MA1120-Calculus II
MA1120 Calculus II (1 credit):
Syllabus: Integral Calculus: Definite Integrals as a limit of sums, Applications of integration to area, volume, surface area, Improper integrals. Functions of several variables: Continuity and differentiability, mixed partial derivatives, local maxima and minima for function of two variables, Lagrange multipliers.
Text Book: Thomas' Calculus: Early Transcendentals Thirteen edition
Whatever we discussed in the classroom:
Homework: [All Page numbers are from the above textbook] (Please stick to the 13th edition as page and question numbers may vary.)
Properties of integral on page 320.
Page 361
problem 5
Problems on pages 362-363-364.
Problem 20.
Problem 29.
Problems 31 to 39, 44.
Problem 44.
Problems on page 354.
Problems 47 to 62.
Page 355
Problem 106.
Problems on Page 374.
Problems 15, 16, 17, 18.
Find the volume of a sphere of radius R centered at the origin using the following:
method of cross-section,
method of revolution of curve.
Find the volume of the solid bounded in between the planes y=4, y =3 and the surface of revolution given by the curve y = x^2 +1.
Find the volume of the solid bounded by the rotating curve y = x^{1/2}, around the axis y =1, in the first quadrant. See Figure -1 below.
Problems on page 374.
Problems 15, 16, 17, and 18.
Problems on page 374.
Problems 37, 38, and 44.
Problems on page 381.
Problems 1, 2, 3, 4.
Problems on page 383.
problems 32 and 33.
Pages 388-389
Any four problems from 1-13, and problem 14.
Problem 32 (Hint: Use tangent/slope interpretation of f'(x))
Problems 26, 34.
Pages 393-394
Problems 8, 24, 25.
Pages 327
Problems 86, 87.
Pages 513 and 514
Any five problems from 1 to 34.
Any five problems from 35 to 63.
Problems 73, 77.
Pages 746, 747
Problems 27.
Problems 45.
Problems 13-26.
Reading homework -- pages 793-797.
Reading homework -- page 803 Theorem 1.
Page 808
Any five problems between 13-24.
Page 809
Problem 52.
Problems 56, 57.
Page 765
Any five problems between 1 to 10.
Reading Homework: 793 to 797.
Page 808
Any two problems 41 to 48 (Play with simple paths (like y=mx, y=x^2, or some elementary functions)).
Page 810
Problem 79, 81.
Reading Homework: 810 to 814.
GeoGebra assignment
Draw the graphs of f(x,y) = xy, f(x,y) =x, f(x,y)=x/y, f(x,y) = (xy)/ x^2+y^2, and
f(x,y) = x^2 y/ (x^(4) + y^2).
Show that the function f(x,y) = x^2 y/ (x^4 + y^2), for non-zero (x,y), and f(0,0) = 0 is not continuous at (0,0). (use GeoGebra for visualization).
Show that the function f(x,y) = (sin)(x) y/ (sin^2(x) + y^2), for non-zero (x,y), and f(0,0) = 0 is not continuous at (0,0). (use GeoGebra for visualization). Find the other points of
discontinuities.
Assignment: Click Here << Submit on 22/12/22 (Thursday)>>
Date of Exam: 03/01/23 TIME: 17:30 to 19:30.
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