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- Book: Prealgebra (OpenStax)
- 1: Whole Numbers
- 1.1: Introduction to Whole Numbers (Part 1)
- 1.1: Introduction to Whole Numbers (Part 2)
- 1.2: Add Whole Numbers (Part 1)
- 1.2: Add Whole Numbers (Part 2)
- 1.3: Subtract Whole Numbers (Part 1)
- 1.3: Subtract Whole Numbers (Part 2)
- 1.4: Multiply Whole Numbers (Part 1)
- 1.4: Multiply Whole Numbers (Part 2)
- 1.5: Divide Whole Numbers (Part 1)
- 1.5: Divide Whole Numbers (Part 2)
- 1.E: Whole Numbers (Exercises)
- 1.S: Whole Numbers (Summary)
- 2: Introduction to the Language of Algebra
- 2.1: Use the Language of Algebra (Part 1)
- 2.1: Use the Language of Algebra (Part 2)
- 2.2: Evaluate, Simplify, and Translate Expressions (Part 1)
- 2.2: Evaluate, Simplify, and Translate Expressions (Part 2)
- 2.3: Solving Equations Using the Subtraction and Addition Properties of Equality (Part 1)
- 2.3: Solving Equations Using the Subtraction and Addition Properties of Equality (Part 2)
- 2.4: Find Multiples and Factors (Part 1)
- 2.4: Find Multiples and Factors (Part 2)
- 2.5: Prime Factorization and the Least Common Multiple (Part 1)
- 2.5: Prime Factorization and the Least Common Multiple (Part 2)
- 2.E: Introduction to the Language of Algebra (Exercises)
- 2.S: Introduction to the Language of Algebra (Summary)
- 3: Integers
- 3.1: Introduction to Integers (Part 1)
- 3.1: Introduction to Integers (Part 2)
- 3.2: Add Integers (Part 1)
- 3.2: Add Integers (Part 2)
- 3.3: Subtract Integers (Part 1)
- 3.3: Subtract Integers (Part 2)
- 3.4: Multiply and Divide Integers (Part 1)
- 3.4: Multiply and Divide Integers (Part 2)
- 3.5: Solve Equations Using Integers; The Division Property of Equality (Part 1)
- 3.5: Solve Equations Using Integers; The Division Property of Equality (Part 2)
- 3.E: Integers (Exercises)
- 3.S: Integers (Summary)
- 4: Fractions
- 4.1: Visualize Fractions (Part 1)
- 4.1: Visualize Fractions (Part 2)
- 4.2: Multiply and Divide Fractions (Part 1)
- 4.2: Multiply and Divide Fractions (Part 2)
- 4.3: Multiply and Divide Mixed Numbers and Complex Fractions (Part 1)
- 4.3: Multiply and Divide Mixed Numbers and Complex Fractions (Part 2)
- 4.4: Add and Subtract Fractions with Common Denominators
- 4.5: Add and Subtract Fractions with Different Denominators (Part 1)
- 4.5: Add and Subtract Fractions with Different Denominators (Part 2)
- 4.6: Add and Subtract Mixed Numbers (Part 1)
- 4.6: Add and Subtract Mixed Numbers (Part 2)
- 4.7: Solve Equations with Fractions (Part 1)
- 4.7: Solve Equations with Fractions (Part 2)
- 4.E: Fractions (Exercises)
- 4.S: Fractions (Summary)
- 5: Decimals
- 5.1: Decimals (Part 1)
- 5.1: Decimals (Part 2)
- 5.2: Decimal Operations (Part 1)
- 5.2: Decimal Operations (Part 2)
- 5.3: Decimals and Fractions (Part 1)
- 5.3: Decimals and Fractions (Part 2)
- 5.4: Solve Equations with Decimals
- 5.5: Averages and Probability (Part 1)
- 5.5: Averages and Probability (Part 2)
- 5.6: Ratios and Rate (Part 1)
- 5.6: Ratios and Rate (Part 2)
- 5.7: Simplify and Use Square Roots (Part 1)
- 5.7: Simplify and Use Square Roots (Part 2)
- 5.E: Decimals (Exercises)
- 5.S: Decimals (Summary)
- 6: Percents
- 6.1: Understand Percent
- 6.2: Solve General Applications of Percent
- 6.3: Solve Sales Tax, Commission, and Discount Applications
- 6.4: Solve Simple Interest Applications
- 6.5: Solve Proportions and their Applications (Part 1)
- 6.5: Solve Proportions and their Applications (Part 2)
- 6.E: Percents (Exercises)
- 6.S: Percents (Summary)
- 7: The Properties of Real Numbers
- 7.1: Rational and Irrational Numbers
- 7.2: Commutative and Associative Properties (Part 1)
- 7.2: Commutative and Associative Properties (Part 2)
- 7.3: Distributive Property
- 7.4: Properties of Identity, Inverses, and Zero
- 7.5: Systems of Measurement (Part 1)
- 7.5: Systems of Measurement (Part 2)
- 7.E: The Properties of Real Numbers (Exercises)
- 7.S: The Properties of Real Numbers (Summary)
- 8: Solving Linear Equations
- 8.1: Solve Equations Using the Subtraction and Addition Properties of Equality (Part 1)
- 8.1: Solve Equations Using the Subtraction and Addition Properties of Equality (Part 2)
- 8.2: Solve Equations Using the Division and Multiplication Properties of Equality
- 8.3: Solve Equations with Variables and Constants on Both Sides (Part 1)
- 8.3: Solve Equations with Variables and Constants on Both Sides (Part 2)
