MTH 176 Syllabus
Division:†††††† Arts and Sciences†††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††††† Date:† February 2014
Curricula in Which Course is Taught: ††††††††††† Science, Liberal Arts
Course Number and Title:† ††††††† MTH 176, Calculus of One Variable II
Credit Hours:†† 3††††† †††††††††† ††Hours/Wk Lecture:†† 3†† †† †Hours/Wk Lab:††† †† ††††††††††††††††††††††† Lec/Lab Comb:††† 3
I. Catalog Description: Continues the study of integral calculus of one variable including indefinite integral, definite integral and methods of integration with applications to algebraic and transcendental functions. Designed for mathematical, physical, and engineering science programs.
II. Relationship of the course to curricula objectives in which it is taught: This course allows a student to use logical and mathematical reasoning in problem solving in theoretical and applied areas that require critical thinking.
II. Required background:††
MTH 175 or equivalent.† (Credit will not be awarded for more than one of MTH 174, MTH 176 or MTH 274.)
IV. Course Content:
A. Antiderivatives and Indefinite Integration
B. Area Bounded by a Curve
C. Riemann Sums and Definite Integrals
D. The Fundamental Theorem of Calculus & Mean Value Theorem for Integrals
E. Integration by Substitution
F. Numerical Integration
G. The Natural Logarithmic Function: Integration
H. Inverse Trigonometric Functions: Integration
I. Hyperbolic Functions
J. Slope Fields and Eulerís Method
K. Growth and Decay Differential Equations
L. Area of a Region between Two Curves
M. Volume: The Disk Method
N. Volume: The Shell Method
O. Arc Length and Surfaces of Revolution
P. Basic Integration Rules
Q. Integration by Parts
R. Trigonometric Integrals
S. Trigonometric Substitution
T. Partial Fractions
U. Indeterminate Forms and LíHŰpitalís Rule
V. Improper Integrals
X. Series and Convergence
Y. The Integral Test and p-Series
Z. Comparisons of Series
AA. Alternating Series
BB. The Ratio and Root Tests
CC. Taylor Polynomials and Approximations
V.† Learner Outcomes
Upon completion of the course the students
1. Use indefinite integral notation for antiderivatives.
2. Use basic integration rules to find antiderivatives and a particular solution.
3. Use sigma notation to write and evaluate a sum.
4. Understand the concept of area and approximate the area of a plane region.
5. Find the area of a plane region using limits.
6. Understand the definition of a Riemann sum.
7. Be able to state the definition of the definite integral.
8. Evaluate a definite integral using limits and using properties of definite integrals.
9. Evaluate a definite integral using the Fundamental Theorem of Calculus.
10. Understand and use the Mean Value Theorem for Integrals.
11. Find the average value of a function over a closed interval.
12. Understand and use the Second Fundamental Theorem of Calculus and Net Change Theorem.
13. Use pattern recognition to evaluate an indefinite integral.
14. Use change of variables to evaluate an indefinite integral.
15. Use the General Power Rule for integration to evaluate an indefinite integral.
16. Evaluate an indefinite integral involving an even or odd function.
17. Approximate a definite integral using the Trapezoidal Rule and Simpsonís Rule.
18. Analyze the approximate error in the use of both the Trapezoidal & Simpsonís Rules.
19. Use the Log Rule for Integration to integrate a rational function; use exponential rule for integration.
20. Integrate trigonometric functions.
21. Integrate functions whose antiderivatives involve inverse trig functions.
22. Use the method of completing the square to integrate a function.
23. Develop properties of hyperbolic functions as well as differentiate and integrate them.
24. Use slope fields and Eulerís Method to approximate solutions of differential equations.
25. Use separation of variables to solve simple differential equations.
26. Use exponential functions to model growth and decay in applied problems.
27. Recognize and solve differential equations that can be solved by separation of variables.
28. Using integration find the area of a region between two curves and between intersecting curves.
29. Be able to sketch the three-dimensional solid obtained by rotating a region around the x- or y-axis.
30. Use definite integrals to calculate the volume of solids by disks, slabs, or washers.
31. Use definite integrals to calculate the volume of solids by shells.
32. Find the arc length of a smooth curve and the area of a surface of revolution using definite integrals
33. Find an antiderivatives using integration by parts.
34. Solve trigonometric integrals involving powers of sine and cosine; involving powers of secant and tangent; and
35. involving sine-cosine products with different angles.
36. Use trigonometric substitution to solve an integral.
37. Use integrals to model and solve real life applications.
38. Evaluate indefinite integrals by partial fractions.
39. State LíHŰpitalís Rule and the conditions for which it is valid.
40. Calculate limits of various indeterminate forms using LíHŰpitalís Rule.
41. Evaluate an improper integral that has an infinite limit of integration.
42. Evaluate an improper integral that has in infinite discontinuity.
43. Define and test the convergence of sequences and series.
44. Define and test the convergence of geometric series.
45. Apply integral test and comparison test for series with positive elements.
46. Apply the ratio and root test to alternating series and power series.
47. Find a representation of a function as a power series, and find its radius and interval of convergence.
48. Find Taylor and Maclaurin Series of simple functions.
Test, quizzes, written assignments
†VII. This course supports the following objectives:
DCC Educational Objectives: