Calculus Basics
- Definite and indefinite integrals of functions of a single variable. Applications of the definite integral to area, volume, arc length and surface of revolution Fundamental Theorem of Calculus. Techniques of integration including integration by substitutions, by parts, by partial fractions and by reduction. Mean value theorems and L'Hopital's rule. Definition of Hyperbolic and Inverse Hyperbolic functions and its differentiations and integrations. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series.
- Definite and indefinite integrals of functions of a single variable. Applications of the definite integral to area, volume, arc length and surface of revolution Fundamental Theorem of Calculus. Techniques of integration including integration by substitutions, by parts, by partial fractions and by reduction. Mean value theorems and L'Hopital's rule. Definition of Hyperbolic and Inverse Hyperbolic functions and its differentiations and integrations. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series.
efinite and indefinite integrals of functions of a single variable. Applications of the definite integral to area, volume, arc length and surface of revolution Fundamental Theorem of Calculus. Techniques of integration including integration by substitutions, by parts, by partial fractions and by reduction. Mean value theorems and L'Hopital's rule. Definition of Hyperbolic and Inverse Hyperbolic functions and its differentiations and integrations. Improper integrals. Sequences and series: convergence tests, integral, comparison, ratio and root tests. Alternating series. Absolute and conditional convergence. Power series. Taylor and Maclaurin series.
Basic Mathematics
Set theory-symbols and expressions-union-intersection- difference- complement- Ven's diagram - sets. Numbers - natural numbers - integers numbers - rational numbers-real numbers. Relations and functions- cartesian product- binary relations-.operations on relations- composition of relations- equivalence relations and partitions. Maps- injective, surjective and bijective. Equivalence and countable sets- finite and infinite sets- power of a set- countable and uncountable sets.
Analytic Geometry
Cartesian and polar coordinates-Vectors in plane- algebra of vectors- angle between two vectors- dot product- vector product- triple product- area of triangle-Vectors in three dimensions-.Straight lines in plane- Straight lines in space- parametric representation of straight line-Conic sections- circle- parabola- ellipse- hyperbola-Polar form of conic sections-Applications of conic sections in Astronomy, Cylindrical coordinates- Spherical coordinates.
Advanced Calculus
Cylinderical and Spherical Polar Coordinates. Functions of several variables: partial derivatives, chain rules. Tangent planes. The gradient and directional derivatives. Extreme of Functions of several variables. Lagrange Multipliers. Multiple Integrals. Double Integrals. Area, Volume and Surface Area. Double Integrals in Polar Coordinates. Triple Integrals. Change of variables in Multiple Integrals. Vector Calculus. Vector Field. Line Integrals. Green’s Theorem. Curl and Divergence. Surface Integrals. The Divergence Theorem. Stoke’s Theorem. Applications of vector calculus.
Differential Equations I
ntroduction to ordinary differential equations. Solution methods of first order differential equations. Solution method of second order homogeneous and non homogeneous of linear ordinary differential equations. Variational Method.
Linear Algebra
Introduction to systems of linear equations: Gaussian elimination and Gauss-Jordan elimination for solving Equations; Matrices: Operations on matrices, properties of matrix operations, inverse of a matrix; Determinant of a matrix: Elementary row operations, properties of determinants, Cramer’s rule; Vector spaces: Subspaces, linear combinations, linear independence, bases and dimensions; Rank of a matrix: The coordinates, change of bases; Linear transformations: Kernel, range, nullity of a linear transformation, linear transformations and matrices; symmetric matrices; Eigenvectors: Introduction to eigen values, eigenvectors and eigen spaces.
General Statistics
Methods of collection and Presentation Of Statistical Data by different ways, calculate some Measures of Central Tendency, measures of dispersion, Correlation and Regression. The main Principles of Probability, random variables and some Statistical Distributions.
Differential Equations (2)
System of linear ordinary differential equations with an emphasis on applications on initial value problems. Topics include power series solutions, Laplace transform, solution of initial value problems, and nonlinear differential equations
Real Analysis I
This course concerns itself with the concepts of limit and continuity, which are the basis of mathematical analysis and the calculus from which it evolved. We focus on limits of sequences and of functions, and continuity of functions and the the concept of differentiability. While the main context is the real numbers, i.e. limits of sequences of real numbers, continuity of functions from the real numbers to the real numbers,... Existence of global extrema and the Intermediate Value Theorem are studied…
Probability Theory
The course focuses on the importance and the efficiency of the random variables idea in statistical mechanism. The several types of discrete and continuous random variables in addition to Some applications of random variables beside the mathematical illustration of several issues related to random variables and statistical distributions.