Multivariable Calculus-PNU

ubject Sections and Topics Exercises Week قابلة للتعديل CH 9 9.1 (1) Definition of sequence. (2) Def 9.1.1+ Graph of seq. (3) Limit of seq. + Def. 9.1.2+ Th.9.1.3 (4) The squeezing theorem: (5) Th. 9 1.5 , Th.9.1.6 Examples 1,2,3,5,7,8,9. Page 605: 1(a,d), 2 a ,4 a, 7,8,14,19, 23,30 1 9.2 (1) Terminology, Def. 9.2.1, Table 9.2.1 as examples (2) Testing for monotonicity, Table 9.2.2 (3) Convergence of monotone seq. + Th. 9.2.3+ Th.9.2.4 Examples 1,2,4 Page 613: 1,2,3,7,11,17,23 9.3 (1) Sums of infinite series, Def. 9.3.1 (2) Quick look of example page 615, Def. 9.3.2 (3) Geometric series, Th. 9.3.3 (4) Harmonic series Examples 1,2,4 Page 621: 1(a),2(a),5,6,12,13, 30(a,c),31(a,c). 2 9.4 (1) Divergence test, Th. 9.4.1 , Th. 9.4.2 (5) Algebraic properties, Th. 9.4.3 (6) P-series, Th.9.4.5 Examples 1,2,3,5 Page 629: 1,2,4, 6, 8, 9, 10, 12,14,18,22. 9.5 (1) The limit comp.test: Th.9.5.4 (2) The ratio test: Th.9.5.5 (3) The root test: Th.9.5.6 Examples 2,3,4 Page 636: 5,6,11,15, 18, 20 & 28, 30, 38 ,40,47 9.6 (1) Alternating series, Th. 9.6.1. (2) Absolute convergence: Def. 9.6.3. (3) Th. 9.6.4 with proof. (4) Conditional convergence: Ex. 5 (5) The ratio test for absolute conv., Th. 9.6.5 Examples 1,3,4,5,6. Page 646: 1(a),2(b),3(b),4(a), 5(a),6(d),7(a), 10,14,16. 3+4 9.8 (6) Maclaurin and Taylor SERIES: Def 9.8.1. (7) Power series in x. (8) Radius and interval of conv. Th. 9.8.2 (9) Finding the interval of conv. (10)Power series in x-x0, Th. 9.8.3. Examples 1,2,3,4. Page 667: 1,2,4,7,10,11,17,21, 29,43. 9.9 (1) Binomial series : Def+ equation 18+ Table 9.9.1 668 2 10.2 Polar Coordinates (1) Polar Coordinate Systems (2) Relationship Between Polar and Rectangular Coordinates Examples 1 & 2 Page 716: 3,4,7,8,9,10,11 5 10.4 Conic sections (1) Conic Sections in standard position (2) Translated conics equations (12)-(19). Examples 2 &4 &6,9,10 Page 745: 15,18,19,20,25,59(a, b) CH11 11.1 Rectangular Coordinates In 3 Space; Spheres (1) Rectangular coordinate system (2) Distance in 3-Space; (3) Spheres (equations (4), (5)) and table +Th. 11.1.1 Examples 1 & 2 Page 771: 9,12, 13 6+7 11.8 Cylindrical and Spherical Coordinate Systems (1) Constant Surfaces (2) Converting Coordinates (3) Equations of Surfaces in Cylindrical and Spherical Coordinates Examples 1-3 Page 837: 1(a,b),2(a,b),3(a,b) ,4(a,b),7(a,b),8(a,b ) & 19-23,27 30,35-40 Ch 13 13.1 Functions of two & more variables (1) Def 13.1.1+ Def 13.1.2 Examples 1-2 Page 914: 1(a,b),2(a,b),7(a),1 7(a,d),21,23 26,27,28(a,b). 