Lecture 01 - Jan 5

Topics Covered

• General theory of IVP
• Linear system
• Non-linear system
• BVP

Weightage

• Endsem - 50%
• Midsem - 30%
• Quiz - 20%

What about ODE?

Real world → Conceptual world → Observation → Modeling → Prediction

Scientific Method Flow: System → Observation → Model → Test → Predict → Validate (with feedback loop)

Example: Population Growth

denotes the number of people living in a city at a time .

Initially, , .

So at a later time,

Let , then

Classification of Differential Equations

DE

• ODE
  • Linear
  • Non-linear
• PDE
  • Linear
  • Nuclear

Examples:

(Linear)

(Non-linear)

(Linear)

Formation of DE

From (arb. const):

---

From (arb. const):

---

Again, can have implicit and explicit solutions.