MAT2102 Differential Equations I

This course is a foundation course that introduces learners to the basic mathematical concepts such as First Order Differential Equations and Second Order Differential Equations, Higher Order Differential Equation, Power Series, and Systems of First Order Differential Equation among others.

General Course Objectives
On successful completion of this course unit, the learners should be able to:

• Give the general representation of differential equations and their characteristics; solve simple separable equations; establish exact equation and integrating factor technique.
• Characterize and solve homogeneous differential equations, solve various problems involving application of first order differential equations and work with Bernoulli equation.
• Characterize various second order differential equations, use various techniques in solving second order differential equations including the Wronskian, Abel’s formula, order reduction, and application to higher order differential equations.
• Solve various higher differential equations, constant coefficient differential equations, the inverse operator method, the auxiliary equation method, the undetermined coefficients and variation of parameters for homogeneous equations, and the Cauchy-Euler equation.  
• State the basic concepts of power series, determine convergence of power series and radius of convergence, determine the regular and singular points, solve for power series solution at singular points and well us Frobenius method. 
• Reducing a higher order equation to a system of first order differential equations and vice versa; solve the systems by elimination method; matrix method, eigenvalue method; and method of undetermined coefficient and variation of parameters

Expected Learning Outcomes
This course unit is meant:

• To discuss the basic competence in the concepts, principles, and procedures of differential equations and their applications to mathematical modeling and computation.
• To encourage orderliness, speed and accuracy in the presentation of mathematical expressions in differential calculus.
• To help learners acquire the skills of expression in proper mathematical language and using mathematical symbols correctly.
• To provide instruction that contributes to the learners’ abilities to think critically and solve real life problems, to reason mathematically and apply computational skills.
• To build a strong foundation in mathematical presentation as preparation for subsequent courses in applied mathematics and biomathematics.