Corequisite Codex

Mathematics

Author: Roy Simpson
Publisher: Cosumnes River College
Source: LibreTexts
License: CC BY-NC-SA
Language: EN
Category: Basic Sciences

Read online Download PDF (open licence)

Contents· 262 sections

01: Sets and Numbers
1.01: The Language of Algebra
1.02: Sets and Set Notation
1.03: Sets of Numbers
1.04: Properties of Real Numbers
1.05: Scientific Notation
1.06: Inequalities and Inequality Notation
1.07: Intervals and Interval Notation
1.08: Set-Builder Notation
1.09: Complex Numbers
02: Arithmetic
2.01: Factors Prime Factorizations and Least Common Multiples
2.02: Mathematical Operations - Addition Subtraction Multiplication and Division
2.03: Factorials
2.04: Mathematical Operations - Powers and Square Roots
2.05: The Order of Operations
2.06: Simplifying Fractions and Mixed Numbers
2.07: Multiplying and Dividing Fractions
2.08: Adding and Subtracting Fractions
2.09: Mathematical Operations - Higher-Index Roots
2.10: The Absolute Value of a Number
2.11: Ratios Proportions and Proportional Reasoning
2.12: The Arithmetic of Complex Numbers
2.13: Percents
2.14: Unit Analysis and Unit Conversion
2.15: Measurement Approximation Rounding and Significant Figures
03: Geometry
3.01: Types of Angles and Degree Measure
3.02: Vertical Alternate and Corresponding Angles
3.03: Triangles
3.04: The Triangle Inequality Theorem
3.05: The Pythagorean Theorem Distance Formula and Midpoint Formula
3.06: Similar Triangles
3.07: Special Triangles
3.08: Circles - Properties Area and Circumference
3.09: Area and Perimeter of Triangles and Quadrilaterals
3.10: Volumes and Surface Areas of Common Shapes
04: Factoring Techniques
4.01: Greatest Common Factor
4.02: Factoring by Grouping
4.03: Factoring Trinomials
4.04: Factoring Differences of Squares
4.05: Factoring Sums and Differences of Cubes
4.06: Factoring Expressions Using the Rational Roots Theorem
4.07: Factoring Expressions Involving Negative Rational Exponents
4.08: Factoring Expressions that are Quadratic-in-Form
05: Simplifying Expressions
5.01: Algebraic Vocabulary and Evaluating Expressions
5.02: Laws of Exponents - Product and Quotient Rules
5.03: Laws of Exponents - Power Rules
5.04: Laws of Exponents - Zero and Negative Exponent Rules
5.05: Adding and Subtracting Polynomials
5.06: Multiplying Polynomials and the Distributive Property
5.07: Simplifying Ratios of Polynomials
5.08: Dividing Polynomials - Long Division
5.09: Dividing Polynomials - Synthetic Division
5.10: Multiplying and Dividing Rational Expressions
5.11: Adding and Subtracting Rational Expressions
5.12: Simplifying Compound Rational Expressions
5.13: Simplifying Products of Radical Expressions
5.14: Simplifying Sums and Differences of Radical Expressions
5.15: Rationalizing Denominators and Numerators Simplifying Quotients of Radical Expressions
5.16: Simplifying Expressions Involving Positive Rational Exponents
5.17: Simplifying Expressions Involving Negative Rational Exponents
06: Solving Equations
6.01: Solving Literal Equations
6.02: Solving Linear Equations
6.03: Solving Absolute Value Equations
6.04: Solving Quadratic Equations by Factoring
6.05: Solving Quadratic Equations Using Extraction of Roots
6.06: Solving Quadratic Equations by Completing the Square
6.07: Solving Quadratic Equations Using the Quadratic Formula
6.08: Applications Involving Quadratic Equations
6.09: Solving Polynomial Equations
6.10: Solving Rational Equations
6.11: Solving Radical Equations
6.12: Solving Exponential Equations
6.13: Solving Logarithmic Equations
