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Richard_Notes_Winter_2007

# Richard_Notes_Winter_2007 - M ATH-203S YLLABUS TEXT C...

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MATH-203 SYLLABUS TEXT: CALCULUS bv STEWART (5th Ed) The following relates to the course objectives established by the calculus committee. Individual instructors may use a different syllabus directed at the same objectives or add additional problems that relate to other topics as time permits. Students will be assigned suggested problems at the end of each lecture and may find many other related problems in the text that can be used for further practice toward mastering course objectives. SECTION l0.l r0.3 12.1 12.2 12.3 12.4 12.5 12.6 l4.l 14.2 14.3 14.4 14.5 14.6 14.7 14.8 l5.l t5.2 l 5.3 I 5.4 15.7 12.'7 I 5.8 TOPIC PAGE Parametric Equations 651 Polar Coordinates 669 Three Dimensional Coordinate Systems 793 Vectors 198 The Dot Product 807 Tlre Cross Product 814 Equations of Lines and Planes 822 Cylinders & Quadric Surfaces 832 Functions of Several Variables 887 Limits and Continuity 902 Partial Derivatives 909 TangentPlanes and Differentials 923 The Chain Rule 931 Directional Derivatives and Gradient 940 Maximum and Minimum Values 953 LaGrange Multipliers 965 Double Integration over Rectangles 981 Iterated lntegrals 989 Double Integration over General Regions 995 Double Integration in Polar Coordinates 1003 Triple Integrals 1023 Cylindrical & SphericalCoordinates 839 Integrals in Cylindrical & Spherical Coordinates 1033

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TERM: WINTER 2007 COURSE: MATH-203 INSTRUCTOR: DT. P. RICHARD OFFICE: 2-135A PHONE: 762-7925 e-MAIL : pri [email protected] OFFICE HOLIRS: MWRF I l:20AM_t: tOpM oT BY APPOINTMENT GRADING: There wi, be 4 (four) in-crass exams each worth 100 points and a Finar Examination wo,th ioo point, r"r, i",ar of 600 possibie points. EXAM I: Third Week over Sections 10.1, 10.3, I 2.1_12.5 EXAM II: Fifth Week over Section, t 2.6, I4.l_14.5 EXAM III: Seventh Week ou.. Sections I 4.6_14.g, l5.l_15.3 EXAM IV: Tenth Week ou". s..,ion. tl.+,\i.i,"r5.7_15.g Grade Conversion on 100 point exams: Grade:0.7(Score on exam) + 30
SECTION 10.1 PARAMETRIC REPRESENTATIONS OF CURVES Let f and g be continuous functions of t on an interval I. Then the equations x:f(t)andy:g(t) are called parametric equations forthe curu'e C inthe xl-plane generatedbythe set of ordered pairs (x. "v): (f(t),g(t)) fbr some r in l. Example: Sketchthepath r : tr-t t,y: 3 t lbr-2 <t<2. Solutionl: (Plottine points) lior various values of t between -2 and 2 we corrpute x: tr + t and y:3 - t. then plot the (x. y) pairs and conncct the dots. Pair t 1 -2.O 2 -L.8 3 -1.6 4 -L.4 5 -L.2 6 -1.0 7 -0.8 8 -0.6 9 -0.4 L0 -o.2 t_L 0.0 L2 0.2 13 0.4 L4 0.6 Ls 0.8 16 1.0 L7 L.2 18 t.4 19 L.6 20 1.8 2L 2.O x = t'+t 2.OO L .44 0. 95 0 .56 o.24 0 .00 -0.t5 -o.24 -o.24 -0.15 0 .00 o.24 0 .56 0. 96 L .44 2.OO 2.64 3.36 4.L6 5.04 6.00 y=3-t 5.0 4.8 4.6 4.4 4.2 4.O 3.8 3.6 3.4 3.2 3.0 2.8 2.6 2.4 2.2 2.O 1.8 1.5 L.4 L.2 1.0

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Solution2: (Elimination of the Parameter) Solving y for the parameter t yields t : 3.: V SuUrtltutittg-thi.ibry inthe expressionfbrxyieldsx:(3 y)-+ (3 -y):l--7f + l2' Wenext detemine the domain of this frmction of y. Note that as t increases^ y decreases. so the rnaximum ralue of y occurs when t: 2 (so y - 5) and the minimurn value of y occurs when t:2 (so ), : I j.
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