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- MTH 210 Calculus I
- 1: Review: Functions and Graphs
- Chapter 2 Limits
- 2.0: Introduction
- 2.0E: Introduction Exercises
- 2.1: The Idea of Limits
- 2.1E The Idea of Limits
- 2.2: Limits of Functions
- 2.2E: Limits of Functions Exercises
- 2.3: Limit Laws
- 2.3E: Limit Laws and Techniques for Computing Limits EXERCISES
- 2.4: Infinite Limits
- 2.4E: Infinite Limits EXERCISES
- 2.5: Limits at Infinity
- 2.5E: Limits at Infinity EXERCISES
- 2.6: Continuity
- 2.6E: Continuity EXERCISES
- 2.7: The Precise Definition of a Limit
- 2.7E: Precise Definition of Limit EXERCISES
- NEW 2.3E: Limit Laws

- Chapter 3: Derivatives
- 3.0: Prelude to Derivatives
- 3.0E: Exercises
- 3.1: Definition of the Derivative
- 3.1E: Definition of the Derivative (Exercises)
- 3.2: The Derivative as a Function
- 3.2E: Derivative as a Function Exercises
- 3.3: (and 3.4) Differentiation Rules
- 3.3E: Both 3.3 and 3.4 Exercises
- 3.5: Derivatives of Trigonometric Functions
- 3.5E: Trig Derivatives Exercises
- 3.6: Derivatives as Rates of Change
- 3.6 E: Rates of Change Exercises
- 3.7: The Chain Rule
- 3.7 E: Chain Rule Exercises
- 3.8: Implicit Differentiation
- 3.8 E: Implicit Differentiation Exercises
- 3.9: Derivatives of Ln, General Exponential
- 3.9 E: Derivatives Ln, etc. Exercises
- 3. 10: Derivatives of Inverse Trig Functions
- section 3. 10 E: Inverse Trig Derivatives Exercises

- Chapter 4: Applications of Derivatives
- 4.0: Prelude to Applications of Derivatives
- 4.0E: Exercises
- 4.1: Related Rates
- 4.1E: Related Rates Exercises
- 4.2: Maxima and Minima
- 4.2E: Maxima and Minima Exercises
- 4.3: Derivatives and the Shape of a Graph
- 4.3E: Shape of the Graph Exercises
- 4.4: Graphing
- 4.4 E: Sketch the GRAPH Exercises
- 4.5: Optimization Problems
- 4.5 E: Optimization Exercises
- 4.6: Linear Approximations and Differentials
- 4.7: The Mean Value Theorem
- 4.8: Antiderivatives
- 4.8E: AntiDerivative

- Chapter 5: Integration
- 5.0: Prelude to Integration
- 5.0E: Exercises
- 5.1: Approximating Areas
- 5.1 Approximating Area (Riemann Sum) Exercises
- 5.2: The Definite Integral
- 5.2 E: Definite Integral Intro Exercises
- 5.3: The Fundamental Theorem of Calculus Basics
- 5.3 E: FTOC Exercises
- 5.4: Average Value of a Function
- 5.4E: Average Value of a Function Exercises
- 5.5: U-Substitution
- 5.5E
- 5.6: More U-Substitution - Exponential and Logarithmic Functions
- 5.6 Notes
- 5.7: Net Change
- 5.7E: Net Change Exercises
- Xtra full 5.3: includes Proof of The Fundamental Theorem of Calculus

- professor playground
- 0.0 Special Symbols
- 2.E: Limits (Exercises)
- 3.2: The Derivative as a Function
- 3.3: Differentiation Rules
- 3.4: Product
- 3.9: Derivatives of Exponential and Logarithmic Functions
- 3.E: Derivatives (ALL Chapter 3 Exercises)
- 4.6: Limits at Infinity and Asymptotes
- 4.E: Applications of Derivatives (ALL Chap 4 Exercises)
- 4.E: Open Stax 4.1 - 4.5 Exercises
- 5.2: originalThe Definite Integral
- 5.3: original The Fundamental Theorem of Calculus
- 5.4: Original Integration Formulas and the Net Change Theorem
- 5.E: Integration (Exercises)

