MATH 151: Calculus II


Final Exam Review Topics


May 9, 2026


  1. Review of Calculus I: functions and their properties; even and odd functions

  2. Review of Calculus I: limits

  3. Review of Calculus I: differentiation; chain rule; tangents to graphs of functions

  4. Review of Calculus I: antiderivatives; definite integral; Riemann sums

  5. Fundamental Theorem of Calculus; differentiation of the integral function

  6. Integration by substitution

  7. Integration by parts

  8. Trigonometric integrals

  9. Trigonometric substitutions

  10. Integration with the use of partial fractions

  11. Improper integrals of type 1

  12. Improper integrals of type 2

  13. Comparison test for improper integrals

  14. Integrals as areas between curves

  15. Computing volumes of solids by integrating cross-sectional area

  16. Computing volumes with the disk/washer method

  17. Computing volumes with the cylindrical shells method

  18. Parametric equations of curves; conversions from non-parametric to parametric and vice versa

  19. Arc length in parametric and non-parametric forms

  20. Average value of a function in an interval

  21. Applications of integration to mechanics: computing work done when stretching springs or moving objects

  22. Probability density function

  23. Uniform, exponential, and normal density functions

  24. Mean (expected value) of a probability density function

  25. Sequences: explicit and recursive definitions

  26. Limit of a sequence: definition, meaning, convergence vs. divergence

  27. Theorems about limits of sequences: function, squeeze, absolute value, continuous function

  28. Monotonic and bounded sequences

  29. Geometric sequence and its limit

  30. Series: definition and convergence; partial sums; summation notation

  31. Geometric series, finite and infinite sums of geometric series

  32. Repeating decimals as rational numbers

  33. Telescoping series

  34. Theorem about convergent series and its consequences

  35. The integral test of convergence

  36. P-series and its convergence

  37. The comparison test of convergence

  38. The limit comparison test of convergence

  39. Remainder estimate for the integral test; estimating sums of series *)

  40. The alternating series test

  41. Alternating series estimation theorem *)

  42. Absolute convergence

  43. The ratio test

  44. Power series: definition, three cases of convergence, radius of convergence

  45. Differentiation and integration of power series, preservation of radius of convergence

  46. Using power series to integrate functions

  47. Taylor and Maclaurin series; derivation of Taylor series coefficients

  48. Obtaining Taylor/Maclaurin series; finding their radii/intervals of convergence

  49. Important Maclaurin series *)

  50. Approximating functions with Taylor polynomials; applications of Taylor inequality

  51. Introduction to differential equations; initial value problems

  52. Verifying solutions of differential equations

  53. Directly integrable differential equations

  54. Separable differential equations

  55. Exponential growth and decay; applications: population growth, continuously compounded interest, radioactive decay, law of cooling

  56. Polar coordinates: graphing curves, slopes, arc lengths
























*) Formulas will be provided, if needed