Account Information for Houston
University of Houston
College Professor
Limits and Graphs
(Calculus)
The concept of limit from an intuitive, graphical point of view. Left and right-sided limits. Infinite one-sided limits and vertical...
Calculation of Limits
(Calculus)
Using "limit laws" to compute limits. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more...
Trigonometric Limits
(Calculus)
Limits involving sine and cosine. Vertical asymptotes of tan, cot, sec, csc. The limit of sin(x)/x as x -> 0...
Continuity
(Calculus)
Definition of continuity at a point. Continuity of polynomials, rational functions, and trigonometric functions. Left and right continuity. Continuity on...
The Derivative
(Calculus)
Slope of the tangent line; definition of the derivative. Differentiability and non-differentiability at a point. Copyright 2005, Department of Mathematics,...
Calculation of Derivatives
(Calculus)
The power, product, reciprocal, and quotient rules for calculating derivatives. Copyright 2005, Department of Mathematics, University of Houston. Created by...
Derivatives of Trigonometric Functions
(Calculus)
The derivatives of sin, cos, tan, cot, sec, csc. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn...
Leibniz Notation and the Chain Rule
(Calculus)
Liebniz notation for the derivative. The chain rule. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis....
Rates of Change and Related Rates
(Calculus)
The derivative as rate of change. Related rates problems. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn...
Implicit Differentiation
(Calculus)
Implicit differentiation. The power rule for rational powers. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis....
e^x and ln x
(Calculus)
Early Transcendental extra video lecture including exponentials and the natural logarithm. Copyright 2005, Department of Mathematics, University of Houston. Created...
Inverse Trig Functions
(Calculus)
Early Transcendentals extra video lecture on inverse trigonometric functions. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn...
Rectilinear Motion
(Calculus)
Velocity and acceleration. Acceleration due to gravity. Bounce. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis....
Higher-Order Derivatives
(Calculus)
Higher-order derivatives. Concavity. Local approximation by linear, quadratic, and cubic polynomials. Copyright 2005, Department of Mathematics, University of Houston. Created...
The Mean-Value Theorem and Related Results
(Calculus)
Rolle's theorem and the mean-value theorem. Invervals where a function is increasing/decreasing/constant. Copyright 2005, Department of Mathematics, University of Houston....
Critical numbers of a function. The first derivative test for local extrema. Copyright 2005, Department of Mathematics, University of Houston....
Concavity and the Second Derivative Test
(Calculus)
Concavity and the second derivative. The second derivative test for local extrema. Copyright 2005, Department of Mathematics, University of Houston....
Limits at infinity and Horizontal Asymptotes
(Calculus)
Limits at positive and negative infinity and horizontal asymptotes. Calculation of limits at positive / negative infinity. Copyright 2005, Department...
Curve Sketching
(Calculus)
Graphing y = f(x) using the first and second derivatives, infinite limits, and limits at positive / negative infinity. Copyright...
Extreme Values on Intervals
(Calculus)
Global (absolute) maximum and minimum values on closed intervals. Endpoint (one-sided) derivatives. The second derivative and extrema on open intervals....
Applied Optimization Problems
(Calculus)
Several example problems of applied optimization. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more...
Newton's Method
(Calculus)
Learn about Newton's Method and how to use it. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn...
The Area Under a Curve
(Calculus)
Approximation of areas with sums of rectangle areas. Right-endpoint, left-endpoint, and midpoint approximations; upper and lower sums. Copyright 2005, Department...
The Integral
(Calculus)
Definition of the integral. Signed area. Geometric evaluation and symmetries. Interval additivity property. Copyright 2005, Department of Mathematics, University of...
The Fundamental Theorem of Calculus
(Calculus)
Average value theorem. The function p(x) = integral of f(s) ds. The fundamental theorem of calculus. Copyright 2005, Department of...
Antidifferentiation and Indefinite Integrals
(Calculus)
Indefinite integrals. The power rule for antidifferentiation. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find...
Change of Variables (Substitution)
(Calculus)
Differentials. Using basic "u-substitutions" to find indefinite integrals and compute definite integrals. Copyright 2005, Department of Mathematics, University of Houston....