- MTH 210 Calculus I
- Username: jhalpern
- Username: jonathan.poritz@gmail.com

- Butte College
- Borough of Manhattan Community College
- 1.1E: Exercises
- 2.2: Graphs of Linear Functions
- MAT 206 Precalculus
- 0: Review - Linear Equations in 2 Variables
- 1: Functions
- 1.0: Prelude to Functions
- 1.0E: Exercises
- 1.1: Functions and Function Notation
- 1.1E: Exercises
- 1.2: Domain and Range
- 1.2E: Exercises
- 1.3: Rates of Change and Behavior of Graphs
- 1.3E: Exercises
- 1.4: Composition of Functions
- 1.4E: Exercises
- 1.5: Transformation of Functions
- 1.5E: Exercises
- 1.6: Absolute Value Functions
- 1.6E: Exercises
- 1.7: Inverse Functions
- 1.7E: Exercises

- 3: Polynomial and Rational Functions
- 3.0: Prelude to Polynomial and Rational Functions
- 3.0E: Exercises
- 3.1: Complex Numbers
- 3.1E: Exercises
- 3.2: Quadratic Functions
- 3.2E: Exercises
- 3.3: Power Functions and Polynomial Functions
- 3.3E: Exercises
- 3.4: Graphs of Polynomial Functions
- 3.4E: Exercises
- 3.6: Zeros of Polynomial Functions
- 3.6E: Exercises
- 3.7: Rational Functions
- 3.7E: Exercises
- 3.8: Inverses and Radical Functions
- 3.8E: Exercises

- 4: Exponential and Logarithmic Functions
- 4.0: Prelude to Exponential and Logarithmic Functions
- 4.0E: Exercises
- 4.1: Exponential Functions
- 4.1E: Exercises
- 4.2: Graphs of Exponential Functions
- 4.2E: Exercises
- 4.3: Logarithmic Functions
- 4.3E: Exercises
- 4.4: Graphs of Logarithmic Functions
- 4.4E: Exercises
- 4.5: Logarithmic Properties
- 4.5E: Exercises
- 4.6: Exponential and Logarithmic Equations
- 4.6E: Exercises

- 5: Trigonometric Functions
- 6: Periodic Functions
- 7: Trigonometric Identities and Equations
- 7.0: Prelude to Trigonometric Identities and Equations
- 7.0E: Exercises
- 7.1: Simplifying Trigonometric Expressions with Identities
- 7.1E: Exercises
- 7.2: Sum and Difference Identities
- 7.2E: Exercises
- 7.3: Double-Angle, Half-Angle, and Reduction Formulas
- 7.3E: Exercises
- 7.5: Solving Trigonometric Equations
- 7.5E: Exercises

- 9: Systems of Equations and Inequalities

- CSU Chico
- De Anza College
- Diablo Valley College
- Georgia State University - Perimeter College
- MATH 2215: Calculus III
- 2: New Page
- 3: New Page
- 4: New Page
- 5: New Page
- 6: New Page
- 7: New Page
- 8: New Page
- 9: New Page
- 10: New Page
- 11: New Page
- 12: Vectors and the Geometry of Space
- 12.7E: Exercises for Cylindrical and Spherical Coordinates
- Chapter 11 Review Exercises
- Cylindrical and Spherical Coordinates
- Equations of Lines and Planes in Space
- Exercises for Equations of Lines and Planes in Space
- Exercises for Quadric Surfaces
- Exercises for The Cross Product
- Exercises for The Dot Product
- Exercises for Vectors in Space
- Exercises for Vectors in the Plane
- Quadric Surfaces
- The Cross Product
- The Dot Product
- Vectors in Space
- Vectors in the Plane

