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Polynomial and Rational Functions
http://www.mathamazement.com/Lessons/Pre-Calculus/02_Polynomial-and-Rational-Functions
PhD Math, UC Berkeley. 1 Graphs, Functions, and Models. 3 Exponential and Logarithmic Functions. 2 Polynomial and Rational Functions. 23 Quadratic Functions and Their Graphs. 24 Polynomial Functions and Their Graphs. 26 Zeros of Polynomial Functions. 27 Rational Functions and Their Graphs. 28 Polynomial and Rational Inequalities.
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Analytic Trigonometry
http://www.mathamazement.com/Lessons/Pre-Calculus/05_Analytic-Trigonometry
PhD Math, UC Berkeley. 6 Additional Topics in Trigonometry. 51 Verifying Trigonometric Identities. 52 Sum and Difference Formulas. 53 Double-Angle and Half-Angle Formulas. 54 Product-to-Sum and Sum-to-Product Formulas.
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Directrix of a Parabola - Applications and Distances, Focus, Vertex, Equations, Graphs, Reflective Property
http://www.mathamazement.com/Lessons/Pre-Calculus/09_Conic-Sections-and-Analytic-Geometry/parabola.html
PhD Math, UC Berkeley. 9 Conic Sections and Analytic Geometry. 94 Rotation of Axes. A parabola is defined as the locus of points in a plane equidistant from a fixed point F, known as the. And a line L in the plane not containing F, known as the. Note that unlike ellipses and hyperbolas, parabolas have only one focus. A graph of a parabola is shown below, along with its focus F, directrix L (dotted line), points P. Lying on the parabola, and points Q. Shown in the figure, we have. Of the parabola. The.
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Ellipse Foci Line, Major and Minor Axes, Eccentricity, Equations in Rectangular Coordinates, Graphs, and Reflective Property
http://www.mathamazement.com/Lessons/Pre-Calculus/09_Conic-Sections-and-Analytic-Geometry/ellipse.html
PhD Math, UC Berkeley. 9 Conic Sections and Analytic Geometry. In this chapter, we describe three very important types of curves, known as. Figure 9.1.1: The Four Conic Sections. Images taken from www.math2.org). Figure 9.1.2: The Three Degenerate Conic Sections. Images taken from www.math2.org). In this section, we discuss the ellipse, corresponding to the second diagram in Figure 9.1.1. The ellipse is the only one of the three conic sections (not including the circle) which is closed. An. Of the ellips...
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Separable Differential Equations
http://www.mathamazement.com/Lessons/Differential-Equations/index.html
PhD Math, UC Berkeley. Separable differential equations are the simplest type of differential equation. The basic form of a separable differential equation is as follows:. Where f(x) and g(y) are integrable functions of one variable. To solve Equation (1), we first multiply both sides by g(y) dx, obtaining. Finally we integrate both sides of (2), obtaining the following general solution:. Where c is an arbitrary integration constant. 1 Find the general solution to the following differential equation:.
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Introduction to Calculus
http://www.mathamazement.com/Lessons/Pre-Calculus/11_Introduction-to-Calculus
PhD Math, UC Berkeley. 10 Sequences, Inductioin, and Probability. 11 Introduction to Calculus. 111 Limits and Continuity of Functions. 113 The Product Rule. 114 The Quotient Rule. 115 Physical Applications of Derivatives.
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Graphs, Functions, and Models
http://www.mathamazement.com/Lessons/Pre-Calculus/01_Graphs-Functions-and-Models
PhD Math, UC Berkeley. P Prerequisites: Fundamental Concepts of Algebra. 2 Polynomial and Rational Functions. 1 Graphs, Functions, and Models. 11 Graphs and Graphing Utilities. 12 Lines and Slopes. 13 Distance and Midpoint Formulas. 15 Basics of Functions. 16 Graphs of Functions. 17 Transformations of Functions. 18 Combinations of Functions. 110 Modeling with Functions.
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Additional Topics in Trigonometry
http://www.mathamazement.com/Lessons/Pre-Calculus/06_Additional-Topics-in-Trigonometry
PhD Math, UC Berkeley. 7 Systems of Equations and Inequalities. 6 Additional Topics in Trigonometry. 61 The Law of Sines. 62 The Law of Cosines. 64 Graphs of Polar Equations. 65 Complex Numbers in Polar Form. 66 De Moivre's Theorem. 68 The Dot Product.
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Systems of Equations and Inequalities
http://www.mathamazement.com/Lessons/Pre-Calculus/07_Systems-of-Equations-and-Inequalitites
PhD Math, UC Berkeley. 6 Additioinal Topics in Trigonometry. 8 Matrices and Determinants. 7 Systems of Equations and Inequalities. 71 Systems of Linear Equations in Two Variables. 72 Systems of Linear Equations in Three Variables. 74 Systems of Noninear Equations in Two Variables. 75 Systems of Inequalities in Two Variables.
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Hyperbola Equation and Eccentricity - Foci, Asymptotes, Eccentricity, Equation in Rectangular Coordinates, and Graphs
http://www.mathamazement.com/Lessons/Pre-Calculus/09_Conic-Sections-and-Analytic-Geometry/hyperbola.html
PhD Math, UC Berkeley. 9 Conic Sections and Analytic Geometry. The hyperbola is the second of the three conic sections we discuss in this chapter. We already saw an example of a hyperbola in Section 1.6, namely Figure 1.6.2, the graph of the function y = 1/x. We will see in Section 9.4 that this graph is indeed a hyperbola, but for now, we discuss more general properties of hyperbolas. D(P, F1) - d(P, F2) = 2a. Figure 9.2.2: A hyperbola. Image taken from MathWorld). B = √ c. Y = ±(b/a)x. In order to be a...
