: videos

: self-testing

: explanations / worked examples

**pre-calculus topics****chain rule****concavity (concave up & concave down)****continuity****critical points****curve sketching****decreasing/increasing functions & local max/min****derivatives**- see also: chain rule
- see also: graphing functions
- see also: implicit differentiation
- see also: product rule
- see also: quotient rule
- Basic Derivative Examples
- Sketching the Derivative of a Function
- More Complicated Derivative Examples
- More Complicated Derivative Examples
- Derivatives — Product + Chain Rule + Factoring

**derivatives — limit definition****differentiation**- see: derivatives

**exponents**- see also: logarithmic differentiation
- Are You Ready for Calculus III? [Select "Logs & Exponentials"]
- Are You Ready for College Algebra? [Select "Exponents"]
- Integration: The Exponential Form
- The Integration of Exponential Functions/
- General Exponential and Logarithmic Functions
- Logs and Exponentials

**graphing functions****implicit differentiation****increasing functions**- see: decreasing/increasing functions & local max/min

**l'Hôpital's rule (AKA l'Hospital's rule AKA l'Hopital's rule)****limits**- see also: derivatives — limit definition
- see also: squeeze theorem
- Limits of Functions as
*x*Approaches a Constant - Limit Theorems
- Limits of Functions as
*x*Approaches Infinity - What is a Limit? Basic Idea of Limits
- Calculating a Limit by Factoring and Canceling
- Calculating a Limit by Getting a Common Denominator
- Calculating a Limit by Expanding and Simplifying
- Calculating a Limit by Multiplying by a Conjugate
- Limits Involving Absolute Value
- Calculus — Infinite Limits
- Limits at Infinity — Basic Idea and Shortcuts
- Calculating a Limit at Infinity with a Radical

**local max/min (via 2nd derivative)**- see also: decreasing/increasing functions & local max/min
- Finding Local Maximums and Local Minimums using the Second Derivative Test

**logarithmic differentiation****logarithms**- Are You Ready for Calculus III? [Select "Logs & Exponentials"]
- Derivative of the Logarithmic Function
- Integration: The Basic Logarithmic Form
- Logarithmic Differentiation
- Logs and Exponentials
- Just Math Tutorials [Search for "logarithm"]
- Derivatives of Logarithmic Functions and Examples
- Properties of Logarithms — Logarithmic Functions

**maxima/maximization/maximizing/maximum**- see: minimum & maximum function values

**minima/minimization/minimizing/minimum**- see: minimum & maximum function values

**minimum & maximum function values****optimization**- see: minimum & maximum function values

**product rule****quotient rule****related rates****tangent line**

- Calculus Problems and Solutions
- http://www.khanacademy.org/#Calculus (Numerous videos on various calculus topics)
- When Will I Use Math?

[ Department of Mathematics and Computer Science | Santa Clara University ]