Courses

Catalog Description: Functions, combining functions, shifting and scaling graphs, trigonometric functions, exponential functions, inverse functions and logarithms, limits of functions, continuity, limits involving infinity and asymptotes of graphs, tangents derivative and tangents, differentiation rules and chain rule, implicit differentiation, extreme values of functions, mean value theorem, monotonic functions and first derivative test, concavity and curve sketching, indeterminate forms, L'Hospital's rule, anti-derivatives, area and estimating with finite sums, definite integrals, fundamental theorem of calculus, indefinite integrals and the substitution method, area between curves.

Catalog Description: Hyperbolic Functions, Integration of Transcendental Functions, Techniques of Integration: Integration by Substitution (Review), Integration by Parts, Integration Including Powers of Trigonometric Functions, Integration by Trigonometric Substitution, Partial Fractions, Other Techniques, Improper Integrals, Sequences, Limit of Sequence; Series: Convergent and Divergent Series; Series Tests for Convergence: Partial Sums, Telescoping Series, Geometric Series, Base Divergence Test, Integral Test, P-series Test, Ratio Test, Root Test, Absolute Convergence Test, Alternating Series Test, Conditional Convergence; Power Series and Taylor series, Interval and Radius of Convergence, Parametric Equations of Curves in Plane, Polar Coordinates, Graphs in Polar Coordinates.

Catalog Description: Three dimensional coordinate system, vectors, dot and cross products, lines and planes in space, cylindrical and quadratic surfaces, curves in space and their tangents, integral of vector functions, projectile motion, arc length in space, curvature and normal vectors of a curve, tangential and normal components of acceleration, velocity and acceleration in polar coordinates, functions of several variables, limits and continuity in higher dimensions, partial and directional derivatives, chain rule, gradient vector, tangent planes and differentials, extreme values and saddle points, Lagrange multipliers, double integrals in Cartesian and polar coordinates, triple integrals in Cartesian, cylindrical and spherical coordinates.

Catalog Description: Propositional logic, Propositional equivalences, Predicates and quantifiers, Rules of inference, Proof methods, Sets and their operations, Functions, Cardinality of sets, Sequences and summations, Matrices, Mathematical induction, Solving linear recurrence relations, Relations and their properties, Graphs and graph models, Graph terminology and special types of graphs, Trees.

Catalog Description: Basic concepts and ideas, Separable equations, Exact equations, Linear and Bernoulli equations, Homogeneous equations, Homogeneous equations with constant coefficients, Complex roots, Euler-Cauchy equation, Wronskian, Non-homogeneous equations, Undetermined coefficients, Variation of parameters, Higher ODEs, Modeling , Higher ODE with constant coefficients, Higher order non-homogeneous ODEs, Vectors and Matrices, Homogeneous systems, Non-homogeneous systems, Power series method , Theory of power series, Frobenius method, Laplace transform, Transformation of derivatives and integrals, Unit step function, Differentiation and integration of transforms, Convolution, Partial fractions.

Catalog Description: Vector Fields, Divergence of a Vector Field, Curl of a Vector Field, Line Integrals, Path Independence of Line Integral, Green’s Theorem in the Plane, Surfaces for Surface Integrals, Surface Integrals, Divergence Theorem for Gauss, Stokes’s Theorem, Fourier Series, Functions of Any Period, Even and Odd Functions, Fourier Integral, Fourier Cosine and Sine Transforms, Fourier Transform, Tables of Transforms, PDEs: Basic Concepts, Modeling: Vibrating String, Wave Equation, Separation of Variables, Heat Equation, Heat Equation: Solution by Fourier Integrals, Laplacian in Polar Coordinates, Laplace’s Equation in Cylindrical and Spherical Coordinates, Solution by Laplace Transform.

Catalog Description: System of Linear Equations: row-echelon form, reduced row-echelon form, Gaussian elimination, Gauss-Jordan method, etc. Matrices: arithmetics, operations, multiplications, properties of matrix arithmetics matrix transpose, inverse, special matrices, etc. Determinants: the determinant function, properties of determinants, the method of co-factors, adjoint matrix, using row reduction to compute determinants, Cramer's rule. Euclidean n-space: introduction, vectors, dot product, cross product, Euclidean n-space, linear transformations. Vector spaces: vector spaces, sub-spaces, span, linear independence/dependence, basis and dimensions, change of basis, fundamental sub-spaces, inner product spaces, orthonormal basis, least squares, QR-decomposition, orthogonal matrices. Eigenvalues and Egienvectors: review of determinants,Eigenvalues and Egienvectors, diagonalization.

Catalog Description: 

• Complex Analysis: Complex numbers in Cartesian and polar coordinates; Powers and roots; Analytic functions and their derivatives; Cauchy-Riemann equations and Laplace equation; Exponential, trigonometric, and hyperbolic functions; Euler’s formula; Logarithm, general power; Line integral in complex plane; Cauchy’s integral formula; Power series and Taylor series in complex variable; Laurent series; singularities and zeros of a complex function; Residue Theorem and applications.

• Special Functions: Series solutions of ODEs using power series, Legendre’s equation and polynomials, Frobenius Method, Bessel’s equation and functions.

• Fourier Analysis: Sturm-Liouville problems, Orthogonal functions, Orthogonal series, Generalized Fourier series.

Catalog Description: 

Hyperbolic Functions, Integration of Transcendental Functions, Techniques of Integration: Integration by Substitution (Review), Integration by Parts, Integration Including Powers of Trigonometric Functions, Integration by Trigonometric Substitution, Partial Fractions, Improper Integrals, Sequences, Limit of Sequence; Series: Convergent and Divergent Series; Series Tests for Convergence: Partial Sums, Telescoping Series, Geometric Series, Base Divergence Test,  P-series Test, Ratio Test, Root Test, Absolute Convergence Test, Alternating Series Test, Conditional Convergence; Power Series and Taylor series, Interval and Radius of Convergence, Parametric Equations of Curves in Plane, Polar Coordinates, Graphs in Polar Coordinates, Functions of Several Variables: Partial Derivatives, Second Order Pratial Derivative Test, Double Integrals: Double Integrals on Rectangular Region, Double Integral on General Region, Double Integrals in polar Coordinates     

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Catalog Description: 

Introduction to Descriptive Statistics: Measures of Central Tendency, Measures of Dispersion, Measures of Position, and Graphical and Tabular Displays; Introduction to Inferential Statistics: Point Estimate, Confidence Interval and Hypothesis Testing; Basic Probability and Set Theory, Conditional Probability and Independence, Random Variables and Moments, Special Probability Distributions (Discrete and Continuous Distributions), Multiple Random Variables, Covariance and Correlation Coefficient, Functions of Random Variables, Transforms and Moment Generating Function, Practical Applications.

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Catalog Description: 

Distributions of Random Variables, Conditional Probability and Stochastic Independence, Some Special Distributions (Discrete and Continuous Distributions), Univariate, Bivariate and Multivariate Distributions, Distributions of Functions of Random Variables

(Distribution Function Method, Moment Generating Function Method, and Transformation Methods), Limiting Distributions. 

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