MTH 112

CALCULUS II

A continuation of MTH 111. Topics include inverse functions, techniques of integration, applications of the integral, and infinite sequences and series. Not open to students with credit in MTH 106. Prerequisite: MTH 111. Offered every fall, spring, and summer. (Four Credits)


Assignments:

    Calculus I (Dawkins)               Calculus II (Dawkins)

  1. MTH 111 Final Exam

  2. Radiium-226 has a half-life of 1600 years. If A 0 indicates the initial amount of Radium-226 present in a test object, then the amount present, A(t) after t years is given by the functiion A(t) = A 0 (1/2) t/1600 . Express A(t) in terms of the exponetial function e . Check also that you can reverse this process.

  3. Introductory Antiderivatives
  4. "Area" Hunters
  5. Mean Value Theorem
  6. Exercises 5.3: 9 - 62   .....  The Definite Integral
  7. The Definite Integral
  8. Exercises 5.4: 1 - 70, 75 - 78   .....  The Fundamental Theorem of Calculus
  9. Exercises 5.5: 1 - 78   .....  Indefinite Integrals, Guess, Check, and Adjust, and Substitution
  10. Exercises 5.6: 1 - 110   .....  Area Between Curves

    11. --- Important General Statement ---

  11. Exercises 8.1: 1 - 52   .....  Reduction Technique: Integration by Parts, Table of Integrals
  12. Exercises 8.4: 1-54   .....  Partial Fraction Decomposition , Integration by Partial Fraction Decomposition
  13. (Dawkins) Assignment Problems 1 - 6   .....  Integrals Involving Roots
  14. Integrals Involving Quadratics
  15. Exercises 7.2: 1-30   .....  Separable Differential Equations
  16. Exercises 8.2: 1 - 68   .....  Trigonometric Integrals ( Identities )
  17. Exercises 8.3: 1-34   .....  Trigonometric substitions
  18. Summary of algebraic manipulation techniques
  19. Exercises 8.7: 1-64   .....  Improper Integrals and Asymptotics
  20. First Order Linear Ordinary Differential Equations (MIT OpenCourseware - Dr. Arthur Matuck)
    • Solve the first order linear differntial equations listed below:



  21. Sample unit problems

  22. Arc Length and Centroids
  23. Exercises 6.3: 1-22   .....  Arc Length
  24. Exercises 6.6: 1-34   .....  Moments and Centers of Mass
  25. Exercises 6.1: 4,5,6,15-55   .....  Volumes Using Cross Sections
  26. Exercises 6.1: 4,5,6,15-55   .....  Volumes Using Disks and Washers
  27. Volumes Using Disks
  28. Volumes Using Washers
  29. Exercises 6.1: 4,5,6,15-55   ..... Volumes Using Cylindrical Shells
  30. Exercises 6.4: 1-24   .....  Areas of Surfaces of Revolution
  31. Sphere and Torus
  32. Exercises 6.5: 1-20   .....  Work
  33. Work
  34. (Dawkins) Assignment Problems 1 - 7   .....  Hydrostatic Pressure and Force
  35. Hydrostatics

  36. A triangular plate whose edges are 5ft, 5ft and 8ft is placed vertically in water with its longest edge uppermost, horizontal, and 3 ft below the water level. Calculate the force on the side of the plate.
  37. Find the force on the end of a trough in the form of a semicircle of radius 2 ft.
  38. Parametric Equations and Curves
  39. Tangents with Parametric Equations
  40. Area with Parametric Equations
  41. Arc Length with Parametric Equations

  42. Polar Coordinates
  43. Tangents with Polar Coordinates
  44. Area with Polar Coordinates
  45. Arc Length with Polar Coordinates

  46. Exercises 8.6: 1-10   .....  Numerical Integration

  47. Exercises 9.1: 27-90   .....  Sequences
  48. Exercises 9.2: 1-68   .....  Infinite Series
  49. Numerical series
  50. Exercises 9.3: 1-40   .....  The Integral Test
  51. Geometric series
  52. Exercises 9.4: 1-54   .....  Comparison Tests
  53. Exercises 9.5: 1-62   .....  Ratio and Root Tests
  54. Exercises 9.6: 1-48   .....  Power Series
  55. Sample unit problems
  56. Special Series

  57. Intervals of convergence
  58. Taylor's Theorem
  59. Power Series and Taylor Series
  60.   .....  The Binomial Series and Applications of Taylor Series
  61. Binomial Series Exercises

On-line Tests (Fall 2020)

Contact R.L. Pryor