{"id":45,"date":"2014-07-07T21:40:36","date_gmt":"2014-07-07T21:40:36","guid":{"rendered":"http:\/\/faculty.pencol.edu\/randyanderson\/?page_id=45"},"modified":"2014-07-24T19:46:15","modified_gmt":"2014-07-24T19:46:15","slug":"precalculus-video-textbook","status":"publish","type":"page","link":"https:\/\/faculty.pencol.edu\/randyanderson\/precalculus-video-textbook\/","title":{"rendered":"Precalculus Video Textbook"},"content":{"rendered":"

Precalculus Video Textbook<\/h3>\n
Below you will find lessons for most of the material found in Precalculus I and II courses. The videos introduce the mathematical concepts along with a few examples to help get those concepts across. Study well.<\/div>\n
<\/div>\n
\n

Precalculus<\/h2>\n

Preliminaries:<\/h4>\n

Interval and Set Notation<\/a>
\nIntercepts<\/a><\/p>\n

Part 1 – An Introduction to Functions<\/h4>\n

1.1 – The Concept of a Function<\/p>\n

Relations<\/a>
\nWhat is a Function?<\/a>
\nFunctions: A Graphical View<\/a>
\nFunction Notation<\/a><\/p>\n

1.2 – More With Functions<\/p>\n

Six Basic Functions<\/a>
\nOperations on Functions<\/a>
\nWhat is a Zero of a Function?<\/a>
\nSymmetry<\/a>
\nEven and Odd Functions<\/a><\/p>\n

1.3 – Graphs of Functions<\/p>\n

Piecewise Functions<\/a>
\nIncreasing, Decreasing, and Constant<\/a>
\nAbsolute and Local Extrema<\/a><\/p>\n

1.4 – Translations of Graphs<\/p>\n

Horizontal and Vertical Translations<\/a>
\nReflecting Graphs<\/a>
\nVertically Stretching and Shrinking Graphs<\/a><\/p>\n

1.5 – Linear Functions<\/p>\n<\/div>\n

Slope<\/a>
\nHorizontal and Vertical Lines<\/a>
\nSlope-Intercept Form of a Line<\/a>
\nPoint-Slope Form of a Line<\/a>
\nFinding Equations of Lines<\/a><\/p>\n

Part 2 – Polynomial, Rational, and Radical Functions<\/h4>\n

2.1 – Quadratic Functions<\/p>\n

Quadratic Functions<\/a>
\nThe Vertex Formula<\/a>
\nThe Quadratic Formula<\/a>
\nThe Discrminant<\/a><\/p>\n

2.2 Reading Graphs, Absolute Value Equations and Inequalities, and Quadratic Inequalities<\/p>\n

Reading Graphs to Determine the Solutions of Equations and Inequalities<\/a>
\nAbsolute Value Equations and Inequalities – Part 1<\/a>
\nAbsolute Value Equations and Inequalities – Part 2<\/a>
\nQuadratic Inequalities<\/a><\/p>\n

2.3 – Introduction to Polynomial Functions<\/p>\n

Definition of a Polynomial Function<\/a>
\nEnd Behavior of a Polynomial Function<\/a>
\nRecall –\u00a0What is a Zero of a Function?<\/a>
\nRepeated Zeros<\/a><\/p>\n

2.4 – The Remainder and Factor Theorems<\/p>\n

Synthetic Division<\/a>
\nThe Remainder and Factor Theorems<\/a><\/p>\n

2.5 – Zeros of Polynomial Functions<\/p>\n

Complex Zeros<\/a>
\nFinding the Zeros of a Polynomial Function<\/a><\/p>\n

2.6 – Rational Functions<\/p>\n

Rational Functions<\/a>
\nAsymptotes of Rational Functions<\/a>
\nGraphing Rational Functions<\/a><\/p>\n

2.7 – Rational Equations and Inequalitites<\/p>\n

Rational Equations<\/a>
\nRational Inequalities<\/a><\/p>\n

2.8 – Radical Equations and Inequalities<\/p>\n

Radical Functions<\/a>
\nRadical Equations<\/a><\/p>\n

Part 3 – Exponential and Logarithmic Functions<\/h4>\n

3.1 – Inverse Functions<\/p>\n

Composition of Functions<\/a>
\nOne-to-One Functions<\/a>
\nInverse Functions<\/a><\/p>\n

3.2 – Exponential and Logarithmic Functions<\/p>\n

Exponential Functions<\/a>
\nDefinition of Logarithm<\/a>
\nProperties of Logarithms<\/a>
\nChange of Base Formula<\/a>
\nLogarithmic Functions<\/a><\/p>\n

3.3 – Exponential and Logarithmic Equations<\/p>\n

Exponential Equations<\/a>
\nLogarithmic Equations<\/a>
\nCompound Interest<\/a>
\nExponential Growth and Decay<\/a>
\nMillion, Billion, Trillion<\/a><\/p>\n

Part 4 – Matrices<\/h4>\n

4.1 – Matrices and Reduce Row Echelon Form<\/p>\n

The General Idea of a Matrix<\/a>
\nMatrices – Row Operations – Part 1<\/a>
\nMatrices – Row Operations – Part 2<\/a>
\nMatrices – Row Operations – Part 3<\/a>
\nMatrices – Row Operations – Part 4<\/a><\/p>\n

