Shorif Hossan (MSH)
Of General Educational Development (GED), FSIT,
Room: 505 (AB-4), PC, DIU.
Today's fast-moving information technology field requires professionals with math skills that will require them to manipulate mathematical concepts and interpret data. Computer Networking and database technologies require knowledge in Ordinary and partial differential equations, and this course will give the students a good working knowledge of these areas.
In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.
Mathematics III is a branch of applied mathematics concerning mathematical methods and techniques that are typically used in computer engineering and industry. Along with fields like engineering physics and engineering geology, both of which may belong in the wider category engineering science, engineering mathematics is an interdisciplinary subject motivated by engineers' needs both for practical, theoretical and other considerations out with their specialization and to deal with constraints to be effective in their work. Historically, mathematics III consisted mostly of applied analysis, most notably: differential equations; ordinary differential equation, and partial differential equations. The success of modern numerical computer methods and software has led to the emergence of computational mathematics, computational science, and computational engineering, which occasionally use high-performance computing for the simulation of phenomena and the solution of problems in the sciences and engineering. These are often considered interdisciplinary fields but are also of interest to mathematics III. Engineering mathematics in tertiary education typically consists of mathematical methods and model courses.
A mathematics course has more than one purpose. Students should learn a particular set of mathematical facts and how to apply them; more importantly, such a course should teach students how to think logically and mathematically. To achieve these goals, this text stresses mathematical reasoning and the different ways problems are solved.
will be able to apply the concepts and methods described in the syllabus
will be able to solve problems using the differential equation
will know a number of applications.
text and class discussion will introduce the concepts, methods, applications,
and logical arguments;
will practice them and solve problems on daily assignments, and they will be
tested on quizzes, midterms, and the final.
On successful completion of this
course students will be able to:
Differential Equation: Formation of Differential Equation; First order and a first-degree differential equation, Separation of Variables, Homogenous
equation, Equation reducible to homogenous, Exact equation, Linear Equation,
Reducible to Linear Equation, Linear Differential Equations with Constant Coefficients, Linear Differential Equation with right-hand side non zero, Variation of
parameter, Method of Successive approximation, Reduction of Order, Method of undermined
Coefficient, Matrix method, Various types of Application of
Differential Equation: Formation of Partial Differential equation, Linear and
Non-Linear first-order equation, Standard forms, Linear Equation of higher
order, Partial Differential Equations With Constant Coefficients, Equation of second order with variable coefficients, Wave & Heat
equations, Particular solution with boundary and initial conditions.
Will be declared in the class.
Five Short Question
Based on the class lectures
Will be given in class
After the Midterm exam
The topic will be announced in the class
According to the date declared by the University
Five out of six questions
Marks will be distributed equally according to the number of classes attended
out of 100
80 - 100
75 - 79
70 - 74
65 - 69
60 - 64
55 - 59
50 - 54
45 - 49
40 – 44
00 - 39
Besides, ‘W’ and ‘I’ grade may be awarded as
per university rule.
The final course grade will be awarded based on the marks distribution shown in the table above. Percentages of marks for the different
heads are given below
Formation to the PDE
1. A First Course In Differential Equations With Modeling Applications by Dennis G. Zill
2. Differential Equations by Shepley L. Ross
3. Differential Equations by Paul Dawkins
class code: ojaeqww
In this class, an Ordinary differential equation will be discussed. In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and the derivatives of those functions. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.
After studying this unit you will be able to
In this class, the order and degree of a differential equation will be discussed.
The exponent of each of the derivatives should be minimum. The exponent of the variables need not be an integer.Under such conditions,i) the order of the differential equation is the order of the highest derivative in it.ii) the degree of the differential equation is the largest exponent of the highest order derivative
In this class, a Homogeneous differential equation will be discussed.
A differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives. In the case of linear differential equations, this means that there are no constant terms. The solutions of any linear ordinary differential equation of any order may be deduced by integration from the solution of the homogeneous equation obtained by removing the constant term. A homogeneous differential equation is of prime importance in the physical applications of mathematics due to its simple structure and useful solution.
In this class, the first order and integrating factor of differential equations will be discussed.
In mathematics, an integrating factor is a function that is chosen to facilitate the solving of a given equation involving differentials. It is commonly used to solve ordinary differential equations, but is also used within multivariable calculus when multiplying through by an integrating factor allows an inexact differential to be made into an exact differential (which can then be integrated to give a scalar field). This is especially useful in thermodynamics where the temperature becomes the integrating factor that makes entropy an exact differential.
In this class, the Bernoulli differential equation will be discussed.
In mathematics, an ordinary differential equation of the form is called a Bernoulli differential equation where is any real number other than 0 or 1. It is named after Jacob Bernoulli, who discussed it in 1695. Bernoulli equations are special because they are nonlinear differential equations with known exact solutions. A famous special case of the Bernoulli equation is the logistic differential equation.
In this class, the Initial value problem will be discussed.
In the field of differential equations, an initial value problem (also called a Cauchy problem by some authors) is an ordinary differential equation together with a specified value, called the initial condition, of the unknown function at a given point in the domain of the solution. In physics or other sciences, modeling a system frequently amounts to solving an initial value problem; in this context, the differential initial value is an equation that is an evolution equation specifying how, given initial conditions, the system will evolve with time.
In this class, the application of ODE will be discussed.
In this class, the Partial differential equation will be discussed.
A partial differential equation (or briefly a PDE) is a mathematical equation that involves two or more independent variables, an unknown function (dependent on those variables), and partial derivatives of the unknown function with respect to the independent variables. The order of a partial differential equation is the order of the highest derivative involved. A solution (or a particular solution) to a partial differential equation is a function that solves the equation or, in other words, turns it into an identity when substituted into the equation. A solution is called general if it contains all particular solutions of the equation concerned.
Partial differential equations are used to mathematically formulate, and thus aid the solution of, physical and other problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, etc.
In this class, the formation of PDE will be discussed.
Partial differential equations can be obtained by the elimination of arbitrary constants or by the elimination of arbitrary functions.
In this class, the Linear partial differential equation of order one will be discussed. In mathematics, a first-order partial differential equation is a partial differential equation that involves only the first derivatives of the unknown function of n variables. The equation takes the form
Such equations arise in the construction of characteristic surfaces for hyperbolic partial differential equations, in the calculus of variations, in some geometrical problems, and in simple models for gas dynamics whose solution involves the method of characteristics. If a family of solutions of a single first-order partial differential equation can be found, then additional solutions may be obtained by forming envelopes of solutions in that family. In a related procedure, general solutions may be obtained by integrating families of ordinary differential equations.
In this class, the Linear partial differential equation of order two will be discussed. A second-order linear partial differential equation with two independent variables has the form
In this class, the Partial differential equation with constant coefficients will be discussed.
In this class, the application of PDE will be discussed. Partial differential equations are used to mathematically formulate, and thus aid the solution of, physical and other problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, etc.