  Equations: linear, quadratic, cubic; functions: linear, polynomials, rational, exponential, logarithmic, multivariable functions; differentiation: derivative , rules of derivation, partial derivative, extrema of one variable functions, and two variable functions; integration: definite, rules of integration, by substitution, by parts, by partial fractions, improper integral, applications; matrices: algebra of matrices, element2ary operations, Echelon form and solution of system of linear equations, determinants and Cramer’s rule and solutions of system of linear equations, applications to economics.
 First Year    Functions: domain, operations on functions, graphs of functions; trigonometric functions; limits: meaning of a limit, computational techniques, limits at infinity, infinite limits ;continuity; limits and continuity of trigonometric functions; the derivative: techniques of differentiation, derivatives of trigonometric functions; the chain rule; implicit differentiation; differentials; Roll’s Theorem; the mean value theorem; the extended mean value theorem; L’Hopital’s rule; increasing and decreasing functions; concavity; maximum and minimum values of a function; graphs of functions including rational functions (asymptotes) and functions with vertical tangents (cusps); antiderivatives; the indefinite integral; the definite integral; the fundamental theorem of calculus ; the area under a curve; the area between two curves; transcendental functions: inverse functions, logarithmic and exponential functions; derivatives and integrals; limits (the indeterminate forms); hyperbolic functions and their inverses; inverse trigonometric functions; some techniques of integration.  First Year    Three dimensional space and vectors rectangular coordinates in 3space; spheres, cylindrical surfaces; quadric surfaces; vectors: dot product, projections, cross product, parametric equations of lines. planes in 3spaces; vector valued functions: calculus of vector valued functions, change of parameters, arc length, unit tangent and normal vectors, curvature, functions of two or more variable: domain, limits, and continuity; partial derivatives; differentiability; total differentials; the chain rule; the gradient; directional derivatives; tangent planes; normal lines; maxima and minima of functions of two variables; Lagrange multipliers; multiple integrals: double integral, double integrals in polar coordinates; triple integrals; triple integrals in cylindrical and spherical coordinates; change of variables in multiple integrals; Jacobian .  Second Year    Numerical analysis; numerical methods in linear algebra; numerical methods for ordinary and partial differential equations.
 Fourth Year    Techniques of integration: integration by substitution; integration by parts, integrating powers of trigonometric functions, trigonometric substitutions, integrating rational functions, partial fractions, rationalization, miscellaneous substitution; improper integrals; application of definite integral: volumes, length of a plane curve, area of a surface of revolution polar coordinates and parametric equations: polar coordinates, graphs in polar coordinates , conics in polar coordinates, area in Polar coordinates; parametric equations; tangent lines and arc length in parametric curves and polar coordinates; infinite series: sequences, infinite series, convergence tests, absolute convergence, conditional convergence; alternating series; power series: Taylor and Maclurine series, differentiation and integration of power series: topics in analytic geometry : the parabola, the ellipse, the hyperbola; second degree equations: rotation of  First Year    Systems of linear equations; matrices and matrix operations; homogeneous and nonhomogeneous systems; Gaussian elimination; elementary matrices and a method for finding ; determinants; Euclidean vector spaces; linear transformations from to and their properties; general vector spaces; subspaces; basis; dimension; row space; column space; null space of a matrix; rank and nullity; inner product spaces; eigenvalues and diagonalization; linear transformations.  Second Year    Vector spaces; subspaces; quotient spaces; linear independence and bases; dual spaces; inner product spaces; orthonormal bases; linear transformations; eigenvalues, eigenvectors and determinants of linear transformations; matrix representation; change of basis and similarity; invariant subspaces; canonical forms of linear transformations; diagonal form; triangular form; nilpotent transformations; Jordan form; companion matrices; commutators; the trace functional and Jacobson’s lemma; normal transformations and the spectral theorem.  Fourth Year 