- 8.4: Solve Equations with Fraction or Decimal Coefficients
- 8.E: Solving Linear Equations (Exercises)
- 8.S: Solving Linear Equations (Summary)
- 9: Math Models and Geometry
- 9.1: Use a Problem Solving Strategy (Part 1)
- 9.1: Use a Problem Solving Strategy (Part 2)
- 9.2: Solve Money Applications
- 9.3: Use Properties of Angles, Triangles, and the Pythagorean Theorem (Part 1)
- 9.3: Use Properties of Angles, Triangles, and the Pythagorean Theorem (Part 2)
- 9.4: Use Properties of Rectangles, Triangles, and Trapezoids (Part 1)
- 9.4: Use Properties of Rectangles, Triangles, and Trapezoids (Part 2)
- 9.5: Solve Geometry Applications: Circles and Irregular Figures
- 9.6: Solve Geometry Applications: Volume and Surface Area (Part 1)
- 9.6: Solve Geometry Applications: Volume and Surface Area (Part 2)
- 9.7: Solve a Formula for a Specific Variable
- 9.E: Math Models and Geometry (Exercises)
- 9.S: Math Models and Geometry (Summary)
- 10: Polynomials
- 10.1: Add and Subtract Polynomials
- 10.2: Use Multiplication Properties of Exponents (Part 1)
- 10.2: Use Multiplication Properties of Exponents (Part 2)
- 10.3: Multiply Polynomials (Part 1)
- 10.3: Multiply Polynomials (Part 2)
- 10.4: Divide Monomials (Part 1)
- 10.4: Divide Monomials (Part 2)
- 10.5: Integer Exponents and Scientific Notation (Part 1)
- 10.5: Integer Exponents and Scientific Notation (Part 2)
- 10.6: Introduction to Factoring Polynomials
- 10.E: Polynomials (Exercises)
- 10.S: Polynomials (Summary)
- 11: Graphs
- 11.1: Use the Rectangular Coordinate System (Part 1)
- 11.1: Use the Rectangular Coordinate System (Part 2)
- 11.2: Graphing Linear Equations (Part 1)
- 11.2: Graphing Linear Equations (Part 2)
- 11.3: Graphing with Intercepts (Part 1)
- 11.3: Graphing with Intercepts (Part 2)
- 11.4: Understand Slope of a Line (Part 1)
- 11.4: Understand Slope of a Line (Part 2)
- 11.E: Graphs (Exercises)
- 11.S: Graphs (Summary)
- Appendix
- 1: Whole Numbers
- Algebra
- Supplemental Modules (Algebra)
- Book: Intermediate Algebra (OpenStax)
- Map: College Algebra (OpenStax)
- 1: Prerequisites
- 2: Equations and Inequalities
- 3: Functions
- 4: Linear Functions
- 5: Polynomial and Rational Functions
- 5.1: Prelude to Polynomial and Rational Functions
- 5.2: Quadratic Functions
- 5.3: Power Functions and Polynomial Functions
- 5.4: Graphs of Polynomial Functions
- 5.5: Dividing Polynomials
- 5.6: Zeros of Polynomial Functions
- 5.7: Rational Functions
- 5.8: 5.7 Inverses and Radical Functions
- 5.9: Modeling Using Variation
- 6: Exponential and Logarithmic Functions
- 6.1: Prelude to Exponential and Logarithmic Functions
- 6.2: Exponential Functions
- 6.3: Graphs of Exponential Functions
- 6.4: Logarithmic Functions
- 6.5: Graphs of Logarithmic Functions
- 6.6: Logarithmic Properties
- 6.7: Exponential and Logarithmic Equations
- 6.8: Exponential and Logarithmic Models
- 6.9: Fitting Exponential Models to Data
- 7: Systems of Equations and Inequalities
- 7.1: Prelude to Systems of Equations and Inequalities
- 7.2: Systems of Linear Equations - Two Variables
- 7.3: Systems of Linear Equations with Three Variables
- 7.4: Systems of Nonlinear Equations and Inequalities - Two Variables
- 7.5: Partial Fractions
- 7.6: Matrices and Matrix Operations
- 7.7: Solving Systems with Gaussian Elimination
- 7.8: Solving Systems with Inverses
- 7.9: Solving Systems with Cramer's Rule
- 8: Analytic Geometry
- 9: Sequences, Probability, and Counting Theory
- Book: Algebra and Trigonometry (OpenStax)
- 1: Prerequisites
- 2: Equations and Inequalities
- 3: Functions
- 4: Linear Functions
- 5: Polynomial and Rational Functions
- 6: Exponential and Logarithmic Functions
- 6.1: Prelude to Exponential and Logarithmic Functions
- 6.2: Exponential Functions
- 6.3: Graphs of Exponential Functions
- 6.4: Logarithmic Functions
- 6.5: Graphs of Logarithmic Functions
- 6.6: Logarithmic Properties
- 6.7: Exponential and Logarithmic Equations
- 6.8: Exponential and Logarithmic Models
- 6.9: Fitting Exponential Models to Data
- 7: The Unit Circle - Sine and Cosine Functions
- 8: Periodic Functions
- 9: Trigonometric Identities and Equations
- 10: Further Applications of Trigonometry
- 11: Systems of Equations and Inequalities
- 11.0: Prelude to Systems of Equations and Inequalities
- 11.2: Systems of Linear Equations - Two Variables
- 11.3: Systems of Linear Equations with Three Variables
