Maricopa Community Colleges  MAT231   19956-19965 
Official Course Description: MCCCD Approval: 03/28/95
MAT231 19956-19965 LEC 5 Credit(s) 5 Period(s)
Analytic Geometry and Calculus II
Includes working on the elementary transcendental functions, techniques of integration, vector functions, and infinite series. Prerequisites: Grade of "C" or better in MAT220, or MAT224, or equivalent.
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MCCCD Official Course Competencies:
 
MAT231   19956-19965 Analytic Geometry and Calculus II
1. Use L'Hospital's rules to evaluate limits having indeterminate form. (I, III, VI)
2. Use algebraic and numerical techniques for evaluating integrals. (II)
3. Use integration in applied problems. (IV, V)
4. Determine the convergence or divergence of an improper integral. (III)
5. Analyze curves in the plane defined using parametric and polar equations. (V)
6. Determine the convergence or divergence of sequences and series having numerical terms. (VI)
7. Find a power series representation for a given function and determine its domain. (VI)
8. Extend the operations of differentiation and integration to functions defined by a power series. (VI)
9. Find a polynomial which approximates a given function to a specified degree of accuracy on a specified interval. (VI)
10. Perform operations on vectors. (VII)
11. Use vector operations in applied problems. (VII)
12. Use technology when appropriate (IV, V)
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MCCCD Official Course Outline:
 
MAT231   19956-19965 Analytic Geometry and Calculus II
    I. Limits involving an indeterminate form
        A. L'Hospital's rule and the forms: 0/0 or /
        B. Indeterminate products, differences, and powers
      II. Methods of integration
          A. Integration by parts
          B. Trigonometric integrals
          C. Trigonometric substitution
          D. Integration of rational functions by partial fractions
          E. Integration tables
        III. Improper integrals
            A. Definitions
            B. Evaluation
          IV. Applications of integral calculus
              A. Area and volume
              B. Arc length
              C. Physics
              D. Economics (optional)
            V. Elements of analytic geometry
                A. Parametric equations
                  1. Parametric equations for a given curve
                  2. The graph of the curve defined using parametric equations
                  3. Applications
                B. Conic sections
                C. Polar equations
                  1. The relation between polar and cartesian equations
                  2. Graphing
                  3. Applications
                  4. Conic sections
              VI. Sequences and series
                  A. Basic definitions
                    1. Geometric series
                    2. P-series
                    3. Alternating series
                    4. Convergence and absolute convergence
                  B. Tests for convergence
                    1. A test for divergence
                    2. p-test
                    3. Comparison test
                    4. Limit comparison test
                    5. Alternating series test
                    6. Ratio test
                    7. Root test
                    8. Integral test
                  C. Power series
                    1. Definition
                    2. The ratio test and the radius of convergence
                    3. Interval of convergence
                    4. Term-by-term differentiation and integration
                    5. Taylor and Maclaurin series
                    6. Taylor polynomials and function approximation
                VII. Vector spaces
                    A. Basic operations
                      1. Dot product
                      2. Cross product
                      3. Scaler triple product
                    B. Applications
                      1. Vector projections
                      2. Geometric applications
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