The College Algebra Video Tutor series consists of 8 videos containing approximately 14 hours of video instruction. Topics include factoring, rational expressions, radicals, rational exponents, complex numbers, linear equations and inequalities and applications, solving quadratic equations, absolute value equations and inequalities, polynomial and rational inequalities, circles, functions and graph sketching, rational root theorem, graphing rational functions, exponential and logarithmic functions, induction, and the Binomial Theorem.
Video 1 - Factoring, Radical Expressions, Rational Exponents
This segment covers factoring in general for polynomials of several variables, reviewing the techniques for binomials, trinomials and factoring by grouping for polynomials with more than three terms. Also covered are examples where unknowns appear as exponents.
- Operations on Rational Expressions.
This segment reviews addition, subtraction, multiplication, and division of rational expressions at the college algebra or precalculus level of difficulty.
This segment reviews the properties of radicals and covers the simplification of algebraic expressions in several variables with radicals. Rationalizing denominators is also covered.
This segment reviews the laws of exponents and covers simplification of algebraic expressions involving rational number exponents as well as factoring with negative and rational exponents.
Video 2 - Complex Numbers, Word Problems, Linear Equations.
This segment covers addition, subtraction, multiplication, conjugation, and division of complex numbers and their use in solution of quadratic equations.
- Solving Linear Equations.
This segment reviews strategies for solving linear equations of college algebra or precalculus level of difficulty which can be rearranged to linear form.
This segment covers word problems of college algebra or precalculus level of difficulty including problems of mixtures, speed, distance and time, and interest rates.
- Solving Quadratic Equations.
This segment covers solution of equations which can be rearranged to quadratic form. The methods of solution by factoring, by completing the square, and by quadratic formula are all covered.
Video 3 - Inequalities, Absolute Value Equations, Polynomial
This segment covers equations in general, some involving radicals which can be rearranged to linear or quadratic form. Only real roots are considered for this segment.
This segment covers inequalities in one variable including examples with factored polynomials, with rational expressions, as well as compound inequalities.
- Absolute Value Inequalities.
This segment reviews the definition and properties of absolute value and absolute value inequalities as well as solution of absolute value inequalities.
- Polynomial and Rational Inequalities.
This segment covers polynomial and rational inequalities in general in one variable. The examples covered are at the college algebra or precalculus level of difficulty.
Video 4 - Circles, Equations of Straight Lines, Functions
- Circles, The Midpoint Formula, and The Distance Formula.
This segment covers analytic geometry problems involving distances between pairs of points, midpoints, and determination of radius and center for quadratic equations of two variables which describe circles.
- Equations of Straight Lines.
This segment covers slope, its meaning, as well as methods for calculation. Perpendicular and parallel lines, point-slope form for equations of lines, and general form for linear equations in two variables are covered.
This segment covers the mathematical definition of the word "function", the function notation, computation of values of given functions, problems of finding domains for functions specified by algebraic expressions, as well as the difference quotient.
This segment covers elementary graphing techniques for functions including definitions of even, odd, increasing, and decreasing functions.
Video 5- Graphs, Functions, Inverse & Quadratic Functions.
- Shifting and Reflecting Graphs.
This segment covers methods for vertical and/or horizontal shifting so as to reduce graphing problems for functions to simpler forms. Examples involving absolute value, radicals, and quadratic and cubic functions are included.
This segment covers This segment covers addition, subtraction, multiplication, division and composition of functions.
This segment covers the definition of mutually inverse functions, one-to-oneness, problems of showing given pairs of functions to be mutually inverse, the horizontal line test for one-to-oneness and problems of finding inverses for given functions.
This segment covers general quadratic functions and their graphs as well as methods for finding the vertex, horizontal and vertical intercepts, and axis of symmetry.
Video 6- Polynomial Functions, Rational Root Theorem.
This segment covers graphing and finding horizontal and vertical intercepts for general polynomial functions.
- Division of Polynomials, the Remainder Theorem and the Factor Theorem.
This segment covers long division for polynomials, synthetic division, the use of the remainder theorem for calculating function values by synthetic division, and the use of the factor theorem for finding roots of polynomials.
This segment covers the use of the rational root theorem for factorization of polynomials.
- Vertical and Horizontal Asymptotes.
This segment covers methods of finding vertical, horizontal, and oblique asymptotic lines to graphs of rational functions.
Video 7- Rational Functions, Exponential Functions, Logs
- Graphing Rational Functions.
This segment covers the graphing of rational functions using techniques of shifting and reflecting, as well as intercepts and asymptotes.
- Exponential Functions and Their Graphs.
This segment covers exponential functions, the number e, continuously compounded interest, growth and decay problems, as well as problems of graphing exponential functions.
- Logarithms and Their Properties.
This segment covers the definition of logarithmic functions as inverse to exponential functions, properties of logarithms, and computations involving logarithms as well as logarithmic equations.
- Logarithmic functions and Their Graphs.
This segment covers graphing of logarithmic functions, the change of base formula, and the use of logarithms to solve exponential equations.
Video 8- Nonlinear Equations, Binomial Theorem, Induction.
- Systems of Nonlinear Equations.
This segment covers substitution and elimination methods for solving two equations in two unknowns without linearity restrictions but with use of graphing to illustrate the solutions.
This segment covers This segment covers the definition of proof by mathematical induction and the use of mathematical induction for proving certain identities. Binomial Theorem.
This segment covers factorial notation, binomial coefficients and the use of the binomial theorem for expansion of a binomial raised to a power as well as determination of specific terms of the expansion in case of large powers.
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