KindiakMath

Differential Equations

Here are my write-ups on the theory of differential equations and some non-trivial exercises therein. The results derived in these discussions are useful for solving various applied physics and engineering problems. Enjoy!

Theory

First-Order Differential Equations

  1. The Separable Variables Method
  2. Differential Equation Magic
  3. The Power of Substitutions

Second-Order Differential Equations

  1. Two-Dimensional Differential Equations
  2. Differential Polynomials
  3. The Inverse-D Recipe

Laplace Transforms

  1. Who Cares about Laplace Transforms?
  2. The Step Functions
  3. The Shift Theorems

Exercises

First-Order Differential Equations

  1. Investigating Exponential Models
  2. The Power of Substitutions
  3. Un-abusing the Product Rule

Second-Order Differential Equations

  1. The Mass-Spring System
  2. Breaking the Rules

Laplace Transforms

  1. More Laplace Transforms
  2. Laplace Multipliers
  3. Differential Equations Recap (Polytechnic)

Weekly Practice

  1. Radioactive Decay
  2. Mutated Integrating Factors
  3. Differential Equation Rally
  4. A Two-Part Strategy
  5. Damped Oscillations
  6. Mid-Term Rally
  7. The Jump Strategy
  8. Substitutions…Again!
  9. Laplace Rally
  10. Applied Laplace Transforms
  11. Infinite Addition
  12. End-Term Rally
  13. Kindiak Gauntlet