| Description |
xviii, 382 pages : illustrations ; 24 cm. |
| Series |
--For dummies |
|
--For dummies.
|
| Note |
Includes index. |
| Contents |
Introduction -- About this book -- Conventions used in this book -- Foolish assumptions-- How this book is organized -- Part 1: Set it up, solve it, graph it -- Part 2: Essentials of trigonometry -- Part 3: Analytic geometry and system solving -- Part 4: Part of tens -- Icons used in this book -- Where to go form here -- Part 1: Set It Up, Solve It, Graph It -- 1: Pre-Pre-Calculus -- Pre-calculus: an overview -- All the numbers basics (No, not how to count them!) -- Multitude of number types: terms to know -- Fundamental operations you can perform on numbers -- Properties of numbers: truths to remember -- Putting mathematical statements in visual form: fun with graphs -- Digesting basic terms and concepts -- Graphing equalities versus inequalities -- Gathering information from graphs -- Getting a grip on a graphing calculator -- 2: Dealing With Real Numbers -- Solving inequalities -- Brief how-to inequality recap -- Solving equations and inequalities when absolute value is involved -- Expressing solutions for inequalities with interval notation -- Variations on dividing and multiplying: working with radicals and exponents -- Defining and relating radicals and exponents -- Rewriting radicals as exponents (or, creating rational exponents) -- Getting a radical out of a denominator: rationalizing -- 3: Foundation Of Pre-Calc: Functions -- Qualities of even and odd functions and their graphs -- Dealing with parent functions (the most common) and their graphs -- Quadratic functions -- Square root functions -- Absolute value functions-- Cubic functions -- Cube root functions -- Transforming the parent graphs -- Vertical transformations -- Horizontal transformations -- Translations -- Reflections -- Combining various transformations -- Transformation in itself! -- Transforming functions point by point -- Graphing functions that have more than one rule -- Piece-wise functions -- Calculating outputs for rational functions -- Step 1: Search for vertical asymptotes -- Step 2: Look for horizontal asymptotes -- Step 3: Seek out oblique asymptotes -- Step 4: Locate the x-and y-intercepts -- Putting the output to work: graphing rational functions -- Denominator has the greater degree -- Numerator and denominator have equal degrees -- Numerator has the greater degree -- No scalpel necessary: operating on functions -- Adding and subtracting -- Multiplying and dividing -- Breaking down a composition of functions-- Adjusting the domain and range of combined functions (if applicable ) -- Flip-flopping with inverse functions -- Graphing an inverse -- Inverting a function to find its inverse -- Verifying an inverse -- 4: Finding And Using Roots To Graph Polynomial Functions -- Function of degrees and roots -- Factoring a polynomial expression -- Always the first step: look for a GCF -- Wrap it up: the FOIL method for trinomials -- Recognizing and factoring special types of polynomials -- Grouping to factor four or more terms -- Finding the roots of a factored equation -- Cracking a quadratic equation when it won't factor -- Using the quadratic formula -- Completing the square -- Solving unfactorable polynomials with a degree higher than two -- Counting a polynomial's total number of roots -- Tallying the real roots: Descartes rule of signs -- Accounting for imaginary roots: the fundamental -- Theorem of algebra -- Guessing and checking the real roots -- Put it in reverse: using solutions to find factors -- Graphing polynomials -- When all the roots are real numbers -- When some (or all ) of the roots are imaginary numbers: combining all techniques -- 5: Powering Up With Exponential And Logarithmic Functions -- Exploring exponential functions-- Searching the ins and outs of an exponential function -- Graphing and transforming an exponential function -- Logarithms: investigating the inverse of exponential functions -- Getting a better handle on logarithms -- Managing the properties and identities of logs -- Changing a log's base (when the log isn't natural or common) -- Calculating a number when you know its log: inverse logs -- Graphing logs -- Solving equations with exponents and logs -- Stepping through the process of exponential equation solving -- Taking steps to solve logarithm equations -- Surviving exponential word problems -- Part 2: Essentials Of Trigonometry -- 6: Angling In On The Unit Circle -- Introducing radians: the basic pre-calc measurement -- Trig ratios: taking right triangles a step further -- Making a sine -- Looking for a cosine -- Going on a tangent -- Discovering the flip side: reciprocal trig functions -- Working in reverse: inverse trig functions -- Understanding how trig ratios work on the coordinate plane -- Getting a good grasp on the unit circle -- Familiarizing yourself with the most common angles -- Drawing uncommon angles -- Digesting special triangle ratios -- 45er: 45 degree -45 degree -90 degree triangles -- Old 30-60: 30 degree -60 degree -90 degree triangles -- Fusion of triangles and the unit circle: working together for good -- Placing the major angles correctly, sans protractor -- Retrieving trig-function values on the unit circle -- Finding the reference angle to solve for angles on the unit circle -- Not jus a job for Noah: making and measuring arcs -- 7: Graphing and transforming trig functions --Drafting the sine and cosine parent graphs -- Sine graph -- Cosine graph -- Graphing tangent and cotangent -- Tangent -- Cosecant -- Transforming trig graphs -- Screwing with sine and cosine graphs -- Tweaking tangent and cotangent graphs -- Transforming the graphs of secant and cosecant -- 8: Using Trig Identities: The Basics -- Keeping the end in mind: a quick primer on identities -- Lining up the means to the end: basic trig identities -- Reciprocal identities -- Pythagorean identities -- Even-odd identities -- Co-function identities -- Periodicity identities -- Tackling difficult trig proofs: some techniques to know -- Dealing with dreaded denominators -- Going solo on each side -- 9: Pre-Calc, Here I Come! Advanced Identities Lead The Way -- Finding trig functions of sums and differences -- Searching out the sine of (a + b) -- Calculating the cosine of (a + b) -- Taming the tangent of (a + b) -- Doubling an angle's trig value without knowing the angle -- |
