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Single variable calculus : Concepts and contexts / Jeffery A. Cole

By: Publication details: Australia : Brooks/Cole, c2001Edition: 2nd editionDescription: x, 356 p. : ill. ; 24 cmISBN:
  • 0534379230
  • 9780534379230
Subject(s): DDC classification:
  • 22 515.076 COL
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Item type Current library Call number Copy number Status Date due Barcode
Book Closed Access Book Closed Access Engineering Library 515.076 COL 1 (Browse shelf(Opens below)) 1 Available 0011332

1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function.
New Functions from Old Functions.
Graphing Calculators and Computers.
Parametric Curves.
Laboratory Project: Families of Hypocycloids.
Exponential Functions.
Inverse Functions and Logarithms.
Models and Curve Fitting.

2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems.
The Limit of a Function.
Calculating Limits Using the Limit Laws.
Continuity. Limits Involving Infinity.
Tangents, Velocities, and Other Rates of Change.
Derivatives.
Writing Project: Early Methods for Finding Tangents.
The Derivative as a Function.
Linear Approximations.
What does f'' say about f?

3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions.
The Product and Quotient Rules.
Rates of Change in the Natural and Social Sciences.
Derivatives of Trigonometric Functions.
The Chain Rule.
Laboratory Project: Bezier Curves.
Applied Project: Where Should a Pilot Start Descent?
Implicit Differentiation.
Derivatives of Logarithmic Functions.
Discovery Project: Hyperbolic Functions.
Linear Approximations and Differentials.
Laboratory Project: Taylor Polynomials.

4. APPLICATIONS OF DIFFERENTIATION.
Related Rates.
Maximum and Minimum Values.
Applied Project: The Calculus of Rainbows.
Derivatives and the Shapes of Curves.
Graphing with Calculus and Calculators.
Indeterminate Forms and l''Hospital''s Rule.
Writing Project: The Origins of l''Hospital''s Rule.
Optimization Problems.
Applied Project: The Shape of a Can.
Applications to Economics.
Newton''s Method.
Antiderivatives.

5. INTEGRALS. Areas and Distances.
The Definite Integral.
Evaluating Definite Integrals.
Discovery Project: Area Functions.
The Fundamental Theorem of Calculus.
Writing Project: Newton, Leibniz, and the Invention of Calculus.
The Substitution Rule.
Integration by Parts.
Integration Using Tables and Computer Algebra Systems.
Discovery Project: Patterns in Integrals.
Approximate Integration.
Improper Integrals.

6. APPLICATIONS OF INTEGRATION.
More about Areas.
Volumes.
Arc Length.
Average Value of a Function.
Applied Project: Where to Sit at the Movies.
Applications to Physics.
Applications to Economics and Biology.
Probability.

7. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations.
Direction Fields. Euler's Method.
Separable Equations.
Applied Project: Which is Faster, Going Up or Coming Down?
Exponential Growth and Decay.
Applied Project: Calculus and Baseball.
The Logistic Equation. Predator-Prey Systems.
Some Special Second Order Equations.
etc...

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