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Math Help - Preparing for Calculus

  1. #1
    Senior Member vaironxxrd's Avatar
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    Preparing for Calculus

    Hello everyone,

    I have a simple question, because I started college and I'm taking a Precalculus course.
    Sadly is a very independent course... no homework, exercises, etc. Just a do whatever you want course with two grades midterm and final.

    Are there any terms that come up in most Calculus courses?
    Terms which I should look more into?
    My book contains all of the following...

    1. Graphs

    1.1 The Distance and Midpoint Formulas; Graphing Utilities; Introduction to Graphing Equations
    1.2 Intercepts; Symmetry; Graphing Key Equations
    1.3 Solving Equations Using a Graphing Utility
    1.4 Lines
    1.5 Circles
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    2. Functions and Their Graphs

    2.1 Functions
    2.2 The Graph of a Function
    2.3 Properties of Functions
    2.4 Library of Functions; Piecewise-defined Functions
    2.5 Graphing Techniques: Transformations
    2.6 Mathematical Models: Building Functions
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    3. Linear and Quadratic Functions

    3.1 Linear Functions, Their Properties, and Linear Models
    3.2 Building Linear Models from Data
    3.3 Quadratic Functions and Their Properties
    3.4 Building Quadratic Models from Verbal Descriptions and Data
    3.5 Inequalities Involving Quadratic Functions
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    4. Polynomial and Rational Functions

    4.1 Polynomial Functions and Models
    4.2 The Real Zeros of a Polynomial Function
    4.3 Properties of Rational Functions
    4.4 The Graph of a Rational Function
    4.5 Polynomial and Rational Inequalities
    4.6 Complex Zeros; Fundamental Theorem of Algebra
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    5. Exponential and Logarithmic Functions

    5.1 Composite Functions
    5.2 One-to-One Functions; Inverse Functions
    5.3 Exponential Functions
    5.4 Logarithmic Functions
    5.5 Properties of Logarithms
    5.6 Logarithmic and Exponential Equations
    5.7 Financial Models
    5.8 Exponential Growth and Decay Models; Newton's Law; Logistic Growth and Decay Models
    5.9 Building Exponential, Logarithmic, and Logistic Models from Data
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    6. Trigonometric Functions

    6.1 Angles and Their Measure
    6.2 Trigonometric Functions: Unit Circle Approach
    6.3 Properties of the Trigonometric Functions
    6.4 Graphs of the Sine and Cosine Functions
    6.5 Graphs of the Tangent, Cotangent, Cosecant, and Secant Functions
    6.6 Phase Shift; Building Sinusoidal Models
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    7. Analytic Trigonometry

    7.1 The Inverse Sine, Cosine, and Tangent Functions
    7.2 The Inverse Trigonometric Functions (Continued)
    7.3 Trigonometric Equations
    7.4 Trigonometric Identities
    7.5 Sum and Difference Formulas
    7.6 Double-angle and Half-angle Formulas
    7.7 Product-to-Sum and Sum-to-Product Formulas
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    8. Applications of Trigonometric Functions

    8.1 Right Triangle Trigonometry; Applications
    8.2 The Law of Sines
    8.3 The Law of Cosines
    8.4 Area of a Triangle
    8.5 Simple Harmonic Motion; Damped Motion; Combining Waves
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    9. Polar Coordinates; Vectors

    9.1 Polar Coordinates
    9.2 Polar Equations and Graphs
    9.3 The Complex Plane; DeMoivre's Theorem
    9.4 Vectors
    9.5 The Dot Product
    9.6 Vectors in Space
    9.7 The Cross Product
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    10. Analytic Geometry

    10.1 Conics
    10.2 The Parabola
    10.3 The Ellipse
    10.4 The Hyperbola
    10.5 Rotation of Axes; General Form of a Conic
    10.6 Polar Equations of Conics
    10.7 Plane Curves and Parametric Equations
    Chapter Review
    Chapter Test
    Cumulative Review
    Chapter Projects

    11. Systems of Equations and Inequalities

    11.1 Systems of Linear Equations: Substitution and Elimination
    11.2 Systems of Linear Equations: Matrices
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  2. #2
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    Re: Preparing for Calculus

    Pretty much everything in the first eight chapters will appear somewhere in a single-variable calculus course. Pay particular attention to trigonometry (chapters 6-8) since calculus involves quite a bit of trig. For example, the unique general solution to the equation y'' = -kywhere k > 0 involves trig functions. Also, chapter 5 will come in very handy.

    Material in chapters 9-11 probably won't be seen unless you take multi-variable calculus, linear algebra, differential equations, or any other higher-level math.
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