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									DAWSON COLLEGE

MATHEMATICS DEPARTMENT

201-NYA-05        CALCULUS 1         3-2-3

(formerly known as Math 201-103)

STUDY GUIDE

PREREQUISITE: Good standing in High School Functions
              536 or CEGEP Mathematics 004.

OBJECTIVES:   This course introduces the student to       the
fundamental concepts of the differential     calculus:
limits, continuity, and the derivative.
    Antidifferentiation and integration are also
    introduced. These techniques will illustrate the
    power of calculous in solving certain physical
    problems.

STANDARDS:

    The standards expected of students are outlined       on
pages 39 to 43 of the Dawson Science Program.

REQUIRED TEXT: Calculus of a Single Variable,            6th
edition, by Larson, Hostetler, Edwards.

REFERENCES: (1) Calculus, by MUNEM & FOULIS.

              (2) SCHAUM'S OUTLINE SERIES: Calculus.

              (3) Calculus, by JAMES STEWART.

METHODOLOGY: Lectures and problem sessions.

TERM WORK:    The term grade is based on a minimum of
     41⁄2 hours of tests/quizzes.

FINAL EXAMINATION:

          The Final Examination will be a supervised,
     comprehensive examination held during the formal
     examination period. There are no exemptions.

GRADING POLICY:
           A student's grade shall consist of the
     greater of:


(A) Termwork for 50% and Final Exam for 50%.




OR




(B) Final Exam for 100%.


          To qualify for (B) the student must have
     obtained at least 50% of the term marks.

CALCULATORS:

          A scientific calculator, which has no text
     storage or graphing capabilities, is allowed for
     class tests and the final exam.

CHEATING POLICY:

          Students should inform themselves of
     Dawson's Policy on cheating, as stated in the
     College Calendar. Penalties may range from a       zero
grade to suspension or expulsion from the      College.



LITERACY POLICY:

          Problem solving is an essential component       of
this course. Students will be expected to      analyze
problems stated in words, to present      their solutions
logically and coherently, and to                                     display their answers
in a form corresponding to                                the statement of the
problem, including                         appropriate units of measurement.
Marks will be                     deducted for work which is inadequate in
these               respects, even though the answers may be
         numerically correct.
------------------------------------------------------------------------

COURSE CONTENT:

(times listed are approximate)

Algebra Modules 1, II and III                              (6 classes)

Prerequisites 1-7: A Review of Functions.



Chapter 1: LIMITS AND THEIR PROPERTIES (8 classes)

       1.1 A preview of Calculus

      1.2 Finding Limits Graphically and Numerically
    (p.53 prob. 3-20)

       1.3 Evaluating Limits Analytically
           (P.64 prob. 5-56, 73-76, 57-68 (optional))

        1.4 Continuity and One-Sided Limits
           (p.76 prob. 5-46, 55-58)

        1.5 Infinite Limits
           (p.84 prob. 1-40)



Chapter 2: DIFFERENTIATION                                   (10 classes)

       2.1 The Derivative and the Tangent Line Problem
           (p. 98 prob. 1-22, 51-60)

       2.2 Differentiation Rules and Rates of Change
           (p. 110 prob 1-52, 57, 58)

        2.3 The Product and Quotient Rules
            (p. 121 prob 1-58, 63-68, 73-82, 87-90)
     2.4 The Chain Rule
         (p. 130 prob 1-30, 43-64, 69-72, 74-79)

     2.5 Implicit Differentiation
         (p. 139 prob 1-40)

    2.6 Related Rates
        (p. 146 prob.1-43)



Chapter 3: APPLICATIONS OF DIFFERENTIATION(12 classes)

    3.1 Extrema on an Interval
        (p. 160 prob. 1-24 (omit 11, 12, 21))

    3.2 Rolle’s Theorem & the Mean Value Theorem
        (optional)(p. 167, prob. 3-16)

    3.3 Increasing and Decreasing Functions and the
        First Derivative Test
        (P. 176 prob. 1-26.)

    3.4 Concavity and the Second Derivative Test
        (p. 184 prob. 1-18, 21-28)

    3.5 Limits at Infinity
        (p. 193 prob. 1-20)

    3.6 A Summary of Curve Sketching
        (p. 202 prob. 7-18, 23, 24, 29-34)

    3.7 Optimization Problems
        (p. 210 prob. 1-40)

    3.8 Newton’s Method (OPTIONAL)
        (p. 219 prob. 1-10)

    3.9 Differentials (the notation only)
        (p. 226 prob. 11-20)



Chapter 4: INTEGRATION                 (2 classes)

    4.1 Antiderivatives
        (p. 248 prob. 1-30, 45-48, 51-53)
      4.5 Integration by Substitution
          (p. 296 prob 1-3, 7-30)
     (Algebraic Functions only)



Chapter 5: LOGARITHMIC, EXPONENTIAL, AND OTHER
           TRANSCENDENTAL FUNCTIONS    (3 classes)

      5.1 The Natural Logarithmic Function and
          Differentiation
          (p. 318 prob. 41-65, 69-72, 83-88)

      5.4 Exponential Functions: Differentiation and
          Integration
          (p. 345 prob. 29-54)

      5.5 Bases Other Than e, and Applications
          (p. 354 prob. 29-48 )

      5.7 Differential Equations; Separation of
          Variables
          (p. 374 prob. 1-18, 88-91, and applied
           problem notes.)

      5.8 Inverse Trigonometric Functions and
          Differentiation
          (p. 384 prob. 43, 44, 47, 50, 53-56)



http://www.place.dawsoncollege.qc.ca/~math/PreU/Cal1.htm

								
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