Copyright 2009 Department of Mathematics, University of Houston.
Contact Jeff Morgan for more information.

• Limits and Their Properties
  • Calculating limits intuitively
  • Definition of a limit
  • The arithmetic of limits; limits of sums, differences, products and quotients
  • Trigonometric limits
  • Continuity, including the Intermediate and Extreme Value Theorems
  • Quizzes
• Differentiation
  • Definition of the derivative; calculating derivatives using the definition; interpreting the derivative as the slope of the tangent line
  • Differentiation formulas; the power, product, reciprocal, and quotient rules
  • The chain rule
  • Differentiating trigonometric functions
  • Higher Order Derivatives
  • Implicit differentiation
  • Rates of change per unit time; related rates
  • Velocity and Acceleration
  • Differentials and Newton's method
  • Quizzes
• Applications of Derivatives
  • Rolle's Theorem and the Mean Value Theorem
  • Critical numbers and the first derivative test
  • Concavity and the second derivative test
  • Curve sketching
  • Extreme values on intervals
  • Optimization problems.
  • Quizzes
• Integration
  • The definite integral; Riemann sums, area, and properties of the definite integral
  • The fundamental theorem of calculus
  • Anti-differentiation and indefinite integrals
  • Integration by substitution
  • Mean Value Theorem for integrals; average value
  • Quizzes
• Logarithmic, Exponential and other Transcendental Functions
  • Logarithms
  • Exponential Functions
  • Inverse Trig Functions
  • Quizzes
• Differential Equations
  • Differential Equations
  • Other Bases and Exponential Growth
  • Quizzes
• Applications of Integration
  • Area; area under a curve, area between two curves
  • Volume; volumes by slicing
  • Volumes of solids of revolutions; disks and washers, cylindrical shells
  • Center of mass of a rod and centroid of a planar region
  • Quizzes
• Integration Techniques, L'Hopital's Rule, and Improper Integrals
  • Integration by Parts
  • Trig Powers and Trig Substitution
  • Partial Fractions
  • L'Hopital's Rule
  • Improper Integrals
  • Quizzes
• Sequences and Series
  • Sequences
  • Series
  • Alternating Series, Ratio and Root Tests
  • Taylor Polynomials
  • Power Series
  • Taylor and Maclaurin Series
  • Quizzes
• Parametric Equations and Polar Coordinates
  • Plane Curves and Parametrics
  • Polar Coordinates and Graphs
  • Area in Polar Coordinates
  • Quizzes

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Sample Syllabi

Calculus Practice Exams

 

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