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** Lectures on Differential Equations ** written by
** Craig A. Tracy2**
cover the following topics of complex number.

What is a differential equation? Differential equation for the pendulum. Introduction to computer software. Exercises

Linear first order equations. Conservative systems. Level curves of the energy. Exercises

Theory of second order equations Reduction of order, Constant coefficients, Forced oscillations of the mass-spring system, Exercises

Introduction, Constant coefficient difference equations, Inhomogeneous difference equations, Exercises

The matrix exponential, Application of matrix exponential to DEs, Relation to earlier methods of solving constant coefficient DEs, Problem from Markov processes, Application of matrix DE to radioactive decays, Inhomogenous matrix equations, Exercises

Derivation of differential equations, Reduction to an eigenvalue problem, Computation of the eigenvalues, The eigenvectors, Determination of constants, Continuum limit: The wave equation, Inhomogeneous problem, Vibrating membrane, Exercises

Schr¨odinger equation, Harmonic oscillator, Some properties of the harmonic oscillator, The Heisenberg Uncertainty Principle, Comparison of three problems, Exercises

Introduction, Fourier transform, Solving the heat equation by the Fourier transform, Heat equation on the half-line, Heat equation on the circle, Exercises

Matrix version, Structure of (sIn − A)−1 , Exercises

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**WORKSHEETS (Solved):- **

**SHORTCUT TRICKS (Division):- **

- Divisible by 2 Shortcut trick
- Divisible by 3 Shortcut trick
- Divisible by 4 Shortcut trick
- Divisible by 5 Shortcut trick
- Divisible by 6 Shortcut trick
- Divisible by 7 Shortcut trick
- Divisible by 8 Shortcut trick
- Divisible by 9 Shortcut trick
- Divisible by 10 Shortcut trick

**SHORTCUT TRICKS (Prime Number):- **

- Find the prime number from 1 to 100 just in 5 second (MATH PRIME NUMBER SHORTCUT TRICK from 1 to 100 number) ?
- Find a large number "A" is prime number or not (MATH PRIME NUMBER SHORTCUT TRICK By using Square Root method) ?
- Find the composite number from 1 to 100 just in 5 second (MATH COMPOSITE NUMBER SHORTCUT TRICK from 1 to 100 number) ?

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