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:

1.  Integral calculus.

2.  Vectors, limit, and continuity.

3. Partial derivatives in 2 and 3 variables.

Homework: [All Page numbers are from the above textbook] (Please stick to the 13th edition as page and question numbers may vary.)

1. Properties of integral on page 320.

2. Page 361 

• problem 5

3. Problems on pages 362-363-364. 

• Problem 20.

• Problem 29.

• Problems 31 to 39, 44.

•  Problem 44. 

4. Problems on page 354.

• Problems 47 to 62.

5.  Page 355

• Problem 106.

6. Problems on Page 374.

•  Problems 15, 16, 17, 18.

7. 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.

8. 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. 

9. 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.

10.  Problems on page 374.

•  Problems 15, 16, 17, and 18.

11.  Problems on page 374.

• Problems 37, 38, and  44.

12.  Problems on page 381.

•  Problems 1, 2, 3, 4.

13. Problems on page 383.

•  problems 32 and 33.

14. 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.

15. Pages 393-394

• Problems 8, 24, 25.

16. Pages 327

• Problems 86, 87.

17. Pages 513 and 514

•  Any five problems from 1 to 34.

• Any five problems from 35 to 63.

• Problems 73, 77.

18. Pages 746, 747

• Problems 27.

• Problems 45.

• Problems 13-26.

19. Reading homework -- pages 793-797.

20. Reading homework -- page 803 Theorem 1.

21. Page 808

• Any five problems between 13-24. 

22. Page 809

•  Problem 52. 

• Problems 56, 57.

23. Page 765

• Any five problems between 1 to 10.

24. Reading Homework: 793 to 797.

25.  Page 808

• Any two problems 41 to 48 (Play with simple paths (like y=mx, y=x^2, or some elementary functions)). 

26. Page 810

•  Problem 79, 81.

27.  Reading Homework: 810 to 814.

28. 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).

29.  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). 

30. 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.