MATH 241 Lecture Notes - Lecture 11: Ellipse

• School: University of Maryland
• Department: Mathematics
• Course: MATH 241
• Professor: Christian Rosendal

Document Summary

Math241 lecture 11 functions of several variables and equations. Notation: just as functions of one variable are typically denoted by (cid:4666)(cid:1876)(cid:4667), functions of two and three variables will be denoted by (cid:4666)(cid:1876),(cid:1877)(cid:4667) and (cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667) (cid:4666)(cid:1876),(cid:1877)(cid:4667)=(cid:1876)(cid:2870)+(cid:1877)(cid:2870) (cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667)=(cid:1876) (cid:1877)(cid:1878)+(cid:1876)(cid:2870) Examples: (cid:4666)(cid:1876)(cid:4667)=(cid:1876)(cid:2870) (cid:1877) (cid:1876)(cid:2870)=(cid:882) equation of 2 variables (cid:4666)(cid:1876),(cid:1877)(cid:4667)=(cid:1876)(cid:2870) (cid:884)(cid:1877)+(cid:1877)(cid:2870) (cid:1878)=(cid:1876)(cid:2870) (cid:884)(cid:1877)+(cid:1877)(cid:2870) equation in 3 variables (cid:4666)(cid:1876),(cid:1877),(cid:1878)(cid:4667)=(cid:3051)(cid:3052)+(cid:1878)(cid:2871) (cid:1875)=(cid:3051)(cid:3052)+(cid:1878)(cid:2871)equation in 4 variables. Not every equation is a function but some are. A gallery of examples of function and equations. Example: (cid:1877)=(cid:1876)(cid:2870)+(cid:1878)(cid:2870) (cid:1877),(cid:1878) switched so z y x. This is the top part of (cid:4666)(cid:1876),(cid:1877)(cid:4667)= 9 (cid:1876)(cid:2870) (cid:1877)(cid:2870) (cid:1878)= 9 (cid:1876)(cid:2870) (cid:1877)(cid:2870) (cid:1878)(cid:2870)=9 (cid:1876)(cid:2870) (cid:1877)(cid:2870) (cid:1876)(cid:2870)+(cid:1877)(cid:2870)+(cid:1878)(cid:2870)=9 z y. Negative value of (cid:1877), means plot towards left z. Negative sign moves cone upside down while 9 moves cone upwards z x. In 3d, cylinder because (cid:1878) can be anything (cid:1877)(cid:2870)+(cid:1878)(cid:2870)=(cid:886) z x x y y. In 3d (cid:1878)=(cid:1876)(cid:2870) (cid:1877) can be anything in (cid:1876)(cid:1878) plane z x.