- 11.4: Systems of Nonlinear Equations and Inequalities - Two Variables
- 11.5: Partial Fractions
- 11.6: Matrices and Matrix Operations
- 11.7: Solving Systems with Gaussian Elimination
- 11.8: Solving Systems with Inverses
- 11.9: Solving Systems with Cramer's Rule
- 12: Analytic Geometry
- 13: Sequences, Probability, and Counting Theory
- Precalculus
- Map: Precalculus (OpenStax)
- 1: Functions
- 2: Linear Functions
- 3: Polynomial and Rational Functions
- 3.0: Prelude to Polynomial and Rational Functions
- 3.1: Complex Numbers
- 3.2: Quadratic Functions
- 3.3: Power Functions and Polynomial Functions
- 3.4: Graphs of Polynomial Functions
- 3.5: Dividing Polynomials
- 3.6: Zeros of Polynomial Functions
- 3.7: Rational Functions
- 3.8: Inverses and Radical Functions
- 3.9: Modeling Using Variation
- 4: Exponential and Logarithmic Functions
- 4.0: Prelude to Exponential and Logarithmic Functions
- 4.1: Exponential Functions
- 4.2: Graphs of Exponential Functions
- 4.3: Logarithmic Functions
- 4.4: Graphs of Logarithmic Functions
- 4.5: Logarithmic Properties
- 4.6: Exponential and Logarithmic Equations
- 4.7: Exponential and Logarithmic Models
- 4.8: Fitting Exponential Models to Data
- 5: Trigonometric Functions
- 6: Periodic Functions
- 7: Trigonometric Identities and Equations
- 7.0: Prelude to Trigonometric Identities and Equations
- 7.1: Solving Trigonometric Equations with Identities
- 7.2: Sum and Difference Identities
- 7.3: Double-Angle, Half-Angle, and Reduction Formulas
- 7.4: Sum-to-Product and Product-to-Sum Formulas
- 7.5: Solving Trigonometric Equations
- 7.6: Modeling with Trigonometric Equations
- 7.E: Trigonometric Identities and Equations (Exercises)
- 8: Further Applications of Trigonometry
- 8.0: Prelude to Further Applications of Trigonometry
- 8.1: Non-right Triangles: Law of Sines
- 8.2: Non-right Triangles - Law of Cosines
- 8.3: Polar Coordinates
- 8.4: Polar Coordinates - Graphs
- 8.5: Polar Form of Complex Numbers
- 8.6: Parametric Equations
- 8.7: Parametric Equations - Graphs
- 8.8: Vectors
- 8.E: Further Applications of Trigonometry (Exercises)
- 9: Systems of Equations and Inequalities
- 9.0: Prelude to Systems of Equations and Inequalities
- 9.1: Systems of Linear Equations: Two Variables
- 9.2: Systems of Linear Equations: Three Variables
- 9.3: Systems of Nonlinear Equations and Inequalities - Two Variables
- 9.4: Partial Fractions
- 9.5: Matrices and Matrix Operations
- 9.6: Solving Systems with Gaussian Elimination
- 9.7: Solving Systems with Inverses
- 9.8: Solving Systems with Cramer's Rule
- 9.E: Systems of Equations and Inequalities (Exercises)
- 10: Analytic Geometry
- 11: Sequences, Probability and Counting Theory
- 12: Introduction to Calculus
- A: Appendix
- Map: Precalculus (Stitz-Zeager)
- 1: Relations and Functions
- 2: Linear and Quadratic Functions
- 3: Polynomial Functions
- 4: Rational Functions
- 5: Further Topics in Functions
- 6: Exponential and Logarithmic Functions
- 7: Hooked on Conics
- 8: Systems of Equations and Matrices
- 8.1: Systems of Linear Equations: Gaussian Elimination
- 8.2: Systems of Linear Equations: Augmented Matrices
- 8.3: Matrix Arithmetic
- 8.4: Systems of Linear Equations: Matrix Inverses
- 8.5: Determinants and Cramer’s Rule
- 8.6: Partial Fraction Decomposition
- 8.7: Systems of Non-Linear Equations and Inequalities
- 8.E: Systems of Equations and Matrices (Exercises)
- 9: Sequences and the Binomial Theorem
- 10: Foundations of Trigonometry
- 10.1: Angles and their Measure
- 10.2: The Unit Circle: Cosine and Sine
- 10.3: The Six Circular Functions and Fundamental Identities
- 10.4: Trigonometric Identities
- 10.5: Graphs of the Trigonometric Functions
- 10.6: The Inverse Trigonometric Functions
- 10.7: Trigonometric Equations and Inequalities
- 10.E: Foundations of Trigonometry (Exercises)
- 11: Applications of Trigonometry
- 11.1: Applications of Sinusoids
- 11.2: The Law of Sines
- 11.3: The Law of Cosines
- 11.4: Polar Coordinates
- 11.5: Graphs of Polar Equations
- 11.6: Hooked on Conics Again
- 11.7: Polar Form of Complex Numbers
- 11.8: Vectors
- 11.9: The Dot Product and Projection
- 11.10: Parametric Equations
- 11.E: Applications of Trigonometry (Exercises)
- Map: Elementary Trigonometry (Corral)
- Book: Precalculus - An Investigation of Functions (Lippman and Rasmussen)
- 1: Functions
- 2: Linear Functions
- 3: Polynomial and Rational Functions.