6.14: Solving Equations Quadratic-in-Form
07: Solving Inequalities
7.01: Solving Linear Inequalities
7.02: Solving Compound Inequalities
7.03: Solving Absolute Value Inequalities
7.04: Solving Quadratic Inequalities
7.05: Solving Polynomial Inequalities
7.06: Solving Rational Inequalities
7.07: Solving Exponential Inequalities
7.08: Solving Logarithmic Inequalities
08: Graphs
8.01: The Cartesian Coordinate System and the Quadrants
8.02: Ordered Pairs and Graphing Relations by Point-Plotting
8.03: Read Values from Graphs
09: An Overview of Functions
9.01: Relations and Mappings
9.02: The Definition of a Function
9.03: Evaluating Functions
9.04: The Domain and Range of a Function
9.4.01: Handouts
9.4.02: Labs and Worksheets
9.05: Function Arithmetic and Domain
9.06: The Difference Quotient
9.07: Function Composition and Domain
9.08: Inverse Functions
9.09: Restricting Domains and Forcing Invertibility
10: Graphing Functions
10.01: Intercepts and Base Graphs
10.1.01: Handouts
10.1.02: Labs
10.02: Symmetry
10.03: Intervals of Increase and Decrease
10.04: Local Relative and Global Absolute Extrema
10.05: Transformations - Rigid Transformations
10.06: Transformations - Non-Rigid Transformations
10.07: Transformations - Combining Transformations
10.08: Piecewise Functions
10.8.01: Handouts
10.8.02: Labs and Worksheets
11: Linear Functions
11.01: The Slope of a Line
11.02: Equations of Lines - Slope-Intercept Form
11.03: Equations of Lines - Point-Slope Form
11.04: Graphing Linear Equations
11.05: Linear Models
11.06: The Average Rate of Change of a Function
11.07: Parallel and Perpendicular Lines
11.08: Graphing Linear Inequalities in Two Variables
12: Linear Systems
12.01: The Concepts Behind Systems of Equations
12.02: Solving 2x2 Systems of Linear Equations - Substitution Method
12.03: Solving 2x2 Systems of Linear Equations - Elimination Method
12.04: Solving 3x3 Systems of Linear Equations
12.05: Applications Involving Systems of Linear Equations
12.06: Graphing Systems of Linear Inequalities
13: Quadratic Functions
13.01: The Basics of Quadratic Functions and Vertex Form
13.02: Graphing Quadratic Functions Using Properties
13.03: Graphing Quadratic Functions Using Transformations
13.04: Applications Involving Quadratic Functions
13.05: The Discriminant
14: Polynomial Functions
14.01: Power Functions
14.02: The Basics of Polynomial Functions
14.03: The Factor and Remainder Theorems
14.04: Complex Zeros and the Fundamental Theorem of Algebra
14.05: Graphing Polynomial Functions
14.06: Applications Involving Polynomial Functions
14.07: Pascal's Triangle
14.08: The Binomial Theorem
15: Rational Functions
15.01: Asymptotes
15.02: Graphing Rational Functions
15.03: Applications Involving Rational Functions
15.04: Partial Fraction Decomposition
16: Radical Functions
16.01: Graphing Higher-Indexed Radical Functions
16.02: Applications Involving Radical Functions
17: Exponential Functions
17.01: The Basics of Exponential Functions
17.02: Graphing Exponential Functions
17.03: Finding Equations of Exponential Functions
17.04: Applications Involving Exponential Functions
18: Logarithmic Functions
18.01: The Basics of Logarithmic Functions
18.02: Laws of Logarithms - Product and Quotient Laws
18.03: Laws of Logarithms - Power Law
18.04: Laws of Logarithms - Change of Base Formula
18.05: Graphing Logarithmic Functions
18.06: Applications Involving Logarithmic Functions
19: Absolute Value Functions
19.01: The Absolute Value Function
19.02: Graphing the Composition of a Function and the Absolute Value Function
20: Hyperbolic Functions
