**Elementary Calculus** (MATH 003)

**Course Code: **MATH 003

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **n/a

Number System, Functions, New functions from old, Families of functions, Inverse function, Exponential and Logarithmic function, Limit and Continuity, Tangent line and rate of change, The derivative function, Chain Rule.

Integration: An overview of the area problem, the Indefinite Integral, Integration by substitution, The definition of area as a limit, The definite integral, Fundamental theorem of calculus, Area between two curves, Volumes by slicing, disk and Washers, Area of a surface of revolution, length of a plane curve, Cylindrical Shells.

**Differential and Integral Calculus** (MATH 151)

**Course Code: **MATH 151

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **MATH 003

Implicit differentiation, derivatives of logarithmic, exponential and inverse trigonometric function, L’Hospital Rule, Successive Differentiation, Increasing and decreasing function, Maxima, minima, Applied Maxima_ minima, Rolle’s, Mean Value , Taylor’s Theorem and Maclaurin’s series, Partial Derivatives.

An overview of integration, Integration by parts, Integrating trigonometric functions, trigonometric substitution, integration by partial fractions, improper integral, Gamma & beta function, Double Integral over rectangular and nonrectangular regions, Double Integral in Polar coordinates, Triple Integrals.

### Complex Variables (MATH 153)

**Course Code: **MATH 153

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **MATH 201

Complex Variable: Complex number system. General functions of a complex variable. Limits and continuity of a function of a complex variable and related theorems. Complex differentiation and the Cauchy-Riemann equations. Infinite series. Convergence and uniform convergence. Line integral of a complex function Cauchy integral formula. Liouville’s theorem. Taylor’s and Laurent’s theorem. Singular points. Residue, Cauchy’s residue theorem.

### Ordinary and Partial Differential Equations (MATH 155)

**Course Code: **MATH 155

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **MATH 151

Degree and order of ordinary differential equations. Formation of differential equations. Solutions of first order differential equations by various methods. Solutions of general linear equations of second and higher orders with constant coefficients. Solution of homogeneous linear equations. Solution of differential equation of the higher order when the dependent or independent variable is absent. Solution of differential equation by the method based on the factorization of the operators. Frobenious method.

### Fourier and Laplace Transforms (MATH 157)

**Course Code: **MATH 157

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **MATH 151

**Laplace Transforms:** Definition. Laplace transforms of some elementary functions. Sufficient conditions for existence of Laplace transforms. Inverse Laplace transforms. Laplace transforms of derivatives. The unit step function. Periodic function. Some special theorems on Laplace transforms. Partial fraction. Solution of differential equations by Laplace transforms. Evaluation of improper integrals.

**Fourier Analysis:** Real and complex forms of Fourier series. Finite transform. Fourier integral. Fourier transforms and their uses in solving boundary value problems.

### Linear Algebra, Ordinary and Partial Differential Equations (MATH 183)

**Course Code: **MATH 155

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **MATH 003, MATH 151

**Ordinary Differential Equations:** Degree and order of ordinary differential equations. Formation of differential equations, Solutions of first order differential equations by various methods. Solutions of general linear equations of second and higher orders with constant coefficients.

Solution of homogeneous linear equations. Solution of differential equation of the higher order when the dependent or independent variable is absent. Solution of differential equation by the method based on the factorization of the operators. Frobenius method.

**Partial differential equations:** Wave equations, Particular solutions with boundary and initial conditions.

**Matrices:** Definition, equality, addition, subtraction multiplication, transposition, inversion, rank. Equivalence, solution of equations by matrix method. Vector space, Eigen values and Eigen vectors. Bassel’s and Legendre’s differential equations.

### Fourier and Laplace Transformations, and Complex Variables (MATH 187)

**Course Code: **MATH 187

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **MATH 183

**Complex Variable**: Complex number system. General functions of a complex variable, Limits and continuity of a function of a complex variable and related theorems, Complex differentiation and the Cauchy-Riemann equations, Infinite series. Convergence and uniform convergence. Line integral of a complex function Cauchy integral formula. Liouville’s theorem. Taylor’s and Laurent’s theorem. Singular points. Residue, Cauchy’s residue theorem.

**Laplace Transforms**: Definition, Laplace transforms of some elementary functions, Sufficient conditions for existence of Laplace transforms, Inverse Laplace transforms. Laplace transforms of derivatives, The unit step function, Periodic function, Some special theorems on Laplace transforms, Partial fraction, Solution of differential equations by Laplace transforms, Evaluation of improper integrals.

**Fourier Analysis:** Real and complex forms of Fourier series. Finite transform, Fourier integral, Fourier transforms and their uses in solving boundary value problems.

### Co-ordinate Geometry and Vector Analysis (MATH 201)

**Course Code: **MATH 201

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **MATH 151

Two-dimensional co-ordinate Geometry: Change of axes-transformation of co-ordinates, simplification of equations of curves.

Three-dimensional co-ordinate Geometry: System of co-ordinates, distance between two points, section formula, projection, direction cosines, equations of planes and lines.

Vector Analysis: Definition of vectors. Equality, addition and multiplication of vectors. Linear dependence and independence of vectors. Differentiation and integration of vectors together with elementary applications. Definitions of line, surface and volume integrals. Gradient of a scalar function, divergence and curl of a vector function. Physical significance of gradient, divergence and curls. Various formulae. Integral forms of gradient, divergence and curl. Divergence theorem. Stoke’s theorem, Green’s theorem and Gauss’s theorem.

### Linear Algebra & Matrices (MATH 203)

**Course Code: **MATH 203

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **MATH 151

Matrices: Definition, equality, addition, subtraction multiplication, transposition, inversion, rank. Equivalence, solution of equations by matrix method. Vector space, Linear Transformation, Eigen values and Eigen vectors. Bassel’s and Legendre’s differential equations.

### Probability and Statistics (STAT 205)

**Course Code: **STAT 205

**Credit: **3.00

**Credit Hour: **3.00

**Prerequisite: **N/A

**Statistics:** frequency distribution. Mean, median, mode and other measures of central tendency. Standard deviation and other measures of dispersion. Moments, skewness and kurtosis, correlation and regression analysis. Elementary probability theory and discontinuous probability distribution, e.g., binomial, Poisson and negative binomial. Continuous probability distributions, e.g. normal and exponential. Characteristics of distributions. Elementary sampling theory. Estimation of parameter, Hypothesis testing, Index number. Time series analysis and Markov chain.