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MATH 135 : Survey of Calculus

Credits: 3

Course Description: Calculus developed intuitively and applied to problems in biology, economics, psychology, and geometry. A course for non-physical science and non-mathematics majors. Suitable for some pre-medical programs.

Pre-Requisites: Math Placement Test or MATH 130.

Comments: No student receives graduation credit for MATH 135 if it is taken after successful completion of MATH 134 or 140 or a higher Math course. Students may take MATH 140 after 135 only with explicit permission of the Department, and then only for two credits.

Topics:
  1. FUNCTIONS AND CHANGE
    1. WHAT IS A FUNCTION?
    2. LINEAR FUNCTIONS
    3. RATES OF CHANGE
    4. APPLICATIONS OF FUNCTIONS TO ECONOMICS
    5. EXPONENTIAL FUNCTIONS
    6. THE NATURAL LOGARITHM
    7. EXPONENTIAL GROWTH AND DECAY
    8. NEW FUNCTIONS FROM OLD
    9. PROPORTIONALITY, POWER FUNCTIONS, AND POLYNOMIALS
    10. PERIODIC FUNCTIONS
  2. LIMITS, CONTINUITY, LIMITS TO INFINITY AND THE DEFINITION OF THE DERIVATIVE
  3. RATE OF CHANGE: THE DERIVATIVE
    1. INSTANTANEOUS RATE OF CHANGE
    2. THE DERIVATIVE FUNCTION
    3. INTERPRETATIONS OF THE DERIVATIVE
    4. THE SECOND DERIVATIVE
    5. MARGINAL COST AND REVENUE
  4. SHORT-CUTS TO DIFFERENTIATION
    1. DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS
    2. EXPONENTIAL AND LOGARITHMIC FUNCTIONS
    3. THE CHAIN RULE
    4. THE PRODUCT AND QUOTIENT RULES
    5. DERIVATIVES OF PERIODIC FUNCTIONS
  5. USING THE DERIVATIVE
    1. LOCAL MAXIMA AND MINIMA
    2. INFLECTION POINTS
    3. GLOBAL MAXIMA AND MINIMA
    4. PROFIT, COST, AND REVENUE
    5. AVERAGE COST
    6. ELASTICITY OF DEMAND
    7. LOGISTIC GROWTH
    8. THE SURGE FUNCTION AND DRUG CONCENTRATION
  6. ACCUMULATED CHANGE: THE DEFINITE INTEGRAL
    1. DISTANCE AND ACCUMULATED CHANGE
    2. THE DEFINITE INTEGRAL
    3. THE DEFINITE INTEGRAL AS AREA
    4. INTERPRETATIONS OF THE DEFINITE INTEGRAL
    5. THE FUNDAMENTAL THEOREM OF CALCULUS
  7. THE DEFINITE INTEGRAL: THEORY AND USAGE
    1. AVERAGE VALUE
    2. CONSUMER AND PRODUCER SURPLUS
    3. PRESENT AND FUTURE VALUE
    4. INTEGRATING RELATIVE GROWTH RATES
  8. ANTIDERIVATIVES
    1. CONSTRUCTING ANTIDERIVATIVES ANALYTICALLY
    2. INTEGRATION BY SUBSTITUTION
    3. USING THE FUNDAMENTAL THEOREM TO FIND DEFINITE INTEGRALS
    4. ANALYZING ANTIDERIVATIVES GRAPHICALLY AND NUMERICALLY
  9. PROBABILITY
    1. DENSITY FUNCTIONS
    2. CUMULATIVE DISTRIBUTION FUNCTIONS AND PROBABILITY
    3. THE MEDIAN AND THE MEAN
  10. 10 FUNCTIONS OF SEVERAL VARIABLES
    1. UNDERSTANDING FUNCTIONS OF TWO VARIABLES
    2. CONTOUR DIAGRAMS
    3. PARTIAL DERIVATIVES
    4. COMPUTING PARTIAL DERIVATIVES ALGEBRAICALLY
    5. CRITICAL POINTS AND OPTIMIZATION
    6. CONSTRAINED OPTIMIZATION
  11. MATHEMATICAL MODELING USING DIFFERENTIAL EQUATIONS
    1. MATHEMATICAL MODELING: SETTING UP A DIFFERENTIAL EQUATION
    2. SOLUTIONS OF DIFFERENTIAL EQUATIONS
    3. SLOPE FIELDS
    4. EXPONENTIAL GROWTH AND DECAY
    5. APPLICATIONS AND MODELING
    6. MODELING THE INTERACTION OF TWO POPULATIONS
    7. MODELING THE SPREAD OF A DISEASE
  12. GEOMETRIC SERIES
    1. GEOMETRIC SERIES
    2. APPLICATIONS TO BUSINESS AND ECONOMICS
    3. APPLICATIONS TO LIFE SCIENCES
Fall 2017 Schedule:

Section Meetings Instructor Comments
001
TuTh 02:00pm - 03:15pm
Cooper, Joseph
002
TuTh 04:00pm - 05:15pm
Cooper, Joseph


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Information: math-info@math.umb.edu