20.01: The Basics of Hyperbolic Functions
20.02: Graphing Hyperbolic Functions
20.03: Hyperbolic Identities and Proofs Involving Hyperbolic Functions
20.04: Applications Involving Hyperbolic Functions
20.05: Inverse Hyperbolic Functions
21: Matrices
21.01: Introduction to Matrices
21.02: Solving Large Systems Using Gaussian Elimination
21.03: Matrix Operations - Addition Subtraction and Scalar Multiplication
21.04: Matrix Operations - Matrix Multiplication
21.05: Inverse Matrices
21.06: Determinants
21.07: Cramer's Rule
22: Conic Sections
22.01: Circles - Equations and Graphs
22.02: Parabolas
22.03: Ellipses
22.04: Hyperbolas
23: Nonlinear Systems
23.01: Graphing Nonlinear Inequalities in Two Variables
23.02: Solving Systems of Nonlinear Equations
23.03: Graphing Systems of Nonlinear Inequalities
24: Sequences and Series
24.01: The Basics of Sequences
24.02: Arithmetic Sequences
24.03: Geometric Sequences
24.04: Summations and Their Properties
24.05: Partial Sums of Arithmetic Sequences
24.06: Partial Sums of Geometric Sequences
24.07: Geometric Series
25: Mathematical Induction
25.01: Mathematical Induction - Summation Proofs
25.02: Mathematical Induction - Divisibility Proofs
25.03: Mathematical Induction - Inequality Proofs
26: Trigonometry
26.01: Angles on the Coordinate Plane
26.02: Trigonometric Functions - Coordinate Definition
26.03: Evaluating Trigonometric Functions at Special Angles
26.04: Evaluating Trigonometric Functions Using Technology
26.05: Trigonometric Identities - The Reciprocal and Ratio Identities
26.06: Trigonometric Identities - The Symmetry and Cofunction Identities
26.07: Trigonometric Identities - The Pythagorean Identities
26.08: Trigonometric Functions - Right Triangle Definition
26.09: Solving Right Triangles
26.10: Applications Involving Right Triangle Trigonometry
26.11: Converting Between Degrees and Radians
26.12: Reference Angles
26.13: Arc Length
26.14: Trigonometric Functions - Unit Circle Definition
26.15: Sector Area
26.16: Linear and Angular Velocity
26.17: Base Graphs of the Trigonometric Functions
26.18: Non-Rigid Transformations
26.19: Rigid Transformations
26.20: Combining Transformations
26.21: Sinusoidal Models
26.22: Harmonic Motion
26.23: Damped Harmonic Motion
26.24: Trigonometric Identities - Sum and Difference of Angles Identities
26.25: Trigonometric Identities - Harmonic Addition Formula
26.26: Trigonometric Identities - Double-Angle Identities
26.27: Trigonometric Identities - Half-Angle and Power Reduction Identities
26.28: Trigonometric Identities - Sum-to-Product and Product-to-Sum Identities
26.29: The Inverse Trigonometric Functions
26.30: Solving Basic Trigonometric Equations
26.31: Solving Trigonometric Equations Involving Multiple Angles
26.32: Solving Trigonometric Equations Using Identities
26.33: Law of Sines
26.34: Law of Cosines
26.35: Areas and Heron's Formula
27: Vectors
27.01: A Geometric Approach to Vectors
27.02: An Algebraic Approach to Vectors
27.03: Applications Involving Vectors
28: Parametric and Polar Curves
28.01: Parametric Curves
28.02: Graphing Parametric Curves
28.03: Eliminating the Parameter
28.04: Polar Coordinates
28.05: Polar Equations
28.06: Graphs of Polar Functions
28.07: Polar Forms of Complex Numbers
28.08: Powers and Roots of Complex Numbers
29: Miscellaneous Applications
29.01: Rates Unit Rates and Uniform Motion (Distance Rate Time)
29.02: Shared Work Problems
29.03: Mixture Problems
29.04: Simple and Compound Interest
29.05: Variation - Direct Inverse and Joint
29.06: Data Modeling and Regression