Maricopa Community Colleges  MAT212   20006-20045 
Official Course Description: MCCCD Approval: 05/23/00
MAT212 20006-20045 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 MAT150, or MAT151, or MAT152, or equivalent, or satisfactory score on District placement exam.
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MCCCD Official Course Competencies:
 
MAT212   20006-20045 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)
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MCCCD Official Course Outline:
 
MAT212   20006-20045 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
        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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