Areas Between Curves
(Calculus)
How to find the area between two curves. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis....
Volumes I
(Calculus II)
Solids with specified cross-sections. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on...
Volumes II
(Calculus II)
Solids of revolution. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos,...
Volumes III
(Calculus II)
The cylindrical shell method. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on...
The Centroid of a Planar Region
(Calculus II)
Calculation of moments and centroids. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information...
The Natural Logarithm
(Calculus II)
The natural log function defined as the integral of 1/t dt. Copyright 2005, Department of Mathematics, University of Houston. Created...
The Exponential Function
(Calculus II)
The inverse of the natural logarithm. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more...
The Inverse Trigonometric Functions
(Calculus II)
Inverse sine, cosine, tangent, cotangent, secant, and cosecant. Derivatives and companion indefinite integration formulas. Copyright 2005, Department of Mathematics, University...
Integration by Parts
(Calculus II)
Integration by parts. Derivation of reduction formulas. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find...
Integral of (sec x)^m (tan x)^n dx and integral of (csc x)^m (cot x)^n dx. Copyright 2005, Department of Mathematics,...
Trigonometric Substitutions
(Calculus II)
Sine, tangent, and secant substitutions. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information...
Partial Fraction Expansions
(Calculus II)
Partial fraction expansions. Integration of general rational functions. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis....
Numerical Integration
(Calculus)
Trapezoid Rule and Simpson's Rule. Error estimates. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find...
Arc Length and Surface Area
(Calculus II)
Length of an arc y = f(x), a < x < b. Area of a surface of revolution. Copyright 2005,...
Polar Coordinates and Graphs
(Calculus II)
Polar vs. rectangular coordinates; polar graphs; slope of the tangent line to a polar curve. Copyright 2005, Department of Mathematics,...
Areas and Lengths Using Polar Coordinates
(Calculus II)
Area of a polar region; length of a polar arc. Copyright 2005, Department of Mathematics, University of Houston. Created by...
Improper Integrals
(Calculus II)
Integrals over unbounded intervals. Integrals over bounded intervals of functions that are unbounded near an endpoint. Comparison test for convergence/divergence....
Indeterminate Forms and L'Hopital's Rule
(Calculus II)
Indeterminate forms 0/0, infinity/infinity, 0, infinity, 1^infinity, 0^0, infinity^0, and infinity - infinity. L'Hopital's Rule. Copyright 2005, Department of Mathematics,...
Sequences I
(Calculus II)
Sequences; the graph of a sequence; the limit of a sequence; the squeeze theorem. Some special sequences and their limits....
Sequences II
(Calculus II)
Precise definition of the limit of a sequence. Monotonicity and boundedness; convergence of bounded, monotonic sequences. Recursively defined sequences, fixed...
Series
(Calculus II)
Sequences of partial sums. Geometric series and the harmonic series. Copyright 2005, Department of Mathematics, University of Houston. Created by...
The Integral Test
(Calculus II)
The integral test for convergence of series with positive terms; p-series. Remainder estimation. Copyright 2005, Department of Mathematics, University of...
Comparison Tests
(Calculus II)
Comparison and limit-comparison tests. The ratio and root tests. Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn...
Alternating Series and Absolute Convergence
(Calculus II)
Convergence theorem for alternating series. Estimation of the remainder. Absolute versus conditional convergence. Copyright 2005, Department of Mathematics, University of...
Power Series
(Calculus II)
Functions defined by power series. Ratio and root tests for absolute convergence. Differentiation and integration. Closed forms for series derived...
Taylor and Maclaurin Series
(Calculus II)
Maclaurin series. Expansions of e^x, sin x, and cos x, and related series. Taylor series expansions about x0. Copyright 2005,...
Taylor's Theorem
(Calculus II)
Taylor polynomials and the remainder term. Convergence of Taylor series to f(x). Copyright 2005, Department of Mathematics, University of Houston....
Integration of Powers and Products of Sine and Cosine
(Calculus II)
Integral of (cos x)^m (sin x)^n dx. Also, integral of cos(ax) sin(bx) dx, etc.
