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A dif­fer­en­tial equa­tion is an equa­tion that re­lates a func­tion to one or more of its de­riv­a­tives. – The above rather bor­ing de­scrip­tion does lit­tle to con­vey just how fun­da­men­tal, wide­spread, and amaz­ingly ef­fec­tive dif­fer­en­tial equa­tions are in de­scrib­ing the world around us. – Ex­am­ples: Any­thing in mo­tion. Also, many things that are not in mo­tion. Also, many ad­di­tional things to which the word “mo­tion” does not re­ally apply. – Fur­ther ex­am­ples: space­ships in orbit, pop­u­la­tions grow­ing and shrink­ing, a cup of cof­fee slowly cool­ing, springs bounc­ing, fi­nan­cial mar­kets ris­ing and falling, elec­tri­cal cur­rent flow­ing through a cir­cuit, ocean waves, sound waves, light waves, vi­bra­tions in mu­si­cal in­stru­ments and air­plane wings and sus­pen­sion bridges, – More ex­am­ples: Pretty much every­thing. Top­ics in­clude meth­ods of solv­ing or­di­nary dif­fer­en­tial equa­tions and ap­pli­ca­tions to var­i­ous prob­lems. Course Avatar and Site Header from a photo by Flickr user Mat Che: https://​www.​flickr.​com/​photos/​mci​nter​acti​vity/

A differential equation is an equation that relates a function to one or more of its derivatives. – The above rather boring description does little to convey just how fundamental, widespread, and amazingly effective differential equations are in describing the world around us. – Examples: Anything in motion. Also, many things that are not in motion. Also, many additional things to which the word “motion” does not really apply. – Further examples: spaceships in orbit, populations growing and shrinking, a cup of coffee slowly cooling, springs bouncing, financial markets rising and falling, electrical current flowing through a circuit, ocean waves, sound waves, light waves, vibrations in musical instruments and airplane wings and suspension bridges, – More examples: Pretty much everything. Topics include methods of solving ordinary differential equations and applications to various problems. Course Avatar and Site Header from a photo by Flickr user Mat Che: https://www.flickr.com/photos/mcinteractivity/

Soil Me­chan­ics

Soil Mechanics