Maricopa Community Colleges  MAT210   19886-19905 
Official Course Description: MCCCD Approval: 11/10/87
MAT210 19886-19905 LEC 3 Credit(s) 3 Period(s)
Brief Calculus
An introduction to the theory, techniques and applications of the differential and integral calculus of elementary functions with problems of interest to students in business and the social sciences. Prerequisites: Grade of "C" or better in MAT154 or equivalent.
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MCCCD Official Course Competencies:
 
MAT210   19886-19905 Brief Calculus
1. Find limits of function values of algebraic, exponential, and logarithmic functions. (I)
2. Find rates of change and derivatives of functions using both definitions and theorems. (II)
3. Graph algebraic functions using the derivative and its tests. (II)
4. Work business and economics applied problems using the derivative. (III)
5. Find the antiderivative of a function. (IV)
6. Find the indefinite integral of algebraic functions using theorems. (IV)
7. Find the definite integral of algebraic functions using the fundamental theorem of calculus. (IV)
8. Find the area and volume of a surface and solid using the definite integral. (IV)
9. Use integration by parts to find an indefinite and definite integral. (V)
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MCCCD Official Course Outline:
 
MAT210   19886-19905 Brief Calculus
    I. Functions, graphs, limits
        A. Distance formula
        B. Graphs of equations
        C. Lines: slopes of lines
        D. Functions
        E. Limits and continuity
      II. Differentiation
          A. The derivative and slope of curve
          B. Some rules of differentiation
          C. Rates of change: velocity and marginals
          D. The product and quotient rules
          E. The chain rule
          F. Higher order derivatives
          G. Implicit differentiation
          H. Related rates
        III. Applications of the derivative
            A. Increasing and decreasing functions
            B. Extrema and first-derivative test
            C. Concavity and second-derivative test
            D. Optimization problems
            E. Business and economics applications
            F. Differentials
          IV. Integration
              A. Antiderivatives and indefinite integral
              B. The general power rule
              C. Area and fundamental theorem of calculus
              D. The area of a region between two curves
            V. Exponential and logarithmic functions
                A. Exponential functions
                B. Differentiation and integration of exponential functions
                C. The natural logarithm function
                D. Logarithmic functions: differentiation and integration
                E. Exponential growth and decay
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