Differential Equations & Discrete Mathematics | Complete 2nd Year Course Manual | 9 Chapters | Worked Examples + Exercises | 2025/2026

DEPARTMENT OF MATHEMATICS

Faculty of Science & Engineering

Academic Year




DIFFERENTIAL EQUATIONS
& DISCRETE MATHEMATICS

A Comprehensive Course Manual with Worked Examples


2nd YEAR




COURSE TOPICS


Ordinary Differential Equations


Laplace Transforms & Power Series


Systems of Linear ODEs


Sets, Boolean Algebra & Logic Circuits

,Mathematics for Engineers & Scientists | 2nd Year Page 2

, SAMPLE CONTENT — Differential Equations at
a Glance

Key Formula Reference

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Separable ODE f(y)dy = g(x)dx Integrate both sides

Homogeneous
ODE dy/dx = F(y/x) Substitute v = y/x

Exact ODE M dx + N dy = 0, My=Nx Find potential function F

2nd order const.
coeff. ay''+by'+cy=0 Characteristic equation

Laplace
Transform L{f(t)} = integral(e^(-st)f(t)dt,0,inf) Table + algebra



Quick Example: Separable ODE




Mathematics for Engineers & Scientists | 2nd Year Page 3