Use the Continuation method and the Runge-Kutta method of order 4 with A' = 1 on the following nonlinear systems using x(0) = 0. Are the answers here comparable to Newton's method, or are they suitable initial approximations for Newton's method? a. xi(l X|) + 4x2 = 12, b. 5xf x| = 0, (xi 2)2 + (2x2 3)2 = 25. X2 0.25(sinxi + cos X2) = 0. Compare to 10.2(5c). Compare to 10.2(5d). c. 15xi + X2 4x3 =13, d. IOxj 2x| + X2 2x3 5 = 0, x 2 + 10x2 X3 = 11. 8x| -)- 4x| 9 = 0. xl 25x3 = 22 8x2X3 + 4 = 0 Compare to 10.2(6c). Compare to l().2(6d).
Art Notes Week 10 Test 3 Early Northern Renaissance Art a. 3 Main Associates with Renaissance i. The ‘rebirth’ of the culture traditions of Classical Greece & Rome ii. The national systematic study of the natural world iii. The emergence of the ‘self-aware individual’ 1. Flemalle a. “The Annunciation” alter piece i. Triptych – 3scenes ii. Diptych – 2 scenes iii. Polyptych – multiple above 4 separators b. The Patrons – association of who bought the art work. Showing that they care about the annunciation i. Oil paint on Wood Panel c. Intuitive Perspective – eye-balling the lines and depth d. Disguised Symbolism – “disguised from us” we do not know what the symbol is mystical quality, all symbolic of the overall story 2. John van Eyck a. Framed Portraits – stand-alone piece of work b. The signature – name on the frame c. “Giovanni Arfolfi and his Wife” i. Wedding portrait/ endowment of the wedding ii. Symbolism- single candle lit to show that she is not pregnant d. “Ghent Altarpiece” i. Grisaille – monochromatic painting 3. Rogier Vander Wayden a. “Deposition” 4. Hugar Van der Goes a. Portinari altarpiece oil painting b. Iquestry & Embroidery – string sown into the surface i. Gold & colored silk threads c. Print making – engrave lines in the middle & paper pressed & lined comes out of paper i. Wood cut- negative technique 5. Michael Wolgan Early Italian Renaissance Art 1. Humanism bread a study of classical languages of the arts 2. Humanism places ndportance on monumental artworks a. Fame = 2 from immortality 3. Competition for the art a. Led to beautification of Florence 4. The Medici Family – friends manly renaissance competitions 5. Flippo Brunelleschi a. Created numerous Renaissance architecture b. Dome of Florence Cathedral i. Used a ‘double-shell’ approach to create the dome c. “invents’ linear perspective 6. Lorenzo Ghiberti a. Creates 2 sets of doors for baptistery in Florence b. “Gates of Paradise” 7. Donatello a. Brings in the classical sculpture b. Contrapposto – the offset or redistributing of weight in a statue 8. Painting a. Buon fresco – paint is applied to wet plaster (pg. 290) i. 1 Wall (base) nd ii. 2 Amiccio is the first larger plaster (rough) iii. 3 Sinopia (drawing) iv. 4 Intonaco second layer of plaster (smooth) v. 5 water-based paint on damp plaster 1. Giornata – how long the plaster will dry in a day’s work 9. Linear Perspective – painting as a “pyramid of sight” a. Viewing point of where the viewer is standing b. Picture plane – the scene goes “into the painting” c. Horizon Line – land meets sky, same “eye” as the viewing point d. Transversal – parallel to the picture plane e. Orthogonal – perpendicular to the picture plane f. Vanishing Point – single point where the orthogonal converge 10.Masaccio a. “Trinity with the Virgin” i. Symbolism in basic shapes ii. Circle – earth iii. Triangle – heaven iv. Rotating of reds and blues b. Distance – color change & detail lessens 11.Andrea Mantegna a. Ducal Palace 12.Sandro Botticelli a. “Venus and Mars” b. Neoplatonism – a tradition of philosophy incorporated in the renaissance artwork i. Birth of Venus 1. Canvas-tempre paint & oil 2. Contour lines c. Girolamo Savonarola – protested against the renaissance & preached against the Medici family d. Mystical Nativity – repentant of Neo-Platonism & turns to Christianity High Italian Renaissance Art 1. Leonardo da Vinci a. “Baptism of Christ” created by Verrocchio but Leo made the face of the bottom left angel b. “The Last Supper” i. Dry plaster & temper paint ii. Went back & covered it with oil c. “Mona Lisa” i. oil and canvas ii. Varnish – goes on top of the oil paint & adds a smokey-haziness to the top of the painting iii. Modeling effects: 1. Chiaroscuro – smooth & elegant shading that doesn’t show any breaks with light and dark 2. Sfumato – smokey-haziness like a varnish effect on top of the painting d. “Vitruvian Man” i. ideal proportions of the human body 2. Raphael a. “Maddalena Strozzi” b. “The Small Cowper Madonna” i. a lot of Mother & Child paintings (Modanna & Child) c. “The Sistine Modonna” d. The Papacy i. Pope Julius II ii. Pope Leo X e. “The School of Athens” – in poes library, school of athens/ knowledge i. Plato & Arostotle 3. Michelangelo a. Donatello David – David & Goliath, located in the Medici household b. “Pieta” – Virgin Mary holding baby Jesus after the Crucifixion only world of art that he signed c. “The David” – long tradition of statues of David & Goliath i. Similar to Poly Clitus, made out of marble ii. Coiled Spring – an angle that is created from the sculpture, as if he is anticipating motion d. “Sistine Chapel Ceiling” – High renaissance & Old Testament scene e. “The Creation of Adam” – movement of the painting i. Pounding – paper with holes in it & pound graphite into the painting scene. 1. Transfers the artwork onto the scene