- 13: Vector-valued Functions
- Acceleration and Kepler's Laws
- Arc Length and Curvature
- Chapter 12 Review Exercises
- Exercises for Section 12.1
- Exercises for Section 12.2
- Exercises for Section 12.3
- Exercises for Section 12.4
- Exercises for Section 12.5
- Motion in Space
- The Calculus of Vector-Valued Functions
- The Calculus of Vector-Valued Functions II
- Vector-Valued Functions and Space Curves

- 14: Functions of Multiple Variables and Partial Derivatives
- Constrained Optimization
- Differentiation of Functions of Several Variables (Exercise)
- Directional Derivatives and the Gradient
- Directional Derivatives and the Gradient (Exercises)
- Exercises for Lagrange Multipliers
- Exercises for Limits and Continuity
- Functions of Multiple Variables
- Functions of Multiple Variables (Exercises)
- Introduction to Functions of Multiple Variables
- Lagrange Multipliers
- Limits and Continuity
- Optimization of Functions of Several Variables
- Optimization of Functions of Several Variables (Exercises)
- Partial Derivatives
- Partial Derivatives (Exercises)
- Tangent Planes, Linear Approximations, and the Total Differential
- Tangent Planes, Linear Approximations, and the Total Differential (Exercises)
- Taylor Polynomials if Functions of Two Variables (Exercises)
- Taylor Polynomials of Functions of Two Variables
- The Chain Rule for Functions of Multiple Variables
- The Chain Rule for Functions of Multiple Variables (Exercises)

- 15: Multiple Integration
- Calculating Centers of Mass and Moments of Inertia
- Change of Variables in Multiple Integrals (Jacobians)
- Double Integrals in Polar Coordinates
- Double Integrals in Polar Coordinates (Exercises)
- Double Integrals Over General Regions
- Double Integrals Over Rectangular Regions
- Double Integrals Part 1 (Exercises)
- Double Integrals Part 2 (Exercises)
- Double Integration with Polar Coordinates
- Exercises for Chapter 14
- Iterated Integrals and Area
- Iterated Integrals and Area (Exercises)
- Multiple Integration (Exercises)
- Triple Integrals
- Triple Integrals (Exercises)
- Triple Integrals (Exercises 2)
- Triple Integrals in Cylindrical and Spherical Coordinates

- 16: Vector Fields, Line Integrals, and Vector Theorems
- 17: Appendices

- MATH 2215 Calculus III

- MATH 2215: Calculus III
- Grayson College
- Instituto Tecnológico de Culiacán
- Long Beach City College
- Book: Beginning Algebra
- Book: Intermediate Algebra
- Text
- 1: Foundations
- 1.1: Prelude to Foundations of Algebra
- 1.2: Introduction to Whole Numbers
- 1.3: Use the Language of Algebra
- 1.4: Add and Subtract Integers
- 1.5: Multiply and Divide Integers
- 1.6: Visualize Fractions
- 1.7: Add and Subtract Fractions
- 1.8: Decimals
- 1.9: The Real Numbers
- 1.10: Properties of Real Numbers
- 1.11: Systems of Measurement

- 2: Solving Linear Equations and Inequalities
- 2.1: Solve Equations Using the Subtraction and Addition Properties of Equality
- 2.2: Solve Equations using the Division and Multiplication Properties of Equality
- 2.3: Solve Equations with Variables and Constants on Both Sides
- 2.4: Use a General Strategy to Solve Linear Equations
- 2.5: Solve Equations with Fractions or Decimals
- 2.6: Solve a Formula for a Specific Variable
- 2.7: Solve Linear Inequalities

- 3: Math Models
- 4: Graphs
- 5: Systems of Linear Equations
- 6: Polynomials
- 7: Factoring
- 8: Rational Expressions and Equations
- 8.1: Simplify Rational Expressions
- 8.2: Multiply and Divide Rational Expressions
- 8.3: Add and Subtract Rational Expressions with a Common Denominator
- 8.4: Add and Subtract Rational Expressions with Unlike Denominators
- 8.5: Simplify Complex Rational Expressions
- 8.6: Solve Rational Equations
- 8.7: Solve Proportion and Similar Figure Applications
- 8.8: Solve Uniform Motion and Work Applications
- 8.9: Use Direct and Inverse Variation

