MAT-272 Calculus II

A continuation of the topics studied in Calculus I, in particular anti-differentiation and integration of functions and their applications. Also included are various techniques of integration, improper integrals, infinite series, Taylor polynomials, power series, and an introduction to differential equations. Graphing calculator required; see department chair for specific model. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.

Credits

4

Prerequisite

Students earn a C- or better in MAT-271.

Lecture Contact Hours

4

Lab Contact Hours

0

Other Contact Hours

0

Department

• Mathematics

Grading Scheme

• Letter

SUNY Gen Ed Credit

• Yes

Semesters Course Will Be Offered

• Fall
• Spring
• Summer

Course Learning Outcomes

1. Understand the connections between definite integrals, total change in quantities, and geometry.
2. Determine indefinite integrals.
3. Apply the Fundamental Theorem of Calculus and techniques of integration to solve problems.
4. Use series to represent functions and approximate values.

View Course Outline

MAT 272: Calculus II

Department

Mathematics

Course Description

A continuation of the topics studied in Calculus I, in particular anti-differentiation and integration of functions and their applications. Also included are various techniques of integration, improper integrals, infinite series, Taylor polynomials, power series, and an introduction to differential equations. Graphing calculator required; see department chair for specific model. This course carries SUNY General Education Mathematics (and Quantitative Reasoning) credit.

Credit Hours

4

Contact Hours

Lecture	4
Lab	0
Other	0

Grading Scheme

Letter

Semester(s) Course Will Be Offered

Fall, Spring, Summer

Prerequisites

Students earn a C- or better in MAT-271.

SUNY General Education Course

• Mathematics and Quantitative Reasoning

First Year Experience Course

No

Capstone Course

No

Course Learning Outcomes

1. Understand the connections between definite integrals, total change in quantities, and geometry.
2. Determine indefinite integrals.
3. Apply the Fundamental Theorem of Calculus and techniques of integration to solve problems.
4. Use series to represent functions and approximate values.

Topic Outline

1. I. Definite Integrals

2. a. Riemann Sums and sigma notation

3. b. Definition using limits

4. c. Approximation Techniques

5. i. using area

6. ii. using sums: left, right, midpoint, trapezoid, Simpson’s rule

7. d. Properties

8.

9. II. Fundamental Theorem of Calculus

10. a. Net-Change viewpoint

11. b. Construction theorem viewpoint

12. c. Evaluating definite integrals

13.

14. III. Applications

15. a. Basic Mechanics

16. b. Geometry: Area of bounded region

17. c. Solids of Revolution: Volume using “Washers” and “Shells”

18. d. Finding mass given density function

19. e. Center of Mass

20. f. Arclength and Surface Area

21. g. Polar coordinates

22.

23. IV. Antiderivatives

24. a. Definition

25. b. Approximating antiderivatives graphically and numerically

26. c. Solving Initial Value Problems (IVP)- y' = f(x), f(x_o) = y_o

27.

28. V. Indefinite Integrals

29. a. Reversing basic derivative rules (elementary antiderivatives)

30. b. Properties

31. c. Integration Techniques

32. i. Substitution

33. ii. Integration by Parts

34. iii. Partial Fraction Decomposition

35. iv. Trigonometric substitution

36. d. Table of integrals

37. e. Appropriate use of technology

38.

39. VI. Improper Integrals

40. a. Definition

41. b. Convergence vs. divergence

42. c. Application

43.

44. VII. Series

45. a. Convergence vs. divergence

46. b. Geometric series

47. c. Applying convergence tests

48. i. Divergence Test

49. ii. Integral Test

50. iii. Comparison Test

51. iv. Alternating Series Test

52. v. Ratio Test

53. vi. Absolute vs. conditional convergence

54. d. Taylor Series

55. i. Defining

56. ii. Recognizing known series

57. iii. Applications

58. e. Power Series

59. i. Radius of Convergence

60.