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MAT142 - Calculus 2
Catalog Description: Examines applications of the definite integral; analysis of the natural logarithmic, exponential, trigonometric, and hyperbolic functions; introduction to differential equations; techniques of integration; L'Hopital's Rule and indeterminate forms; improper integrals; and infinite series. Prerequisite: MAT 141 with a grade of ‘C’ or higher or by placement.
Lecture: 4 hrs.
Course Learning Outcomes (CLOs):
A student who has successfully completed MAT142 is expected to be able to perform the following in an exam setting, without the use of notes, using a scientific or graphing calculator as appropriate:
1. Evaluate the derivative of any exponential, logarithmic, trigonometric, or inverse trigonometric functions
2. Given any integrable function, the student must recognize and apply the correct technique used to integrate (in exact form) from among the following techniques: fundamental integral formulas, U-substitution, method of parts, trigonometric substitution, method of partial fractions, powers of trig functions, or by use of integral tables*
3. Apply the Fundamental Theorem of Calculus to evaluate a definite integral
4. Using integrals, find the area between the two curves
5. Using integrals, sketch any plane region defined by one or more simple curves, and find the volume of the solid generated by revolving the plane region about the x- or y-axis
6. Apply any of the standard approximation techniques (midpoint, trapezoid, Simpson's) to evaluate a definite integral involving any simple function, accurate to three decimal places.
7. Use L'Hopital's Rule to evaluate any limit involving the indeterminate form 0 / 0 or oo/oo
8. Given an infinite series, determine the convergence or divergence of the series using any of the following tests (as appropriate to the particular series): divergence, ratio, root, comparison, limit comparison, geometric, harmonic, integral, p-series.
9. Given a power series, find the interval of convergence.
10. Given a function of a single variable, find and evaluate a Taylor polynomial or Taylor series for the function at a given point.
* This course objective has been identified as a student learning outcome that must be formally assessed as part of the Comprehensive Assessment Plan of the college. All faculty teaching this course must collect the required data and submit the required analysis and documentation at the conclusion of the semester to the Office of Institutional Research and Assessment.
I. Review Basic Integration Techniques
a. Integration of Fundamental forms
b. Integration by U-substitution
c. Fundamental Theorem of Calculus
II. Applications of Integration
a. Area between two curves
b. Volume: The Disc Method
c. Volume: The Shell Method
d. Arc Length and Surface Area
f. Additional applications at discretion of instructor
III. Transcendental Functions
b. Calculus of Inverse Functions
c. Exponential Functions
d. Inverse Trigonometric Functions
e. Hyperbolic Functions
IV. Introduction to Differential Equations
a. First-Order Separable Differential Equations
b. Exponential Growth & Decay applications
c. Linear First-Order Differential Equations
V. Integration Techniques
a. Powers of Trigonometric Functions (supplement needed)
b. Integration by Parts
c. Partial Fractions
d. Trigonometric Substitutions
e. Tables of Integrals
f. L'Hopital's Rule
g. Improper Integrals
h. Numerical Integration Techniques (Midpoint, Trapezoid, Simpson's)
VI. Infinite Series
b. Series and convergence
c. The Integral Test and p-Series
d. Comparisons of series
e. Alternating series
f. The Ratio and Root Tests
g. Power series
h. Taylor & Maclaurin Series and Associated Applications
Effective Term: Fall 2012