- 4: Exponential and Logarithmic Functions
- 5: Trigonometric Functions of Angles
- 6: Periodic Functions
- 7: Trigonometric Equations and Identities
- 8: Further Applications of Trigonometry
- 9: Conics
- Map: Precalculus (OpenStax)
- Calculus
- Supplemental Modules (Calculus)
- Differential Calculus
- Integral Calculus
- 1: Area and Volume
- 2: Techniques of Integration
- 3: L'Hopital's Rule and Improper Integrals
- 4: Transcendental Functions
- 5: Work and Force
- 6: Moments and Centroids
- Vector Calculus
- 1: Vector Basics
- 2: Vector-Valued Functions and Motion in Space
- 3: Multiple Integrals
- 3.1: Double and Iterated Integrals Over Rectangles
- 3.2: Area by Double Integration
- 3.3: Double Integrals Over General Regions
- 3.4: Double Integrals in Polar Form
- 3.5: Triple Integrals in Rectangular Coordinates
- 3.6: Triple Integrals in Cylindrical and Spherical Coordinates
- 3.7: Moments and Centers of Mass
- 3.8: Jacobians
- 3.9: Substitutions in Multiple Integrals
- 4: Integration in Vector Fields
- 4.1: Differentiation and Integration of Vector Valued Functions
- 4.2: Surfaces and Area
- 4.3: Line Integrals
- 4.4: Conservative Vector Fields and Independence of Path
- 4.5: Path Independence, Conservative Fields, and Potential Functions
- 4.6: Vector Fields and Line Integrals: Work, Circulation, and Flux
- 4.7: Surface Integrals
- 4.8: Green’s Theorem in the Plane
- 4.9: The Divergence Theorem and a Unified Theory
- 4.10: Stokes’ Theorem
- Multivariable Calculus
- Book: Calculus (OpenStax)
- 1: Functions and Graphs
- 2: Limits
- 3: Derivatives
- 3.0: Prelude to Derivatives
- 3.1: Defining the Derivative
- 3.2: The Derivative as a Function
- 3.3: Differentiation Rules
- 3.4: Derivatives as Rates of Change
- 3.5: Derivatives of Trigonometric Functions
- 3.6: The Chain Rule
- 3.7: Derivatives of Inverse Functions
- 3.8: Implicit Differentiation
- 3.9: Derivatives of Exponential and Logarithmic Functions
- 3.E: Derivatives (Exercises)
- 3.S: Derivatives (Summary)
- 4: Applications of Derivatives
- 4.0: Prelude to Applications of Derivatives
- 4.1: Related Rates
- 4.2: Linear Approximations and Differentials
- 4.3: Maxima and Minima
- 4.4: The Mean Value Theorem
- 4.5: Derivatives and the Shape of a Graph
- 4.6: Limits at Infinity and Asymptotes
- 4.7: Applied Optimization Problems
- 4.8: L’Hôpital’s Rule
- 4.9: Newton’s Method
- 4.10: Antiderivatives
- 4.E: Applications of Derivatives (Exercises)
- 5: Integration
- 5.1: Approximating Areas
- 5.2: The Definite Integral
- 5.3: The Fundamental Theorem of Calculus
- 5.4: Integration Formulas and the Net Change Theorem
- 5.5: Substitution
- 5.6: Integrals Involving Exponential and Logarithmic Functions
- 5.7: Integrals Resulting in Inverse Trigonometric Functions
- 5.E: Integration (Exercises)
- 6: Applications of Integration
- 6.0: Prelude to Applications of Integration
- 6.1: Areas between Curves
- 6.2: Determining Volumes by Slicing
- 6.3: Volumes of Revolution: Cylindrical Shells
- 6.4: Arc Length of a Curve and Surface Area
- 6.5: Physical Applications of Integration
- 6.6: Moments and Centers of Mass
- 6.7: Integrals, Exponential Functions, and Logarithms
- 6.8: Exponential Growth and Decay
- 6.9: Calculus of the Hyperbolic Functions
- 6.E: Applications of Integration (Exercises)
- 7: Techniques of Integration
- 8: Introduction to Differential Equations
- 9: Sequences and Series
- 10: Power Series
- 11: Parametric Equations & Polar Coordinates
- 12: Vectors in Space
- 13: Vector-Valued Functions
- 14: Differentiation of Functions of Several Variables
- 14.0: Prelude to Differentiation of Functions of Several Variables
- 14.1: Functions of Several Variables
- 14.2: Limits and Continuity
- 14.3: Partial Derivatives
- 14.4: Tangent Planes and Linear Approximations
- 14.5: The Chain Rule for Multivariable Functions
- 14.6: Directional Derivatives and the Gradient
- 14.7: Maxima/Minima Problems
- 14.8: Lagrange Multipliers
- 14.E: Differentiation of Functions of Several Variables (Exercises)
- 15: Multiple Integration
- 15.0: Prelude to Multiple Integration
- 15.1: Double Integrals over Rectangular Regions
- 15.2: Double Integrals over General Regions
- 15.3: Double Integrals in Polar Coordinates
- 15.4: Triple Integrals
- 15.5: Triple Integrals in Cylindrical and Spherical Coordinates
- 15.6: Calculating Centers of Mass and Moments of Inertia
- 15.7: Change of Variables in Multiple Integrals
- 15.E: Multiple Integration (Exercises)
- 16: Vector Calculus
- 17: Second-Order Differential Equations
- Appendices
- Book: Active Calculus (Boelkins et al.)