- 9: Roots and Radicals
- 10: Quadratic Equations

- 1: Foundations

- Text
- Book: College Algebra

- Misericordia University
- MTH 226: Calculus III
- Chapter 12: Vectors and the Geometry of Space
- 12.1: Vectors in the Plane
- 12.1E: Exercises for Vectors in the Plane
- 12.2: Vectors in Space
- 12.2E: Exercises for Vectors in Space
- 12.3: The Dot Product
- 12.3E: Exercises for The Dot Product
- 12.4: The Cross Product
- 12.4E: Exercises for The Cross Product
- 12.5: Equations of Lines and Planes in Space
- 12.5E: Exercises for Equations of Lines and Planes in Space
- 12.6: Quadric Surfaces
- 12.6E: Exercises for Quadric Surfaces
- 12.7: Cylindrical and Spherical Coordinates
- 12.7E: Exercises for Cylindrical and Spherical Coordinates
- Chapter 12 Review Exercises
- New Material

- Chapter 13: Vector-valued Functions
- 13.1: Vector-Valued Functions and Space Curves
- 13.1E: Exercises for Section 13.1
- 13.2: The Calculus of Vector-Valued Functions
- 13.2B: The Calculus of Vector-Valued Functions II
- 13.2E: Exercises for Section 13.2
- 13.3: Motion in Space
- 13.3E: Exercises for Section 13.3
- 13.4: Arc Length and Curvature
- 13.4E: Exercises for Section 13.4
- 13.5: Acceleration and Kepler's Laws
- 13.5E: Exercises for Section 13.5
- Chapter 13 Review Exercises

- Chapter 14: Functions of Multiple Variables and Partial Derivatives
- 3.1: Introduction to Functions of Multiple Variables
- 3.2: Functions of Multiple Variables
- 3.3: Functions of Multiple Variables (Exercises)
- 3.4: Limits and Continuity
- 3.5: Exercises for Limits and Continuity
- 3.6: Partial Derivatives
- 3.7: Partial Derivatives (Exercises)
- 3.8: Tangent Planes, Linear Approximations, and the Total Differential
- 3.9: Tangent Planes, Linear Approximations, and the Total Differential (Exercises)
- 3.10: The Chain Rule for Functions of Multiple Variables
- 3.11: The Chain Rule for Functions of Multiple Variables (Exercises)
- 3.12: Directional Derivatives and the Gradient
- 3.13: Directional Derivatives and the Gradient (Exercises)
- 3.14: Taylor Polynomials of Functions of Two Variables
- 3.15: Taylor Polynomials if Functions of Two Variables (Exercises)
- 3.16: Optimization of Functions of Several Variables
- 3.17: Optimization of Functions of Several Variables (Exercises)
- 3.18: Constrained Optimization
- 3.19: Lagrange Multipliers
- 3.20: Exercises for Lagrange Multipliers
- 3.21: Differentiation of Functions of Several Variables (Exercise)

- Chapter 15: Multiple Integration
- 4.1: Iterated Integrals and Area
- 4.2: Iterated Integrals and Area (Exercises)
- 4.3: Double Integrals Over Rectangular Regions
- 4.4: Double Integrals Part 1 (Exercises)
- 4.5: Double Integrals Over General Regions
- 4.6: Double Integrals Part 2 (Exercises)
- 4.7: Double Integration with Polar Coordinates
- 4.8: Double Integrals in Polar Coordinates
- 4.9: Double Integrals in Polar Coordinates (Exercises)
- 4.10: Triple Integrals
- 4.11: Triple Integrals (Exercises)
- 4.12: Triple Integrals (Exercises 2)
- 4.13: Triple Integrals in Cylindrical and Spherical Coordinates
- 4.14: Calculating Centers of Mass and Moments of Inertia
- 4.15: Change of Variables in Multiple Integrals (Jacobians)
- 4.16: Multiple Integration (Exercises)
- 4.17: Exercises for Chapter 14

