MAT2202: Differential Equations II

This course is a foundation course that introduces learners to the basic mathematical concepts. It covers the following topics: Introduction to Difference Equations; Power Series and Laplace Transforms; First Order Partial Differential Equation; Second Order Partial Differential Equation; and Applications of Partial Differential Equations.

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

• Give the general representation of difference equations and their characteristics; solve first order difference equations; and extend such techniques to second constant coefficient equations.  
• Explore the concept of linear dependence and Casoratian as applies to difference equations 
• Characterize power series and their applications, explain the concept orthogonal polynomials, Lap Lace Transform and applications in solving differential equations. 
• Generate the characteristic/auxiliary equation for PDEs, state boundary conditions in formulation of PDEs, state and solve first order PDEs.  
• Generate characteristic equations for second order PDEs, state boundary conditions, solve by separation of variables, and explore hyperbolic, parabolic and elliptic equations.  
• Explore the various applications of PDEs more in particular wave equations, heat/diffusion equations, and Lap Lace equation.  
• Establish boundary value problems, solutions by Fourier Series, Solutions by Bessel/Legendary functions  

Expected Learning Outcome
This course unit is meant: 

• To discuss the basic competence in the concepts, principles, and procedures of partial differential equations and their applications to mathematical modeling and biological processes. 
• 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.