This self-paced program features over 25 hours of video instruction with a login feature that returns students to their place in the lesson. The series contains 56 video segments covering the material in a standard college freshman year calculus course, and suitable for science and engineering majors. Topics covered include limits, continuity, differentiation, applications of differential calculus to graphing and optimizing functions, transcendental functions and their derivatives, integral calculus and applications to areas and volumes, L'Hôpital's Rule, sequences and series, elementary vector algebra with dot products and cross-products. The series will gradually guide students through mastering Calculus.
The first 32 segments can also be used to supplement the typical one-semester elementary or basic calculus course, suitable for business majors and students of the liberal arts.
CD 1 - Basics
- Rectangular Coordinates and Graphing
- Functions and their Graphs
- Average Rate of Change and Slopes of Lines
- Formulas for Lines
- Limits and Continuity
CD 2 - Derivatives
- The Delta-Process and Instantaneous Rates of Change
- Tangent Lines
- Differentiation Rules (Powers and Sums)
- The Product and Quotient Rules
- Composite Functions and the Chain Rule
- Optimization Using Differentiation: Critical Points
- Second Derivative, Inflection Points and Concavity
- Implicit Differentiation
- Inverse Functions and their Derivatives
- EXP, Log and Differentiation.
CD 3 - Advanced Derivatives
- Logarithmic Differentiation
- Applications to Growth and Decay
- Trig Functions
- Related Rates
- Differentiation and Approximation
- Taylor’s Formula
CD 4 - Integration
- Areas, Anti-differentiation and the Fundamental Theorem of Calculus
- Integration Formulas
- Substitution
- Integration by Parts
- Definite Integrals and Areas
- Definite Integrals, Substitution and Integration by Parts
- Advanced Area Problems
- Volume Problems
- Advanced Volume Problems
- Applications to Physics
- Applications to Business
CD 5 - Integration II
- Special Trigonometric Limits
- General Limits
- One-Sided Limits
- Limits Using Continuity
- Hyperbolic Functions
- L’Hôpital’s Rule
- Trigonometric Integrals
- Trigonometric Substitutions
- Partial Fractions
- Improper Integrals
- Area in Polar Coordinates
CD 6 - Sequences & Series
- Sequences and Convergence
- Summation Notation
- Infinite Series
- Comparison Test
- Integral Test
- Absolute Convergence and Alternating Series
- Ratio Test and Root Test
CD 7 - Vectors
- Power Series
- Taylor Series
- Vectors
- Dot Product and Length
- Vector Component Computations
- Vector Cross Product
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