz I)||(3+0+2) 4|
|Complex numbers, power series and convergence, limits. Exponential function and logarithm, branch points and cuts. Continuity, derivative, Cauchy-Riemann equations. Contour integrals, Cauchy-Goursat theorem, Morera's theorem, integration by residues, Liouville's theorem. Maximum moduli of functions, Taylor and Laurent series.
Prerequisite: MATH 201
|MATH 214||Introduction to Mathematical Analysis (Matematiksel Analize Giriş)||(3+0+0) 3|
|Real numbers, completeness axiom. Sequences, Cauchy sequences, continuity, uniform continuity; sequences and series of functions. Differentiation. Integration.
Prerequisite: MATH 102
|MATH 220||Differential Equations (Diferansiyel Denklemler)||(3+0+2) 4|
|Basic definitions, first order differential equations, second order linear differential equations with constant coefficients. Systems of first order linear differential equations with constant coefficients, Laplace transforms and its applications to linear differential systems. Linear differential equations with variable coefficients, series solutions of second-order linear differential equations.
Prerequisite: MATH 101
|MATH 230||Probability (Olasılık)||(3+1+0) 3|
|Basic topics in probability theory; sample space, combinatorics, Bayes theorem and conditional probability. Random variables, marginal, joint and conditional distributions; expectations and conditional expectations; hypergeometric, binomial, geometric distributions; Poisson, exponential, gamma distributions and the Poisson arrival model; moment generating functions, central limit theorem, and the normal distribution; variance, covariance, and correlation.|
|MATH 231||Statistics I (İstatistik I)||(3+0+0) 3|
|Introduction to statistics; describing data, frequency distributions, graphic presentation, numerical measures; probability concepts; discrete probability distributions; normal probability distribution; sampling methods; estimation and confidence intervals; one-sample hypotheses testing.|
|MATH 232||Statistics II (İstatistik II)||(3+0+0) 3|
|Two-sample hypothesis testing; analysis of variance; linear regression and correlation; multiple regression and correlation analysis; chi-square applications for nominal data; time-series analysis.
Prerequisite: MATH 231
|MATH 235||Statistics for Economics and Administrative Sciences I (Ekonomi ve İdari Bilimler için İstatistik I)||(3+1+0) 3|
|Introduction to the use of statistics in economics and administrative science analysis. Basic statistical concepts used by social scientists. Displaying data. Measures of central tendency and variability. Frequency distributions. Normal distribution. Basic concepts of probability. Sampling distribution and hypothesis testing. One-sample hypothesis testing in social research.|
|MATH 236||Statistics for Economics and Administrative Sciences II (Ekonomi ve İdari Bilimler için İstatistik II)||(3+1+0) 3|
|Correlation and regression for social research in the fields of economics and administrative sciences. Multiple regression analysis. Two-sample hypothesis testing. Analysis of variance. Application of Chi-square test in social sciences.|
|MATH 252||Introduction to Mathematical Engineering (Matematik Mühendisliğine Giriş)||(3+0+0) 3|
|Concept of mathematical modeling, examples from physics, mechanics, and engineering applications. Statics of rigid bodies, general principles; force and moment equilibrium. Structural analysis, modeling of 3D bodies as 1D body, internal loading, stress and strain, mechanical properties of materials. Analysis of bars under several type of loading.|
|MATH 302||Numerical Methods (Sayısal Yöntemler)||(3+0+0) 3|
|Solution of non-linear equations, fixed point iteration; interpolation, Chebyshev polynomials, cubic spline interpolation. Numerical differentiation and integration, solution of system of linear equations: direct and iterative methods. Numerical solution of ordinary differential equations.
