This course aims to provide students with general knowledge on formulating problems that arises in applied sciences as mathematical models, solving such models through analytical and qualitative as well as interpreting solutions within the concept of physical problem at hand.

Learning Outcomes

CTPO

TOA

Upon successful completion of the course, the students will be able to :

LO - 1 :

formulate mathematical models for a variety of problems

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1

LO - 2 :

solve the model using analytical, qualitative and some numerical methods,

1,2

1

LO - 3 :

interprate the phenomenon via the solution of model

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1

LO - 4 :

obtain solution for properly posed problems within the scope of the course.

1,2

1

CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome

Contents of the Course

Initial value problems, slope fields and solution curves, existence and uniqueness, separable equations, first order lineer equations, homogeneous equations, Bernoulli equation, exact differential equations. Second order reducible equations, logistic equation, steady solution and stability, Euler method, second-order equations, applications, matrices and linear system of differential equations, method of eigenvalues, second-order systems and applications, Laplace transform and solution by Laplace transform, power series solution around an ordinary point.