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Finding the sine of a doubled angle -- Calculating cosines for two -- Squaring your cares away -- Having twice the fun with tangents -- Taking trig functions of common angles divided in two -- Glimpse of calculus: traveling from products to sums and back -- Expressing products as sums (or differences) -- Transporting from sums (or differences) to products -- Eliminating exponents on trig functions with power-reducing formulas -- 10: Solving Oblique Triangles With The Laws Of Sines and cosines -- Solving a triangle with the law of sines -- When you know two angle measures -- When you know two consecutive side lengths (SSA) -- Conquering a triangle with the law of cosines -- SSS: Finding angles using only sides -- SAS: Tagging the angle in the middle (and the two sides ) -- Filling in the triangle by calculating area-- Finding area with two sides and an included angle (for SAS scenarios) -- Heron's formula (for SSS scenarios) -- Heron's formula (for SSS scenarios) -- Part 3: Analytic Geometry And System Solving -- 11: New Plane Of Thinking: Complex Numbers And Polar Coordinates -- Understanding real versus imaginary -- According to mathematicians -- Combining real and imaginary: the complex number system -- Grasping the usefulness of complex numbers -- Performing operations with complex numbers -- Graphing complex numbers -- Plotting around a pole: Polar coordinates -- Wrapping your brain around the polar coordinate plane -- Graphing polar coordinates with negative values -- Changing to and from polar coordinates -- Picturing polar equations -- 12: Cutting It Up With Conics -- Cone to cone: identifying the four conic sections -- In picture (graph form) --In print (equation form) -- Going round and round with circles -- Graphing a circle -- Riding the ups and downs with parabolas -- Labeling the parts -- Understanding the characteristics of a standard parabola -- Plotting the variations: parabolas all over the plane (not at the origin) -- Finding the vertex, axis of symmetry, focus, and directrix -- Identifying the min and max on vertical parabolas -- Fat and the skinny on the ellipse (fancy word of oval) -- Labeling ellipses and expressing them with algebra -- Identifying the parts of the oval: vertices, co-vertices, axes, and foci -- Pair two parabolas and what do you get? Hyperbolas -- Visualizing the two types of hyperbolas and their bits and pieces -- Graphing a hyperbola from an equation -- Finding the equation of asymptotes -- Expressing conics outside the realm of cartesian coordinates -- Graphing conic sections in parametric form -- Equations of conic sections on the polar coordinate plane -- 13: Solving Systems And Mingling With Matrices -- Primer on your system-solving options -- Finding solutions of two-equation systems algebraically -- Solving linear systems -- Working nonlinear systems -- Working nonlinear systems -- Solving systems with more than two equations -- Decomposing partial fractions -- Surveying systems of inequalities -- Introducing matrices: the basics -- Applying basic operations to matrices -- Multiplying matrices by each other -- Simplifying matrics to ease the solving process - Writing a system in matri form -- Reduced row echelon form -- Augmented form -- Conquering matrices -- Using gaussian elimination to solve systems -- Multiplying a matrix by its inverse -- Using determinants: Cramer's rule -- 14: Sequences, Series, And Expanding Binomials -- Speaking sequentially : grasping the general method -- Calculating a sequences terms by using the sequence expression -- Working in reverse: forming an expression from terms -- Recursive sequences: one type of general sequence -- Covering the distance between terms: arithmetic sequences -- Using consecutive terms to find another in an arithmetic sequence -- Using any two terms -- Sharing ratios with consecutive paired terms: geometric sequences -- Identifying a term when you know consecutive terms -- Going out of order: finding a term when the terms are nonconsecutive -- Creating a series: summing terms of a sequence -- Reviewing general summation notation -- Summing an arithmetic sequence -- Seeing how a geometric sequence adds up -- Expanding with the binomial theorem -- Breaking down the binomial theorem -- Starting at the beginning: binomial coefficients -- Expanding by using the binomial theorem -- 15: Looking Forward To Calculus -- Differences between pre-calc and calc -- Understanding and communicating about limits -- Finding the limit of a function -- Graphically -- Analytically -- Algebraically -- Operating on limits: the limit laws -- Exploring continuity in functions -- Determining whether a function is continuous -- Dealing with discontinuity -- Part 4: Part Of Tens -- 16: Ten Habits Hat Help You Attack Calculus -- Figure out what the problem is asking -- Draw pictures (and plenty of em) -- Plan your attack -- Write down any formulas -- Show each step of your work -- Know when to quit -- Check your answers -- Practice plenty of problems -- Make sure you understand the concepts -- Pepper you teacher with questions -- 17: Ten Habits To Break Before Calculus -- Operating out of order -- Squaring without FOILing -- Splitting up denominators -- combining the wrong terms -- Forgetting the reciprocal -- Losing track of minus signs -- Oversimplifying radicals -- Erring in exponential dealings -- Canceling out too quickly -- Distributing improperly -- Index. |
| Summary |
From the Publisher: Getting ready for calculus, but feel confused? Have no fear! This unintimidating, hands-on guide walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. You'll understand the concepts-not just the number crunching-and see how to perform all tasks, from graphing to tackling proofs. Apply the major theorems and formulas; Graph trig functions like a pro; Find trig values on the unit circle; Tackle analytic geometry; Identify function limits and continuity. |
| Subject |
Algebra.
|
|
Trigonometry.
|
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Functions.
|
| Added Author |
Burger, Christopher.
|
|
Gilman, Michelle Rose.
|
|
Rumsey, Deborah J. (Deborah Jean), 1961-
|
| ISBN |
9780470169841 paperback |
|
0470169842 paperback |
|