Prerequisite: MATH 200
|MATH 311||Introduction to Real Analysis (Reel Analize Giriş)||(3+0+0) 3|
|Algebra of sets, the axiom of choice, countable sets, relations and equivalences, partial orderings and the maximal principle. Outer measure, measurable sets and Lebesgue measure, measurable functions. The Lebesgue integral and its properties.|
|MATH 313||Complex Analysis II (Karmaşık Analiz II)||(3+0+0) 3|
|Mittag-Leffler's formula, numbers of zeros of regular functions; Rouches theorem, regularity of functions defined by definite integrals, Fourier and Laplace transforms. Analytic continuation, entire functions, infinite products. Applications in physics and engineering.|
|MATH 314||Functional Analysis (Fonksiyonel Analiz)||(3+0+0) 3|
|Differentiation of monotone functions, functions of bounded variations. Differentiation of an integral, absolute continuity. The spaces, Minkowski and Hölder inequalities, convergence and completness. Approximation in , bounded linear functionals on the spaces.|
|MATH 321||Partial Differential Equations (Kısmi Diferansiyel Denklemler)||(3+0+0) 3|
|Basic definitions, first-order partial differential equations; types of second-order partial differential equations. The wave equation, the diffusion equation; maximum principle. Boundary value problems, separation of variables. Laplace's equation, Green's identities and functions.|
|MATH 322||Special Functions (Özel Fonksiyonlar)||(3+0+0) 3|
|Gamma and Beta functions; hypergeometric series and functions; confluent hypergeometric functions, generalized hypergeometric functions; Bessel's functions; Legendre's functions.|
|MATH 323||Calculus of Variations (Değişimler Hesabı)||(3+0+0) 3|
|Historical approach to basic problems; variation of a functional; weak and strong extrema; Euler-Lagrange equations; variational derivative, higher order derivatives, subsidiary conditions; variable end point problems; broken extremals. Noether's theorem, Hamilton-Jacobi Equation, Jacobi's theorem; quadratic functionals, second variation of a functional. Direct methods, Ritz and Kantorovich methods.|
|MATH 324||Methods of Applied Mathematics I (Uygulamalı Matematiğin Yöntemleri I)||(3+0+0) 3|
|Application of special functions, orthogonal series, boundary-value problems in mechanics and engineering, introduction to Sturm-Liouville systems. Solution techniques for boundary-value problems in curvilinear coordinates, integral transforms; Green's functions, potentials, applications.|
|MATH 343||Advanced Linear Algebra (İleri Doğrusal Cebir)||(3+0+0) 3|
|Vector spaces, subspaces, bases and dimension, quotient spaces, field, linear independence, orthonormal basis, and Gram-Schmidt orthogonalization. Linear transformations; kernel, image, rank, invertibility, diagonalization, matrix of a linear transformation. Determinants. Canonical forms: eigenvectors, eigenvalues, characteristic polynomial, minimal polynomial, symmetric matrix, direct sum decomposition, invariant subspaces, Jordan canonical forms of a matrix, the Cayley-Hamilton theorem.|
|MATH 352||Mathematical Theory of Elasticity (Esnekliğin Matematiksel Kuramı)||(3+0+0) 3|
|Small deformations and stress analysis; constitutive equations of linear elasticity, field equations of elasticity; basic equations of elastostatics, existence and uniqueness theorems. Plane elasticity, plane stress and strain cases; compatibility equations, Airy's functions, polynomial solutions; variational principles. Propagation of elastic waves, reflection and diffraction of elastic waves.|
|MATH 361||Differential Geometry (Diferansiyel Geometri)||(3+0+0) 3|
|Space curves, Frenet formulas; surfaces in three dimensional Euclidean space, Gauss map. First and second fundamental forms, geodesics.|
|MATH 425||Methods of Applied Mathematics II (Uygulamalı Matematiğin Yöntemleri II)||(3+0+0) 3|
|Introduction to integral equations, Volterra and Fredholm equations, solutions by Neumann series, eigenvalue problems; calculus of variations, Euler-Lagrange equations. Applications to mechanics.|
|MATH 426||Mathematical Modeling (Matematiksel Modelleme)||(3+0+0) 3|
|Fundamental equations and problems of elasticity theory; uniqueness theorems and variational principles; methods of stress functions and displacement potential; applications. Fundamental equations and problems of fluids; Navier-Stokes equation for viscous fluids, cartesian tensors, stress-strain relations. Applications.|
|MATH 427||Advanced Numerical Methods (İleri Sayısal Yöntemler)||(3+0+0) 3|
|Numerical solution of ordinary differential equations, initial value and boundary value problems; an introduction to the numerical solution of elliptic, parabolic and hyperbolic partial differential equations.|
|MATH 428||Numerical Linear Algebra (Sayısal Doğrusal Cebir)||(3+0+0) 3|
|Numerical methods for solving linear systems of equations, linear least squares problems, matrix eigenvalue problems, nonlinear systems of equations, interpolation, integral, and initial value problems of ordinary differential equations.|
|MATH 441||Introduction to Modern Algebra (Modern Cebire Giriş)||(3+0+0) 3|
|Algebra on sets; basic theory of groups, rings and fields, an introduction to Galois theory.|
|MATH 451||Mathematical Theory of Fluids (Akışkanın Matematiksel Kuramı)||(3+0+0) 3|
|Definitions, kinematics of fluid; velocity, acceleration, material derivative, path and stream lines, vorticity. Equations of motion, stress; constitutive equations. Hydrostatics, ideal fluids, Bernoulli's theorems; incompressible ideal fluids, potential flows, vortex flow, surface waves. Viscous flows, Stokes' approximation; boundary - layer theory.|
|MATH 452||Introduction to Continuum Mechanics (Sürekli Ortamlar Mekaniğine Giriş)||(3+0+0) 3|
|Mathematical preliminaries, deformation and various strain measures; kinematics, stress tensors. Balance laws of a continuum; thermodynamics, constitutive relations. Applications to elasticity and fluid dynamics.|
|MATH 464||Introduction to Topology (Topolojiye Giriş)||(3+0+0) 3|
|Elements of general topology, topological spaces, continuous functions, connectedness, compactness, completeness, separation axioms, and metric spaces.|