**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 Euler’s 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 L’Hôpital’s Rule

V.
Improper Integrals

W. Sequences

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.
Upon
completion of the course the students will be
able to: 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 Simpson’s Rule. 18. Analyze the approximate error in the use of both the
Trapezoidal & Simpson’s 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 Euler’s 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 L’Hôpital’s Rule and the
conditions for which it is valid. 40. Calculate limits of various indeterminate forms using L’Hôpital’s 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. |
VI. Test, quizzes, written assignments |

VII. **This course
supports the following objectives**:

**DCC Educational Objectives:**

Critical
Thinking

Information Literacy

Quantitative Reasoning

Scientific Reasoning