What is Differential: Definition and 1000 Discussions

In mathematics, a differential equation is an equation that relates one or more functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly.
Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

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  1. S

    Learning Differential equations, week 2 level material

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  2. D

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  3. B

    How do I solve these coupled Differential Equation?

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  4. S

    General Relativity & Differential Geometry Q&A

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  5. M

    Find value of K for differential equation to be exact

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  6. M

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  7. wololo

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  8. P

    Series Solution of Differential Equations - Real or Fake?

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  9. nuuskur

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  10. B

    Definition of dx: What is its Domain & Formalization?

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  11. thegirl

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  12. Q

    Gauss' law in differential form

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  13. Shahrokh

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  14. W

    First order integro differential equation

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  15. S

    General Relativity and Differential Geometry textbook problem

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  16. A

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  17. MidgetDwarf

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  18. H

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  19. Kostik

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  20. Mark Brewer

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  21. Mark Brewer

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  22. H

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  23. nearc

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  24. W

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  25. R

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  26. M

    MHB Differential algebra and differential-algebraic equations

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  27. T

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  28. J

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  29. Luterinho

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  30. SSGD

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  31. K

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  32. AXidenT

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  33. S

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  34. synMehdi

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  35. L

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  36. H

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  37. MARECHAL

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  38. Z

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  39. Destroxia

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  40. Lagraaaange

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  41. L

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  42. Destroxia

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  43. Destroxia

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  44. orion

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  45. Destroxia

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  46. M

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  47. E

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  48. M

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  49. T

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  50. Destroxia

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