Course Material for EE1060: Differential Equations and Transform Techniques (Spring 2025)

Lecture Notes

The Lecture Notes is meant for quick reference and review. They do not serve as comprehensive sources and are based on the suggested textbooks and references. Students are strongly encouraged to consult these recommended textbooks and references as well.

Lec. (Date)	Topics Covered	Lecture Notes
1 (02/01)	Introduction Introduction to Differential Equations	Notes
2 (06/01)	Solution of Differential Equations Implicit and Explicit Solutions General Solution and Particular Solution	Notes
3 (08/01)	Linear Differential Equations General Solution and Particular Solution Linear and Nonlinear Differential Equations	Notes
4 (09/01)	First-order ordinary differential equations Separable ordinary differential equations Exact ordinary differential equations	Notes
5 (13/01)	First-order ordinary differential equations Integration Factor Approach	Notes
6 (16/01)	First-order ordinary differential equations Substitution Method Bernoulli Equation	Notes
7 (20/01)	Introduction to Numerical Methods for solving ODE Slope Fields and Isoclines Forward Euler Method and RK2 Method	Notes
8 (22/01)	Implicit Numerical Methods for solving ODE Backward Euler Method Trapezoidal Method	Notes
9 (22/01)	Stability of Numerical Methods Introduction to Numerical Stability Conditions for Stability	Notes
10 (27/01)	First Order Autonomous Systems Equilibrium points and Stability Linearization and Condition for Local Stability	[Scribble \| Notes]
11 (29/01)	Bifurcations Introduction to Bifurcations Saddle-Node, Transcritical and Pitchfork Bifurcations	[Scribble \| Notes]
12 (30/01)	Differential Equations of Higher Order Linear and Homogeneous Differential Equations of order n Linearly independent set of solutions and Wronskian	[Scribble \| Notes]
13 (03/02)	General Solutions of Higher order ODE Linear Dependence and Wronskian General Solutions of Homogeneous ODE	[Scribble \| Notes]
14 (05/02)	Second-order Homogeneous ODE General solution of Second-order Homogeneous ODE Solution of Second-order Homogeneous ODE with constant coefficients	[Scribble \| Notes]
15 (06/02)	Second-order nonhomogeneous ODEs General solution of Second-order nonhomogeneous ODE Idea of Annihilation	[Scribble \| Notes]
16 (10/02)	Second-order nonhomogeneous ODEs Method of Undetermined coefficients	[Scribble \| Notes]
17 (12/02)	Second-order nonhomogeneous ODEs Method of Variation of Parameters	[Scribble \| Notes]
18 (13/02)	Boundary Value Problems Dirichlet Boundary Condition Periodic Boundary Condition	[Scribble \| Notes]
19 (17/02)	Introduction to Fourier Series Solution of Linear ODEs to Periodic Signals Introduction to Fourier Series	[Scribble \| Notes]
20 (19/02)	Fourier Series Inner product, Norm and Orthogonality Fourier Series coefficients	[Scribble \| Notes]
21 (20/02)	Symmetry and Fourier Series Symmetry and Fourier Series coefficients	[Scribble \| Notes]