

Algebra II
The Great Courses Signature Collectionの無料体験または購入
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エピソード
シーズン1エピソード1 - An Introduction to Algebra II
2011年3月3日32分Professor Sellers explains the topics covered in the series, the importance of algebra, and how you can get the most out of these episodes. Then, launch into the fundamentals of algebra by reviewing the order of operations and trying your hand at several problems.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード2 - Solving Linear Equations
2011年3月3日31分Explore linear equations, starting with one-step equations and then advancing to those requiring two or more steps to solve. Next, apply the distributive property to simplify certain problems, and then learn about the three categories of linear equations.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード3 - Solving Equations Involving Absolute Values
2011年3月3日31分Taking your knowledge of linear equations a step further, look at examples involving absolute values, which can be thought of as a distance on a number line, always expressed as a positive value. Use your critical thinking skills to recognize absolute value problems that have limited or no solutions.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード4 - Linear Equations and Functions
2011年3月3日29分Moving into the visual realm, learn how linear equations are represented as straight lines on graphs using either the slope-intercept or point-slope forms of the function. Next, investigate parallel and perpendicular lines and how to identify them by the value of their slopes.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード5 - Graphing Essentials
2011年3月3日29分Reversing the procedure from the previous episode, start with an equation and draw the line that corresponds to it. Then test your knowledge by matching four linear equations to their graphs. Finally, learn how to rewrite an equation to move its graph up, down, left, or right, or by flipping it entirely.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード6 - Functions - Introduction, Examples, Terminology
2011年3月3日31分Functions are crucially important not only for algebra, but for precalculus, calculus, and higher mathematics. Learn the definition of a function, the notation, and associated concepts such as domain and range. Then try out the vertical line test for determining whether a given curve is a graph of a function.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード7 - Systems of 2 Linear Equations, Part 1
2011年3月3日29分Practice solving systems of two linear equations by graphing the corresponding lines and looking for the intersection point. Discover that there are three possible outcomes: no solution, infinitely many solutions, and exactly one solution.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード8 - Systems of 2 Linear Equations, Part 2
2011年3月3日30分Explore two other techniques for solving systems of two linear equations. First, the method of substitution solves one of the equations and substitutes the result into the other. Second, the method of elimination adds or subtracts the equations to see if a variable can be eliminated.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード9 - Systems of 3 Linear Equations
2011年3月3日31分As the number of variables increases, it becomes unwieldy to solve systems of linear equations by graphing. Learn that these problems are not as hard as they look and that systems of three linear equations often yield to the strategy of successively eliminating variables.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード10 - Solving Systems of Linear Inequalities
2011年3月3日29分Make the leap into systems of linear inequalities, where the solution is a set of values on one side or another of a graphed line. An inequality is an assertion such as "less than" or "greater than," which encompasses a range of values.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード11 - An Introduction to Quadratic Functions
2011年3月3日32分Begin your investigation of quadratic functions by visualizing what these functions look like when graphed. They always form a U-shaped curve called a parabola, whose location on the coordinate plane can be predicted based on the individual terms of the equation.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード12 - Quadratic Equations - Factoring
2011年3月3日32分One of the most important skills related to quadratics is factoring. Review the basics of factoring, and learn to recognize a very useful special case known as the difference of two squares. Close by working on a word problem that translates into a quadratic equation.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード13 - Quadratic Equations - Square Roots
2011年3月3日31分The square root approach to solving quadratic equations works not just for perfect squares, such as 3 × 3 = 9, but also for values that don't seem to involve squares at all. Probe the idea behind this technique, and also venture into the strange world of complex numbers.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード14 - Completing the Square
2011年3月3日30分Turn a quadratic equation into an easily solvable form that includes a perfect square, a technique called completing the square. An important benefit of this approach is that the rewritten form gives the coordinates for the vertex of the parabola represented by the equation.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード15 - Using the Quadratic Formula
2011年3月3日30分When other approaches fail, one tool can solve every quadratic equation: the quadratic formula. Practice this formula on a wide range of problems, learning how a special expression called the discriminant immediately tells how many real-number solutions the equation has.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード16 - Solving Quadratic Inequalities
2011年3月3日30分Extending the exercises on inequalities from a previous episode, step into the realm of quadratic inequalities, where the boundary graph is not a straight line but a parabola. Use your skills analyzing quadratic expressions to sketch graphs quickly and solve systems of quadratic inequalities.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード17 - Conic Sections - Parabolas and Hyperbolas
2011年3月3日32分Delve into the algebra of conic sections, which are the cross-sectional shapes produced by slicing a cone at different angles. In this episode, study parabolas and hyperbolas, which differ in how many variable terms are squared in each. Also learn how to sketch a hyperbola from its equation.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード18 - Conic Sections - Circles and Ellipses
2011年3月3日32分Investigate the algebraic properties of the other two conic sections: ellipses and circles. Ellipses resemble stretched circles and are defined by their major and minor axes, whose ratio determines the ellipses' eccentricity. Circles are ellipses whose eccentricity = 1, with the major and minor axes equal.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード19 - An Introduction to Polynomials
2011年3月3日32分Pause to examine the nature of polynomials: a class of algebraic expressions that you've been working with since the beginning of the series. Professor Sellers introduces several useful concepts, such as the standard form of polynomials and their degree, domain, range, and leading coefficients.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード20 - Graphing Polynomial Functions
2011年3月3日31分Deepen your insight into polynomial functions by graphing them to see how they differ from non-polynomials. Then learn how the general shape of the graph can be predicted from the highest exponent of the polynomial, known as its degree. Finally, explore how other terms in the function also affect the graph.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード21 - Combining Polynomials
2011年3月3日34分Switch from graphs to the algebraic side of polynomial functions, learning how to combine them in many different ways, including addition, subtraction, multiplication, and even long division, which is easier than it seems. Discover which of these operations produce new polynomials and which do not.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード22 - Solving Special Polynomial Equations
2011年3月3日32分Learn how to solve polynomial equations where the degree is greater than two by turning them into expressions you already know how to handle. Your "toolbox" includes techniques called the difference of two squares, the difference of two cubes, and the sum of two cubes.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード23 - Rational Roots of Polynomial Equations
2011年3月3日32分Going beyond the approaches you've learned so far, discover how to solve polynomial equations by applying two powerful tools for finding rational roots: the rational roots theorem and the factor theorem. Both will prove very useful in succeeding lessons.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード24 - The Fundamental Theorem of Algebra
2011年3月3日32分Explore two additional tools for identifying the roots of polynomial equations: Descartes' rule of signs, which narrows down the number of possible positive and negative real roots; and the fundamental theorem of algebra, which gives the total of all roots for a given polynomial.The Great Courses Signature Collectionの無料体験または購入シーズン1エピソード25 - Roots and Radical Expressions
2011年3月3日32分Shift gears away from polynomials to focus on expressions involving roots, including square roots, cube roots, and roots of higher degrees (all known as radical expressions). Practice multiplying, dividing, adding, and subtracting a wide variety of radical expressions.The Great Courses Signature Collectionの無料体験または購入