- 1: Understanding the Derivative
- 1.1: How do we Measure Velocity?
- 1.2: The Notion of Limit
- 1.3: The Derivative of a Function at a Point
- 1.4: The Derivative Function
- 1.5: Interpretating, Estimating, and Using the Derivative
- 1.6: The Second Derivative
- 1.7: Limits, Continuity, and Differentiability
- 1.8: The Tangent Line Approximation
- 1.E: Understanding the Derivative (Exercises)
- 2: Computing Derivatives
- 2.1: Elementary Derivative Rules
- 2.2: The Sine and Cosine Function
- 2.3: The Product and Quotient Rules
- 2.4: Derivatives of Other Trigonometric Functions
- 2.5: The Chain Rule
- 2.6: Derivatives of Inverse Functions
- 2.7: Derivatives of Functions Given Implicitely
- 2.8: Using Derivatives to Evaluate Limits
- 2.E: Computing Derivatives (Exercises)
- 3: Using Derivatives
- 4: The Definite Integral
- 5: Finding Antiderivatives and Evaluating Integrals
- 6: Using Definite Integrals
- 7: Differential Equations
- 8: Sequences and Series
- 9: Multivariable and Vector Functions
- 10: Derivatives of Multivariable Functions
- 11: Multiple Integrals
- 1: Understanding the Derivative
- Book: Calculus (Guichard)
- 1: Analytic Geometry
- 2: Instantaneous Rate of Change: The Derivative
- 3: Rules for Finding Derivatives
- 4: Transcendental Functions
- 4.1: Trigonometric Functions
- 4.2: The Derivative of 1/sin x
- 4.3: A Hard Limit
- 4.4: The Derivative of sin x - II
- 4.5: Derivatives of the Trigonometric Functions
- 4.6: Exponential and Logarithmic Functions
- 4.7: Derivatives of the Exponential and Logarithmic Functions
- 4.8: Implicit Differentiation
- 4.9: Inverse Trigonometric Functions
- 4.10: Limits Revisited
- 4.11: Hyperbolic Functions
- 4.E: Transcendental Functions (Exercises)
- 5: Curve Sketching
- 6: Applications of the Derivative
- 7: Integration
- 8: Techniques of Integration
- 9: Applications of Integration
- 10: Polar Coordinates & Parametric Equations
- 11: Sequences and Series
- 11.0: Prelude to Sequences and Series
- 11.1: Sequences
- 11.2: Series
- 11.3: The Integral Test
- 11.4: Alternating Series
- 11.5: Comparison Test
- 11.6: Absolute Convergence
- 11.7: The Ratio and Root Tests
- 11.8: Power Series
- 11.9: Calculus with Power Series
- 11.10: Taylor Series
- 11.11: Taylor's Theorem
- 11.12: Additional Exercises
- 11.E: Sequences and Series (Exercises)
- 12: Three Dimensions
- 13: Vector Functions
- 14: Partial Differentiation
- 15: Multiple Integration
- 16: Vector Calculus
- 17: Differential Equations
- Book: Calculus (Apex)
- 1: Limits
- 2: Derivatives
- 3: The Graphical Behavior of Functions
- 4: Applications of the Derivative
- 5: Integration
- 6: Techniques of Integration
- 7: Applications of Integration
- 8: Sequences and Series
- 9: Curves in the Plane
- 10: Vectors
- 11: Vector-Valued Functions
- 12: Functions of Several Variables
- 12.1: Introduction to Multivariable Functions
- 12.2: Limits and Continuity of Multivariable Functions
- 12.3: Partial Derivatives
- 12.4: Differentiability and the Total Differential
- 12.5: The Multivariable Chain Rule
- 12.6: Directional Derivatives
- 12.7: Tangent Lines, Normal Lines, and Tangent Planes
- 12.8: Extreme Values
- 12.E: Applications of Functions of Several Variables (Exercises)
- 13: Multiple Integration
- 14: Appendix
- Map: Calculus - Early Transcendentals (Stewart)
- 1: Functions and Models
- 2: Limits and Derivatives
- 3: Differentiation Rules
- 3.1: Derivatives of Polynomials and Exponential Functions
- 3.2: The Product and Quotient Rules
- 3.3: Derivatives of Trigonometric Functions
- 3.4: The Chain Rule
- 3.5: Implicit Differentiation
- 3.6: Derivatives of Logarithmic Functions
- 3.7: Rates of Change in the Natural and Social Sciences
- 3.8: Exponential Growth and Decay
- 3.9: Related Rates
- 3.10: Linear Approximations and Differentials
- 3.11: Hyperbolic Functions
- 4: Applications of Differentiation
- 5: Integrals
