DESCRIPTION OF MATHEMATICS SUBJECTS

SUBJECT: CALCULUS
Introduction : Real Number, parabolic, equation graphics. Function and Limit : function and its graphics, trigonometri function, theorem of limit, Continous Function. Derivative : the rule of derivative, derivative of sine and cosine, the chain rule, Leibniz notation, higher order derivative, implicit derivative, derivative and approximation. Applications of the derivative : Maximum and Minimum, Economic Application, The mean value theorem. Integral : Infinite Integral,linear first order diferential equation,de finite integral, integral properties, substitution method in definite integral. Applications of The Integral . The derivative in Rn: Function with two or more variables, partial derivative, Limit and Continuity, Lagrange method. Integral with two or more variables: Double integral, triple integral to (polar coordinat and cartesius coordinat), Taylor and Mclauren Theorems, Jacobian and transformation. Convergence, Riemann and Darboux Integral, Gamma and Beta function, Fourier Series. (160 hours)

SUBJECT : LINEAR ALGEBRA
Linear System and Matrix : Gaussian Elimination, Matrix and its operations, Invertible Matrix. Determinant : Cofactor expansion, Crammer Rule. Vector in R2 and R3: Norm vector, dot product, projection, cross product, line and surface in R3. Vector Spaces : vector space, subspace, linear independence, basis and dimension, basis space and column matrix, rank, gram-schmidt process. Linear Transformation : Introduction to linear transformation, the properties of linear transformation, linear transformation in Rn . Eigen Value and Vector Eigen : Diagonalization, orthogonal diagonalization, simetris matrix. Applications : Application to diferential equation, Application in approximation problems, fourier series. Introduction to numerical methods of lineal algebra : LU decomposition, Gauss-Siedal Method, Jacobi Method. Reduction error. Approximation of Eigen Value. Complex vector space : Demoivre Theorem. (96 hours)
SUBJECT : ALGEBRA
Group, subgroup, permutation group, looping group, homomorphism, isomorphism, Cayley Theorem, Ring, basic theorem of homomorphism, field, field structure, (32 hours)
SUBJECT : NUMERICAL METHODS
Definition of error, flowchart, algorithm and iteration. Roots of nonlinear equation : interval method, bijection method, false position method and its modification, secant method, Newton method, iteration of particular point, convergence velocity, Newton Bairstow Method, Polynomial equation and its properties. Interpolation : Newton interpolation polynomial, Langrange Interpolation Polynomial. Linear Equation System : iterative method, Gauss-Siedal Method, Inverse Matrix. Derivative and Integral : trapezoidal and Simpson Rule, Quadrature Method, diferential equation ( initial value and boundary value problems) (48 hours)