4.2 – Properties of Matrices<\/p>\n

Properties of Matrices<\/a>
\nMatrix Multiplication<\/a>
\nDeterminants<\/a>
\nInverse of a 2×2 Matrix<\/a><\/p>\n

4.3 – Partial Fractions<\/p>\n

Partial Fractions – Part 1<\/a>
\nPartial Fractions – Part 2<\/a><\/p>\n

Part 5 – Conic Sections<\/b><\/p>\n

5.1 – Circles<\/p>\n

Circles – Part 1<\/a>
\nCircles – Part 2<\/a><\/p>\n

5.2 – Parabolas<\/p>\n

Parabolas – Part 1<\/a>
\nParabolas – Part 2<\/a>
\nParabolas – Part 3<\/a>
\nParabolas – Part 4<\/a><\/p>\n

5.3 – Ellipses<\/p>\n

Ellipses – Part 1<\/a>
\nEllipses – Part 2<\/a><\/p>\n

5.4 – Hyperbolas<\/p>\n

Hyperbolas – Part 1<\/a>
\nHyperbolas – Part 2<\/a>
\nHyperbolas – Part 3<\/a><\/p>\n

5.5 – The General Equation of Conic Sections and Eccentricity<\/p>\n

The General Equation of Conic Sections and Eccentricity<\/a><\/p>\n

Part 6 – The Foundations of Trigonometry<\/b><\/p>\n

6.1 – Angles, Radians, and Arc Length<\/p>\n

Angles<\/a>
\nRadians<\/a>
\nArc Length<\/a><\/p>\n

6.2 – Definition of Trigonometric Functions and Fundamental Identities<\/p>\n

Definition of Trigonometric Functions<\/a>
\nFundamental Trigonometric Identities<\/a><\/p>\n

6.3 – Right Triangle Trigonometry<\/p>\n

The Definition of Trigonometric Functions for Right Triangles<\/a>
\nTrigonometric Function Values of Special Angles<\/a>
\nReference Angles<\/a><\/p>\n

6.4 – Graphs of Sine and Cosine Functions<\/p>\n

An Introduction to Graphing to Sine and Cosine<\/a>
\nGraphs of Sine and Cosine – Part 1<\/a>
\nGraphs of Sine and Cosine – Part 2<\/a>
\nGraphs of Sine and Cosine – Part 3<\/a><\/p>\n

6.5 – Verifying Trigonometric Identities<\/p>\n

Verifying Trigonometric Identities<\/a><\/p>\n

6.6 – More Trigonometric Identities<\/p>\n

Derivation of Sum and Difference Identities for Cosine and Sine<\/a>
\nSum and Difference Identities<\/a>
\nDouble Angle Identities<\/a>
\nHalf-Angle Identities<\/a><\/p>\n

6.7 – Inverse Trigonometric Functions<\/p>\n

Inverse Trigonometric Functions<\/a><\/p>\n

6.8 – Trigonometric Equations<\/p>\n

Trigonometric Equations – Part 1<\/a>
\nTrigonometric Equations – Part 2<\/a><\/p>\n

Part 7 – Applications of Trigonometry<\/b><\/p>\n

7.1 – The Law of Sines and The Law of Cosines<\/p>\n

The Law of Sines – Part 1<\/a>
\nThe Law of Sines – Part 2<\/a>
\nThe Law of Cosines<\/a><\/p>\n

7.2 – An Introduction to Vectors<\/p>\n

An Introduction to Vectors – Part 1<\/a>
\nAn Introduction to Vectors – Part 2<\/a>
\nAn Introduction to Vectors – Part 3<\/a><\/p>\n

7.3 – The Polar (Trigonometric) Form of Complex Numbers<\/p>\n

The Polar Form of Complex Numbers<\/a>
\nPowers and Roots of Complex Numbers<\/a><\/p>\n

7.4 – Polar Equations<\/p>\n

Polar Equations<\/a>
\nGraphing Polar Equations<\/a><\/p>\n

7.5 – An Introduction to Parametric Equations<\/p>\n

An Introduction to Parametric Equations<\/a><\/p>\n

<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Precalculus Video Textbook Below you will find lessons for most of the material found in Precalculus I and II courses. The videos introduce the mathematical concepts along with a few examples to help get those concepts across. Study well. Precalculus Preliminaries: Interval and Set Notation Intercepts Part 1 – An Introduction to Functions 1.1 – … Continue reading Precalculus Video Textbook<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":7,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":["post-45","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/faculty.pencol.edu\/randyanderson\/wp-json\/wp\/v2\/pages\/45","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/faculty.pencol.edu\/randyanderson\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/faculty.pencol.edu\/randyanderson\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/faculty.pencol.edu\/randyanderson\/wp-json\/wp\/v2\/users\/7"}],"replies":[{"embeddable":true,"href":"https:\/\/faculty.pencol.edu\/randyanderson\/wp-json\/wp\/v2\/comments?post=45"}],"version-history":[{"count":12,"href":"https:\/\/faculty.pencol.edu\/randyanderson\/wp-json\/wp\/v2\/pages\/45\/revisions"}],"predecessor-version":[{"id":62,"href":"https:\/\/faculty.pencol.edu\/randyanderson\/wp-json\/wp\/v2\/pages\/45\/revisions\/62"}],"wp:attachment":[{"href":"https:\/\/faculty.pencol.edu\/randyanderson\/wp-json\/wp\/v2\/media?parent=45"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}