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Official Course
Description: MCCCD Approval: 02/22/05 |
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MAT251 20052-99999
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LEC |
4 Credit(s) |
4 Period(s) |
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Calculus for Life Science |
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Analysis and interpretation of the properties of functions commonly used in the fields of biology, medicine, ecology, and other life sciences. In depth examination of limits, continuity, and various other principles and formulae germane for differential and integral calculus is provided. Prerequisites: (Grade of "C" or better in (MAT150 or MAT151 or MAT152) and MAT182) or MAT187 or equivalent, or satisfactory score on District placement exam. |
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Go to Competencies Go to Outline
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MCCCD Official Course Competencies: |
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MAT251 20052-99999 |
Calculus for Life
Science |
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1. |
Analyze and interpret the behavior of functions, including end behavior, increasing and decreasing, extrema, asymptotic behavior, and symmetry. (I, II, III) |
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Use transformations to graph functions. (I, II, III) |
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Graph polynomial, rational, exponential, logarithmic, power, absolute value, and piecewise-defined functions. (I, II) |
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Determine domain and range of polynomial, rational, exponential, logarithmic, trigonometric, power, absolute value, and piecewise-defined functions. (I, II) |
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Discuss and choose models for provided data using appropriate technology. (I, II, III, IV, V, VI, VII) |
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Define and evaluate limits. (I, III) |
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Define and identify continuity. (I, III) |
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8. |
Define the derivative. (III, VI) |
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Use the formulas for differentiation. (III, IV, V, VI) |
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Apply the derivative. (III, IV) |
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11. |
Perform indefinite integration. (VII) |
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12. |
Evaluate the definite integral. (VII) |
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13. |
Use the definite integral in applications. (VII) |
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Go to Description Go to top of Competencies
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MCCCD Official Course Outline: |
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MAT251 20052-99999 |
Calculus for Life
Science |
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I. Behavior and Nature of Functions A. Graphic, numeric, and algebraic representations B. Characteristics of basic functions C. Properties, operations and transformations of functions II. Exponential, Logarithmic, and Trigonometric Functions A. Exponential functions and their characteristics B. Common/natural logarithms and their characteristics C. Properties of logarithms D. Definition and properties of trigonometric functions and their inverses E. Modeling data with sinusoids F. Applications of growth and decay models III. Limits A. Informal definition B. Existence C. Continuity D. Average verses instantaneous rate of change E. Graphical representation as tangent line IV. Derivatives A. Rules for differentiating products, powers, and quotients B. Chain rule for exponential, logarithmic, and trigonometric functions V. Graphs and the Derivative A. Increasing/decreasing functions B. Relative extrema C. Higher derivatives and concavity D. Curve sketching VI. Applications of the derivative A. Curve sketching B. Applications of extrema C. Implicit differentiation D. Related rates E. Differentials: linear approximation VII. Integration A. Antiderivatives B. The indefinite integral C. Area and the definite integral D. The fundamental theorem of calculus E. Integrals of trigonometric functions F. Area between two curves |