- 6: Applications of Integration
- 7: Techniques of Integration
- 8: Further Applications of Integration
- 9: Differential Equations
- 10: Parametric Equations And Polar Coordinates
- 11: Infinite Sequences And Series
- 11.1: Sequences
- 11.2: Series
- 11.3: The Integral Test and Estimates of Sums
- 11.4: The Comparison Tests
- 11.5: Alternating Series
- 11.6: Absolute Convergence and the Ratio and Root Test
- 11.7: Strategy for Testing Series
- 11.8: Power Series
- 11.9: Representations of Functions as Power Series
- 11.10: Taylor and Maclaurin Series
- 11.11: Applications of Taylor Polynomials
- 12: Vectors and The Geometry of Space
- 13: Vector Functions
- 14: Partial Derivatives
- 15: Multiple Integrals
- 15.1: Double Integrals over Rectangles
- 15.2: Double Integrals over General Regions
- 15.3: Double Integrals in Polar Coordinates
- 15.4: Applications of Double Integrals
- 15.5: Surface Area
- 15.6: Triple Integrals
- 15.7: Triple Integrals in Cylindrical Coordinates
- 15.8: Triple Integrals in Spherical Coordinates
- 15.9: Change of Variables in Multiple Integrals
- 16: Vector Calculus
- 17: Second-Order Differential Equations
- Chapter 18
- Chapter 19
- Chapter 20
- Map: University Calculus - Early Transcendentals (Hass et al.)
- 1: Functions
- 2: Limits and Continuity
- 3: Differentiation
- 3.1: Tangents and the Derivative at a Point
- 3.2: The Derivative as a Function
- 3.3: Differentiation Rules
- 3.4: The Derivative as a Rate of Change
- 3.5: Derivatives of Trigonometric Functions
- 3.6: The Chain Rule
- 3.7: Implicit Differentiation
- 3.8: Derivatives of Inverse Functions and Logarithms
- 3.9: Inverse Trigonometric Functions
- 3.10: Related Rates
- 3.11: Linearization and Differentials
- 4: Applications of Definite Integrals
- 5: Integration
- 6: Applications of Definite Integrals
- 7: Integrals and Transcendental Functions
- 8: Techniques of Integration
- 9: Infinite Sequence and Series
- 9.10: The Binomial Series and Applications of Taylor Series
- 9.1: Sequences
- 9.2: Infinite Series
- 9.3: The Integral Test
- 9.4: Comparison Tests
- 9.5: The Ratio and Root Tests
- 9.6: Alternating Series, Absolute and Conditional Convergence
- 9.7: Power Series
- 9.8: Taylor and Maclaurin Series
- 9.9: Convergence of Taylor Series
- 10: Parametric Equations and Polar Coordinates
- 11: Vectors and the Geometry of Space
- 12: Vector-Valued Functions and Motion in Space
- 13: Partial Derivatives
- 14: Multiple Integrals
- 14.1: Double and Iterated Integrals over Rectangles
- 14.2: Double Integrals over General Regions
- 14.3: Area by Double Integration
- 14.4: Double Integrals in Polar Form
- 14.5: Triple Integrals in Rectangular Coordinates
- 14.6: Moments and Centers of Mass
- 14.7: Triple Integrals in Cylindrical and Spherical Coordinates
- 14.8: Substitutions in Multiple Integrals
- 15: Integration in Vector Fields
- 15.1: Line Integrals
- 15.2: Vector Fields and Line Integrals: Work, Circulation, and Flux
- 15.3: Path Independence, Conservative Fields, and Potential Functions
- 15.4: Green's Theorem in the Plane
- 15.5: Surfaces and Area
- 15.6: Surface Integrals
- 15.7: Stokes' Theorem
- 15.8: The Divergence Theorem and a Unified Theory
- 16: First-Order Differential Equations
- 17: Second-Order Differential Equations
- Book: Vector Calculus (Corral)
- 1: Vectors in Euclidean Space
- 2: Functions of Several Variables
- 2.1: Functions of Two or Three Variables
- 2.2: Partial Derivatives
- 2.3: Tangent Plane to a Surface
- 2.4: Directional Derivatives and the Gradient
- 2.5: Maxima and Minima
- 2.6: Unconstrained Optimization: Numerical Methods
- 2.7: Constrained Optimization - Lagrange Multipliers
- 2.E: Functions of Several Variables (Exercises)
- 3: Multiple Integrals
- 3.1: Double Integrals
- 3.2: Double Integrals Over a General Region
- 3.3: Triple Integrals
- 3.4: Numerical Approximation of Multiple Integrals
