Great courses

Thirty-six thirty minute lectures

Calculus is the greatest mathematical breakthrough since the pioneering discoveries of the ancient Greeks. Without it, there would be no spaceflight, skyscrapers, jet planes, economic modeling, or accurate weather forecasting. One of the most powerful problem solving tools ever invented, calculus is a skill that can be learned. Its techniques are used to analyze situations involving change, to calculate optimum values, and to measure complex shapes. With crystal-clear explanations of the beautiful ideas of calculus, frequent study tips, pitfalls to avoid, and--best of all--hundreds of examples and practice problems that are specifically designed to explain and reinforce major concepts, this course will be a valuable guide to conquering calculus

Producer, Matt Costanza ; academic content supervisor, Pam Greer ; editors, Dan Shine, Matt Costanza

Lecturer: Dr. Bruce H. Edwards, Professor of Mathematics at the University of Florida

DVD, NTSC

Part 1: Disc 1. Lecture 1. A preview of calculus ;

Lecture 2.

Review: Graphs, models, and functions ;

Lecture 3.

Review: Functions and trigonometry ;

Lecture 4.

Finding limits ;

Lecture 5.

An introduction to continuity ;

Lecture 6.

Infinite limits and limits at infinity --

Disc 2. Lecture 7.

Derivative and the tangent line problem ;

Lecture 8.

Basic differentiation rules ;

Lecture 9.

Product and quotient rules ;

Lecture 10.

Chain rule ;

Lecture 11.

Implicit differentiation and related rates ;

Lecture 12.

Extrema on an interval Part 2: Disc 3. Lecture 13. Increasing and decreasing functions ;

Lecture 14.

Concavity and points of inflection ;

Lecture 15.

Curve sketching and linear approximations ;

Lecture 16.

Applications: Optimization problems, part 1 ;

Lecture 17.

Applications: Optimization problems, part 2 ;

Lecture 18.

Antiderivatives and basic integration rules --

Disc 4. Lecture 19.

Area problem and the definite integral ;

Lecture 20.

Fundamental theorem of calculus, part 1 ;

Lecture 21.

Fundamental theorem of calculus, part 2 ;

Lecture 22.

Integration by substitution ;

Lecture 23.

Numerical integration ;

Lecture 24.

Natural logarithmic function, differentiation Part 3: Disc 5. Lecture 25. Natural logarithmic function, integration ;

Lecture 26.

Exponential function ;

Lecture 27.

Bases other than e ;

Lecture 28.

Inverse trigonometric functions ;

Lecture 29.

Area of a region between 2 curves ;

Lecture 30.

Volume, the disc method --

Disc 6. Lecture 31.

Volume, the shell method ;

Lecture 32.

Applications, arc length and surface area ;

Lecture 33.

Basic integration rules ;

Lecture 34.

Other techniques of integration ;

Lecture 35.

Differential equations and slope fields ;

Lecture 36.

Applications of differential equations