8+9 13.2 Limits & continuity (1) Limits along curves: (2) Open and closed sets – quick look. (3) General limits of functions of two variables: Def 13.2.1-(fig 13.2.7). (4) Relation between general limit and limits along curves:, Th.13.2.2, Example3+ problems 9-11-13-15. (5) Continuity : Def 13.2.3 +Th 13.2.4 (6) Limits at discontinuities : (7) Limits at boundry points : (8) Extinction to 3-variable functions: Def 13.2.5. Examples 1-8 Page 925: 1,4,5,7,8,9,10,16,20 ,24 13.3 Partial derivatives (1) Partial derivative of fn. Of 2-var.: Def 13.3.1. (2) The partial derivative function: (3) Partial derivative notations: (4) Partial derivative viewed as rate of change and slope: (5) Implicit partial diff.: (6) Partial derivative and continuity: (7) Partial derivative of fn. With more than 2 var.: (8) Higher order partial derivatives: (9) Equality of mixed partial der.: Examples 2,3,5,7,9,10,13. Page 936: 1,2,4,9,12,25,26,31, 32, 38, 40,43,49,52 10 13.5 Chain rule (1) The chain rule for derivatives , Th.13.5.1, Remark page 952 (2) Chain rule for partial derivatives: Th.13.5.2 Page 957: 1,3,4,5,8,10, 17,20,21,23,27,31 3 (3) Implicit diff. + Th. 13.5.3+ ex.7+Th.13.5.4 Examples 1,3,4,7,8. 13.8 Extrema (1) Extrema (quick look)+ Def 13.8.1+ Def13.8.2 (2) Bounded sets (quick look) (3) The extreme-value theorem+ Th.13.8.3 (4) Finding relative extrema : Th.13.8.4+ Th.13.8.5 (5) Simple examples of finding critical points as: ( ) ( ) 2 3 2 2 , 14 6 2 , y xy x y x f y x y x y x f + + = + − − + = (6) The 2nd partial test: Th.13.8.6, Ex.3+Ex4 (7) Finding absolute extrema : (8) The steps in the blue box Examples 3,4,5. Page 985: 1-4, 9,11,12,17. 11 13.9 Lagrange Multipliers (1) Lagrange Multipliers Th.13.9.3+ Th.13.9.4 Examples 1-3 Page 996: 5,6,9,11 CH14 14.1 Double Integrals (1) Volume : Quick look(use fig.14.1.2+fig 14.1.3) (2) Def 14.1.2 +Def. of double integral. (3) Evaluating double int.: (4) Th.14.1.3+ Properties of double integral: (5) Equations 9-10-11-12 Examples 1-4 Page 1007: 1,3,4,5,10,13,16,29, 31,36 12 14.2 Double Integral over Nonrectangular Region (1) Iterated integrals : Equations 1+2 (2) Double integral over non- rectangular regions : Def 14.2.1+ Th 14.2.2 (3) Setting up limits of integration: The blue boxes page 1011+Problem 20 (4) Reversing the order of integration + Problem 50. (5) Area calculated as double int.: Examples 1,3,4,7,8 Page 1015: 1,3,4,5,8,15,16,20,2 1,26,29,48,53 14.3 Double Integral in Polar Coordinates (1) Simple polar regions: Quick look+ Def 14.3.1 (2) Double integral in polar coordinates: Quick look –page 1019 , Use fig 14.3.5 (3) Evaluating polar double integrals: Th.14.3.3 + Blue box page 1021+fig 14.3.9+ Problem 24 (4) Finding area using polar double integrals : Problem7 (5) Converting double + Equation 9+ Problem28 Examples 1. Page 1024: 1-10, 23,24,27,28,30 14.5 Triple Integrals (1) Def. of triple integral (quick look) (2) Properties of triple integrals (3) Evaluating triple int. over rectangular boxes: Th.14.5.1 + problem 2 Page 1045: 1-4, 9,11,16,17,27,29 13 & 14