- 3.5: Change of Variables in Multiple Integrals
- 3.6: Application: Center of Mass
- 3.7: Application: Probability and Expectation Values
- 3.E: Multiple Integrals (Exercises)
- 4: Line and Surface Integrals
- Supplemental Modules (Calculus)
- Differential Equations
- Book: Differential Equations for Engineers (Lebl)
- 1: First order ODEs
- 2: Higher order linear ODEs
- 3: Systems of ODEs
- 3.1: Introduction to Systems of ODEs
- 3.2: Matrices and linear systems
- 3.3: Linear systems of ODEs
- 3.4: Eigenvalue Method
- 3.5: Two dimensional systems and their vector fields
- 3.6: Second order systems and applications
- 3.7: Multiple Eigenvalues
- 3.8: Matrix exponentials
- 3.9: Nonhomogeneous systems
- 3.E: Systems of ODEs (Exercises)
- 4: Fourier series and PDEs
- 4.1: Boundary value problems
- 4.2: The Trigonometric Series
- 4.3: More on the Fourier Series
- 4.4: Sine and cosine series
- 4.5: Applications of Fourier series
- 4.6: PDEs, separation of variables, and the heat equation
- 4.7: One dimensional wave equation
- 4.8: D’Alembert solution of the wave equation
- 4.9: Steady state temperature and the Laplacian
- 4.10: Dirichlet problem in the circle and the Poisson kernel
- 4.E: Fourier series and PDEs (Exercises)
- 5: Eigenvalue problems
- 6: The Laplace Transform
- 7: Power series methods
- 8: Nonlinear Equations
- Book: Partial Differential Equations (Walet)
- 1: Introduction to Partial Differential Equations
- 2: Classiﬁcation of Partial Diﬀerential Equations
- 3: Boundary and Initial Conditions
- 4: Fourier Series
- 5: Separation of Variables on Rectangular Domains
- 6: D’Alembert’s Solution to the Wave Equation
- 7: Polar and Spherical Coordinate Systems
- 8: Separation of Variables in Polar Coordinates
- 9: Series Solutions of ODEs (Frobenius’ Method)
- 10: Bessel Functions and Two-Dimensional Problems
- 11: Separation of Variables in Three Dimensions
- Book: Partial Differential Equations (Miersemann)
- 1: Introduction
- 2: Equations of First Order
- 2.0: Prelude to First Order Equations
- 2.1: Linear Equations
- 2.2: Quasilinear Equations
- 2.2.1: A Linearization Method
- 2.2.2: Initial Value Problem of Cauchy
- 2.3: Nonlinear Equations in Two Variables
- 2.3.1: Initial Value Problem of Cauchy
- 2.4: Nonlinear Equations in \(\mathbb{R}^n\)
- 2.5: Hamilton-Jacobi Theory
- 2.E: Equations of First Order (Exercises)
- 3: Classification
- 3.1: Linear Equations of Second Order
- 3.1.1: Normal Form in Two Variables
- 3.2: Quasilinear Equations of Second Order
- 3.2.1: Quasilinear Elliptic Equations
- 3.3: Systems of First Order
- 3.3.1: Examples
- 3.4: Systems of Second Order
- 3.4.1: Examples
- 3.5: Theorem of Cauchy-Kovalevskaya
- 3.5.1 Appendix: Real Analytic Functions
- 3.E: Classification (Exercises)
- 4: Hyperbolic Equations
- 4.1: One-Dimensional Wave Equation
- 4.2: Higher Dimensions
- 4.2.1: Case n=3
- 4.2.2: Case n=2
- 4.3: Inhomogeneous Equations
- 4.4: A Method of Riemann
- 4.5: Initial-Boundary Value Problems
- 4.5.1: Oscillation of a String
- 4.5.2: Oscillation of a Membrane
- 4.5.3: Inhomogeneous Wave Equations
- 4.E: 4: Hyperbolic Equations (Exercises)
- 5: Fourier Transform
- 6: Parabolic Equations
- 7: Elliptic Equations of Second Order
- 7.1: Fundamental Solution
- 7.2: Representation Formula
- 7.2.1: Conclusions from the Representation Formula
- 7.3.1: Boundary Value Problems: Dirichlet Problem
- 7.3.2: Boundary Value Problems: Neumann Problem
- 7.3.3: Boundary Value Problems: Mixed Boundary Value Problem
- 7.4: Green's Function for \(\Delta\)
- 7.4.1: Green's Function for a Ball
- 7.4.2: Green's Function and Conformal Mapping
- 7.5: Inhomogeneous Equation
- 7.E: Elliptic Equations of Second Order (Exercises)
- Bibliography
- Book: Differential Equations for Engineers (Lebl)
- Linear Algebra
- Book: Linear Algebra (Waldron, Cherney, & Denton)
- 1: What is Linear Algebra?
