MAT 1500

Mathematical Analysis I (Science/Engineering Calc)

Textbook:
James Stewart: Calculus: Concepts and Contexts (1997) [ISBN: 0-534-34450-X]
First Four Chapters (Functions, Differentiation, and Applications of Differentiation)

Maple worksheets corresponding to problems in Stewart's textbook

• 0. Preview of Calculus
• 1. Functions and Models
  • 1.1 Four ways to Represent a Function
  • 1.2 New Functions from Old Functions
  • 1.3 Graphing Calculators and Computers
  • 1.4 Parametric Curves [Circle example]
  • 1.5 Exponential Functions
  • 1.6 Inverse Functions and Logarithms
  • 1.7 Models and Curve Fitting
• 2. Limits and Derivatives
  • 2.1 The Tangent and Velocity Problems
  • 2.2 The Limit of a Function
  • 2.3 Calculating Limits Using the Limit Laws
  • 2.4 Continuity
  • 2.5 Limits Involving Infinity
  • 2.6 Tangents, Velocities, and Other Rates of Change
  • 2.7 Derivatives
  • 2.8 The Derivative as a Function
  • 2.9 Linear Approximations
  • 2.10 What does f ' say about f ?
• 3. Differentiation Rules
  • 3.1 Derivatives of Polynomials and Exponential Functions
  • 3.2 The Product and Quotient Rules
  • 3.3 Rates of Change in the Natural and Social Sciences
  • 3.4 Derivatives of Trigonometric Functions
  • 3.5 The Chain Rule
  • 3.6 Implicit Differentiation
  • 3.7 Derivatives of Logarithmic Functions
  • 3.8 Linear Approximations and Differentials
• 4. Applications of Differentiation
  • 4.1 Related Rates
  • 4.2 Maximum and Minimum Values
  • 4.3 Derivatives and Shapes of Curves
  • 4.4 Graphing with Calculus and Calculators
  • 4.5 Indeterminate Forms and L'Hopital's Rule
  • 4.6 Optimization Problems [Least Squares]
  • 4.7 Applications to Economics
  • 4.8 Newton's Method
  • 4.9 Antiderivatives

MAPLE Supplementary Text: http://www.brookscole.com/clclbsblurb.html
D. Barrow et al, CalcLabs with MAPLE for Stewart's Calculus: Concepts and Contexts (1997) [ISBN: 0-534-34442-9]

Also available (ask your instructor):

• Student Solution Manual (all odd problems worked) [ISBN: 0-534-344-356]
• Student Study Guide (more examples, key points) [ISBN: 0-534-34439-9]

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