Calculus I - MATH 1431 - Key Concepts
Copyright 2006 Department of Mathematics, University of Houston.
Contact Jeff Morgan for more information.

The links below contain both static and video help.  The videos require a high speed internet connection, Version 7 of Apple's QuickTime player installed on your computer (it's free), and the Mozilla Firefox Browser (also free).

See the complete list of videos for Calculus I and II.

I. LIMITS

  1. Calculating limits intuitively.

  2. The definition of a limit.

  3. The arithmetic of limits; limits of sums, differences, products and quotients.

  4. Trigonometric limits.

  5. Continuity, including the Intermediate and Extreme Value Theorems.

II. DIFFERENTIATION

  1. Definition of the derivative; calculating derivatives using the definition; interpreting the derivative as the slope of the tangent line.

  2. Differentiation formulas; the power, product, reciprocal, and quotient rules.

  3. The chain rule.

  4. Differentiating trigonometric functions.

  5. Higher Order Derivatives.

  6. Implicit differentiation.

  7. Rates of change per unit time; related rates.

  8. Velocity and Acceleration.

  9. Differentials and Newton's method.

III. APPLICATIONS OF THE DERIVATIVE

  1. Rolle's Theorem and the Mean Value Theorem.

  2. Critical numbers and the first derivative test.

  3. Concavity and the second derivative test.

  4. Curve sketching.

  5. Extreme values on intervals.

  6. Optimization problems.

IV. THE DEFINITE INTEGRAL

  1. The definite integral; Riemann sums, area, and properties of the definite integral.

  2. The fundamental theorem of calculus.

  3. Anti-differentiation and indefinite integrals.

  4. Integration by substitution.

  5. Mean Value Theorem for integrals; average value.

V. APPLICATIONS OF THE DEFINITE INTEGRAL

  1. Area; area under a curve, area between two curves.

  2. Volume; volumes by slicing.

  3. Volumes of solids of revolutions; disks and washers, cylindrical shells.

  4. Center of mass of a rod and centroid of a planar region.

View the complete list of videos for Calculus I and II.