Skip to main content (Press Enter)
Home
Threads
Index
About
Math Insight
log in
Thread: Calculus Refresher
A brief review of the concepts of single variable calculus
Preliminaries
Introduction to Calculus Refresher
Polynomial inequalities
Domain of functions
Lines (and other items in Analytic Geometry)
Elementary limits
Limits with cancellation
Limits at infinity
Limits of exponential functions at infinity
Differentiation
The idea of the derivative of a function
Derivatives of polynomials
Derivatives of more general power functions
The quotient rule
The product rule
The chain rule
Tangent and normal lines
Critical points, monotone increase and decrease
Minimization and maximization refresher
Local minima and maxima (First Derivative Test)
An algebra trick for finding critical points
Linear approximations: approximation by differentials
Implicit differentiation
Related rates
Intermediate Value Theorem, location of roots
Newton's Method
Derivatives of transcendental functions
L'Hospital's rule
Exponential growth and decay: a differential equation
The second and higher derivatives
Inflection points, concavity upward and downward
Another differential equation: projectile motion
Graphing rational functions, asymptotes
Integration
Basic integration formulas
The simplest integration substitutions
Integration substitutions
Area and definite integrals
Length of curves
Numerical integration
Averages and weighted averages
Centers of mass (centroids)
Volumes by cross sections
Volume of surfaces of revolution
Integration by parts
Partial fractions
Trigonometric integrals
Trigonometric substitution
Taylor polynomials
Historical and theoretical comments: Mean Value Theorem
Taylor polynomials: formulas
Classic examples of Taylor polynomials
Computational tricks regarding Taylor polynomials
Prototypes: More serious questions about Taylor polynomials
Determining tolerance/error in Taylor polynomials.
How large an interval with given tolerance for a Taylor polynomial?
Achieving desired tolerance of a Taylor polynomial on desired interval
Integrating Taylor polynomials: first example
Integrating the error term of a Taylor polynomial: example
Threads
Multivariable calculus
Vector algebra
Math 2374
Calculus Refresher
Interactive Gallery of Quadric Surfaces
University of Minnesota, Math 1241
University of Portland, Math 201
Elementary dynamical systems
Network tutorial
Elementary math
Advanced elementary math