Standard |
MAT 195 - Differential Calculus
Emphasizes the use of differential calculus. Applications of techniques include extreme value problems, motion, graphing, and other topics as time allows. Topics include: derivatives and applications, differentiation of transcendental functions, and introduction to integration and applications.
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Competency Areas |
Hours
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Derivatives and Applications |
Class |
5 |
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Differentiation of Transcendental Functions |
D. Lab |
0 |
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Introduction to Integration and Applications |
P. Lab/O.B.I. |
0 |
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Credit |
5 |
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Prerequisite: |
MAT 193 |
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Corequisite: |
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Course Guide |
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Competency |
After completing this
section, the student will: |
Hours |
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Class |
D.Lab |
P.Lab/ O.B.I. |
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DERIVATIVES AND APPLICATIONS |
40 |
0 |
0 |
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Limits |
Find the limits of equations using the four step method. |
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Differentiation theory - slope of the tangent to a curve |
Relate the theory of limits to solving for the slope of the tangent to a curve. |
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Techniques of differentiation |
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Applications |
Solve word problems using derivatives. |
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Derivative graphing |
Employ derivatives for graphing. |
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DIFFERENTIATION OF TRANSCENDENTAL FUNCTIONS |
5 |
0 |
0 |
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Derivatives of the sine and cosine function |
Identify derivatives of these functions. |
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Derivatives of exponential and logarithmic functions |
Differentiate exponential and logarithmic functions. |
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INTRODUCTION TO INTEGRATION AND APPLICATIONS |
5 |
0 |
0 |
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Indefinite integral |
Evaluate indefinite integrals. |
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Definite integral |
Evaluate definite integrals. |
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Definite integral and area under a curve |
Calculate the area under a curve using a definite integral. |
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General power formula |
Use power rule and substitution to integrate functions. |
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Tables |
Evaluate integrals beyond the scope of this course by using integration tables. |
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Suggested Resources |
Benice, D. D. (1989).
Prealgebra and algebra (4th
ed.). Englewood Cliffs, NJ: Prentice
Hall.
Christopher, J. (1991).
Introductory technical mathematics
(2nd ed.). Englewood Cliffs, NJ:
Prentice Hall.
Clar, L. M., &
Hart, J. A. (Latest edition). Mathematics
for the technologies. Englewood
Cliffs, NJ: Prentice Hall.
Cooke, N. M., &
Adams, H. F. (1986). Basic
mathematics for electronics (6th ed.).
New York: McGraw-Hill.
Davis, L. (1990).
Technical mathematics with
calculus. Columbus, OH: Macmillan.
Fleming, W., &
Varberg, D. (1988). Algebra
and trigonometry (3rd ed.). Englewood
Cliffs, NJ: Prentice Hall.
Gilbert, J., et
al. (1981). College algebra. Englewood Cliffs, NJ: Prentice Hall.
Paul, R. S., &
Shaevel, M. L. (1989). Essentials
of technical mathematics with calculus (2nd ed.). Englewood Cliffs, NJ: Prentice Hall.
Radford, L. (1986).
Introduction to technical
mathematics with calculus. Boston:
Brenton.
Singer, B. B., &
Forster, H. (1990). Basic
mathematics for electricity and electronics (6th ed.). New York: McGraw-Hill.
Smith, K. J. (1990).
Precalculus mathematics: A
functional approach (4th ed.). Pacific
Grove, CA: Brooks-Cole.
Swokowski, E. W. (1989).
Fundamentals of algebra and
trigonometry (7th ed.). Boston:
Prindle, Weber & Schmidt.
Washington, A. J. (1990). Basic technical mathematics with calculus
(5th ed.). Redwood City, CA:
Benjamin-Cummings.