All Courses

Syllabus:
- Solutions of equations in one variable: Bisection algorithm. Method of false position. Fixed point iteration, Newton-Raphson method, Error Analysis iteration for iterative method, Accelerating limit of convergence.
- Interpolation and polynomial approximation: Taylor polynomial, interpolation and Lagrange polynomial. Iterated Interpolation. Extrapolation.
- Differentiation and Integration: Numerical differentiation. Richardson’s extrapolation. Elements of Numerical integration. Adaptive quadrature method, Romberg’s integration, Gaussian quadrature. Solutions of linear system, pivoting strategies, L U decomposition method.


Course Objective: This course is designed to achieve the following objectives -
- The objectives of studying this module are to make the students familiarise with the ways of solving complicated mathematical problems numerically.
- To help you become familiar with MATLAB and other convenient numerical software such as Microsoft Excel and with simple programming.
- Obtaining numerical solutions to problems of mathematics.
- Describing and understanding of the several errors and approximations in numerical methods.
- The understanding of several available Solutions of Equations in One Variable.
- The explanation and understanding of the several available methods to Solve the simultaneous equations.
- The study of Curve Fitting and Interpolation.


Learning Outcomes: By the end of this course the students must learn the following -
- Analyse a problem and identify the computing requirements appropriate for its solution.
- The students should be familiarized with the ways of solving complicated mathematical problems numerically.
- The students can use MATLAB and other convenient numerical software such as Microsoft Excel to solve and analyse different mathematical problems.
- The students will be able to analyse and solve several errors and approximations in numerical methods.
- The students will be able to apply several methods to solve the Equations in One Variable.
- The students will be able to apply several methods to solve the simultaneous equations.
- The students will be able to apply several methods to solve Curve Fitting and Interpolation questions and its related techniques.

Syllabus:
Set Theory, Relations, Functions, Graph Theory, Planer Graph and Trees, Direct graphs and Binary Trees, Algebraic Systems, Ordered sets and lattices, Propositional Calculus, Boolean Algebra, Lattices, group theory, cyclic groups, permutation groups, symmetry groups, quotient,
homomorphism, Basic structure theory, Prepositional and Predicate logic, Mathematical reasoning and program techniques. Theories with induction. Counting and countability. Graph and trees. Morphisms, Algebraic structures.

Course Objectives:
The main objectives of the course are to:
1. Introduce concepts of mathematical logic for analyzing propositions and proving theorems.
2. Use sets for solving applied problems, and use the properties of set operations algebraically.
3. Work with relations and investigate their properties.
4. Investigate functions as relations and their properties.
5. Introduce basic concepts of graphs, digraphs and trees.


Learning Outcomes:
1. Analyze logical propositions via truth tables.
2. Prove mathematical theorems using mathematical induction.
3. Understand sets and perform operations and algebra on sets.
4. Determine properties of relations, identify equivalence and partial order relations, sketch relations.
5. Identify functions and determine their properties.
6. Define graphs, digraphs and trees, and identify their main properties.
7. Evaluate combinations and permutations on sets.

Syllabus: Differential Calculus
Function and their graphs (polynomial and rational functions, logarithmic and exponential functions, trigonometric functions and their inverses, hyperbolic functions and their inverses, combination of such functions)

Limits of Functions: Basic limit theorems with proofs, limit at infinity and infinite limits, Continuous functions. Algebra of continuous functions. Properties Continuous functions on closed and boundary intervals (no proof required).

Differentiation: Tangent lines and rates of change. Definition of derivative, one-sided derivatives. Rules of differentiation (proofs and applications). Successive differentiation. Leibnitz theorem. Related rates. linear approximations and differentials.

Rolle’s theorem: Lagrange’s and Cauchy’s mean value theorems. Extrema of functions. problems involving maxima and minima. Concavity and points of inflection.

Taylor’s theorem with the general form of the remainder ; Lagrange’s and Cauchy’s forms the remainder. Taylor’s series. Differentiation and integration of series. Validity of Taylor expansions and computations and computations with series. indeterminate forms. L-Hospital’s rules.


Integral Calculus
Integrals: Antiderivatives and indefinite-integrals. Techniques of Integration. Definite Integration using antiderivatives. Definite Integration using Riemann sums. Fundamental theorems of Calculus, Basic properties of Integration. Integration by reduction.

Application of Integration: Plane areas. Solids of revolutions. Volumes by cylindrical shells volumes by cross-sections. Arc length and Surface of revolution. Improper integrals. Gamma and Beta functions. Graphing in polar coordinates. Tangents to polar curves. Area and length in polar coordinates.




Course Objective:
This course is designed to achieve the following objectives Understanding of the basic concepts of differential and integral calculus The usage of Matlab in order to facilitate understanding and visualization of mathematical problems Theoretical and practical preparation enabling students to apply the acquired knowledge and skills in professional and specialist courses.


Learning Outcomes:
By the end of this course the students must learn the following define the basic concepts and principles of differential and integral calculus of real functions and sequences and series interpret the geometric meaning of differential and integral calculus apply the concept and principles of differential and integral calculus to solve geometric and physical problems analyze the properties of functions based on graph obtained using Matlab organize solving of complex problems by combining the acquired mathematical concepts and principles


Reference Books:
Calculus - Titas Prokashoni
Differential Calculus & Integral Calculus - Md. Abdul Matin