- 2: Systems of Linear Equations
- 3: The Simplex Method
- 4: Vectors in Space, n-Vectors
- 5: Vector Spaces
- 6: Linear Transformations
- 7: Matrices
- 8: Determinants
- 9: Subspaces and Spanning Sets
- 10: Linear Independence
- 11: Basis and Dimension
- 12: Eigenvalues and Eigenvectors
- 13: Diagonalization
- 14: Orthonormal Bases and Complements
- 15: Diagonalizing Symmetric Matrices
- 16: Kernel, Range, Nullity, Rank
- 17: Least Squares and Singular Values
- Appendices: Symbols, Fields, Sample Exams, Online Resources, Movie Scripts Edit section
- Book: Linear Algebra (Schilling, Nachtergaele and Lankham)
- 1: What is linear algebra
- 2: Introduction to complex numbers
- 3. The fundamental theorem of algebra and factoring polynomials
- 4. Vector spaces
- 5: Span and Bases
- 6. Linear Maps
- 7: Eigenvalues and Eigenvectors
- 8. Permutations and the Determinant
- 9. Inner product spaces
- 10. Change of bases
- 11. The Spectral Theorem for normal linear maps
- 12. Supplementary notes on matrices and linear systems
- 13. Appendices
- Book: Linear Algebra (Waldron, Cherney, & Denton)
- Analysis
- Supplemental Modules (Analysis)
- Ordinary Differential Equations
- 1: ODE Fundamentals
- 2: First Order Differential Equations
- 2.1: Difference Equations
- 2.2: Classification of Differential Equations
- 2.3: Modeling with First Order Differential Equations
- 2.4: Separable Differential Equations
- 2.5: Autonomous Differential Equations
- 2.6: First Order Linear Differential Equations
- 2.7: Exact Differential Equations
- 2.8: Theory of Existence and Uniqueness
- 2.9: Theory of Linear vs. Nonlinear Differential Equations
- 3: Second Order Linear Differential Equations
- 3.1: Homogeneous Equations with Constant Coefficients
- 3.2: Complex Roots of the Characteristic Equation
- 3.4: Method of Undetermined Coefficients
- 3.3: Repeated Roots and Reduction of Order
- 3.5: Variation of Parameters
- 3.6: Linear Independence and the Wronskian
- 3.7: Uniqueness and Existence for Second Order Differential Equations
- 4: Applications and Higher Order Differential Equations
- 5: Systems of Differential Equations
- 6: Power Series and Laplace Transforms
- 6.1: Review of Power Series
- 6.2: Series Solutions to Second Order Linear Differential Equations
- 6.3: Series Solutions and Convergence
- 6.4: Regular Singular Points
- 6.5: Euler Equations
- 6.6: The Laplace Transform
- 6.7: Using the Laplace Transform to Solve Initial Value Problems
- 6.8: Step Functions
- 6.9: Discontinuous Forcing
- Partial Differential Equations
- Series and Expansions
- Ordinary Differential Equations
- Book: Introduction to Real Analysis (Lebl)
- Book: Real Analysis (Boman & Rogers)
- Prelude to Real Analysis
- 1: Numbers - Real (ℝ) and Rational (ℚ)
- 2: Calculus in the 17th and 18th Centuries
- 3: Questions Concerning Power Series
- 4: Convergence of Sequences and Series
- 5: Convergence of the Taylor Series: A “Tayl” of Three Remainders
- 6: Continuity - What It Isn’t and What It Is
- 7: Intermediate and Extreme Values
- 8: Back to Power Series
- 9: Back to the Real Numbers
- Epilogue to Real Analysis
- Supplemental Modules (Analysis)
- Abstract Algebra
- Combinatorics and Discrete Mathematics
- Book: Combinatorics and Graph Theory (Guichard)
- Book: Combinatorics Through Guided Discovery (Bogart)
- Book: Discrete Mathematics (Levin)
- Number Theory
- Applied Mathematics
- Book: Introduction to Social Network Methods (Hanneman)
- 1: Social Network Data
- 2: Why Formal Methods?
- 3: Using Graphs to Represent Social Relations
- 4: Working with Netdraw to Visualize Graphs
- 5: Using Matrices to Represent Social Relations
- 6: Working with Network Data
- 7: Connection
- 8: Embedding
- 9: Ego Networks
- 10: Centrality and Power
- 11: Cliques and Sub-groups
- 12: Positions and Roles - The Idea of Equivalence
- 13: Measures of Similarity and Structural Equivalence
- 14: Automorphic Equivalence
- 15: Regular Equivalence
- 16: Multiplex Networks
- 17: Two-Mode Networks
- 18: Some Statistical Tools
- Book: Introduction to the Modeling and Analysis of Complex Systems (Sayama)
- 1: Introduction to Modeling and Analysis
- 2: Fundamentals of Modeling
- 3: Basics of Dynamical Systems
- 4: Discrete-Time Models I - Modeling
- 4.1: Discrete-Time Models with Difference Equations
- 4.2: Classiﬁcations of Model Equations
- 4.3: Simulating Discrete-Time Models with One Variable
- 4.4: Simulating Discrete-Time Models with Multiple Variables
- 4.5: Building Your Own Model Equation
- 4.6: Building Your Own Model Equations with Multiple Variables
- 5: Discrete-Time Models II - Analysis
- 5.1: Finding Equilibrium Points
- 5.2 Phase Space Visualization of Continuous-State Discrete-Time Models
- 5.3 Cobweb Plots for One-Dimensional Iterative Maps
- 5.4 Graph-Based Phase Space Visualization of Discrete-State Discrete-Time Model
- 5.5: Variable Rescaling of Discrete-Time Models
- 5.6: Asymptotic Behavior of Discrete-Time Linear Dynamical Systems
- 5.7 Linear Stability Analysis of Discrete-Time Nonlinear Dynamical Systems
- 6: Continuous-Time Models I - Modeling
- 7: Continuous-Time Models II - Analysis
- Book: Introduction to Social Network Methods (Hanneman)