Maricopa Community Colleges  MAT220   19886-19905 
Official Course Description: MCCCD Approval: 01/01/01
MAT220 19886-19905 LEC 5 Credit(s) 5 Period(s)
Analytic Geometry and Calculus I
Topics from analytic geometry with special emphasis on inequalities and absolute value expressions, limits, continuity, the fundamental principles and formulae for differential and integral calculus along with their applications to geometry and mechanics, the mean value theorems and the fundamental theorem of calculus. Prerequisites: Grade of "C" or better in (MAT154 and MAT159 or equivalent), or satisfactory score on a placement exam.
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MCCCD Official Course Competencies:
MAT220   19886-19905 Analytic Geometry and Calculus I
1. Define and evaluate limits. (I)
2. Define and identify continuity. (I)
3. Apply limits to graphing techniques. (I)
4. Define the derivative. (II)
5. Use the formulas for differentiation. (II)
6. Apply the derivative. (III)
7. Perform indefinite integration. (IV)
8. Evaluate the definite integral. (IV)
9. Use the definite integral in applications. (V)
10. Define and apply the natural logarithmic function. (VI)
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MCCCD Official Course Outline:
MAT220   19886-19905 Analytic Geometry and Calculus I
    I. Limits
        A. Definition
        B. Slope of a curve
        C. Tangent lines to a curve
        D. Derivatives
        E. Rates of change such as velocity
        F. Continuity of a function
      II. Derivatives
          A. Of polynomials
          B. Rules for differentiating products, powers, and quotients
          C. Chain rule
          D. Of trigonometric functions
          E. Differentials and linear approximations
        III. Applications of derivatives
            A. Newton's method
            B. Curve sketching
            C. Rates of change
            D. The mean value theorem
            E. Indeterminate forms of limits including L'Hopital's Rule
          IV. Integration
              A. Indefinite integrals
              B. Of polynomials
              C. Of trigonometric functions
              D. Definite integrals
              E. The fundamental theorem of calculus
              F. Substitutions in integrals
              G. Approximating definite integrals including the trapezoid rule
            V. Applications of definite integrals
                A. Acceleration, velocity, and position of a moving body
                B. Areas between curves
                C. Voilumes of revolution using disks, washers, and cylindrical shells
                D. Length of plane curves
                E. Areas of a surface of revolution
                F. Average value of a function
                G. Work
                H. Hydrostatic force
              VI. Transcendental functions
                  A. Derivatives and integrals of inverse trigonometric functions
                  B. Derivatives and integrals of exponential functions
                  C. Properties and derivatives of logarithms
                  D. Rates of growth
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