- Chapter 16: Vector Fields, Line Integrals, and Vector Theorems
- 5.1: Introduction to Vector Field Chapter
- 5.2: Vector Fields
- 5.3: Vector Fields (Exercises)
- 5.4: Line Integrals
- 5.5: Line Integrals (Exercises)
- 5.6: Conservative Vector Fields
- 5.7: Green's Theorem
- 5.8: Divergence and Curl
- 5.9: Surface Integrals
- 5.10: Stokes' Theorem
- 5.11: The Divergence Theorem
- 5.12: Vector Calculus (Exercises)

- Review for Calculus III
- Appendices

- Chapter 12: Vectors and the Geometry of Space

- MTH 226: Calculus III
- Mission College
- Monroe Community College
- MTH 155 Mathematics for Elementary Teachers I
- MTH 156 Mathematics for Elementary Teachers II
- MTH 175 Precalculus (placeholder)
- MTH 210 Calculus I
- 1: Review: Functions and Graphs
- Chapter 2 Limits
- 2.0: Introduction
- 2.0E: Introduction Exercises
- 2.1: The Idea of Limits
- 2.1E The Idea of Limits
- 2.2: Limits of Functions
- 2.2E: Limits of Functions Exercises
- 2.3: Limit Laws & Techniques for Computing Limits
- 2.3E: Limit Laws and Techniques for Computing Limits EXERCISES
- 2.4: Infinite Limits
- 2.4E: Infinite Limits EXERCISES
- 2.5: Limits at Infinity
- 2.5E: Limits at Infinity EXERCISES
- 2.6: Continuity
- 2.6E: Continuity EXERCISES
- 2.7: The Precise Definition of a Limit
- 2.7E: Precise Definition of Limit EXERCISES
- NEW 2.3E: Limit Laws & Techniques Exercises

- Chapter 3: Derivatives
- 3.0: Prelude to Derivatives
- 3.0E: Exercises
- 3.1: Definition of the Derivative
- 3.1E: Definition of the Derivative (Exercises)
- 3.2: The Derivative as a Function
- 3.2E: Derivative as a Function Exercises
- 3.3: (and 3.4) Differentiation Rules
- 3.3E: Both 3.3 and 3.4 Exercises
- 3.5: Derivatives of Trigonometric Functions
- 3.5E: Trig Derivatives Exercises
- 3.6: Derivatives as Rates of Change
- 3.6 E: Rates of Change Exercises
- 3.7: The Chain Rule
- 3.7 E: Chain Rule Exercises
- 3.8: Implicit Differentiation
- 3.8 E: Implicit Differentiation Exercises
- 3.9: Derivatives of Ln, General Exponential & Log Functions; and Logarithmic Differentiation
- 3.9 E: Derivatives Ln, etc. Exercises
- 3. 10: Derivatives of Inverse Trig Functions
- section 3. 10 E: Inverse Trig Derivatives Exercises

- Chapter 4: Applications of Derivatives
- 4.0: Prelude to Applications of Derivatives
- 4.0E: Exercises
- 4.1: Related Rates
- 4.1E: Related Rates Exercises
- 4.2: Maxima and Minima
- 4.2E: Maxima and Minima Exercises
- 4.3: Derivatives and the Shape of a Graph
- 4.3E: Shape of the Graph Exercises
- 4.4: Graphing
- 4.4 E: Sketch the GRAPH Exercises
- 4.5: Optimization Problems
- 4.5 E: Optimization Exercises
- 4.6: Linear Approximations and Differentials
- 4.7: The Mean Value Theorem
- 4.8: Antiderivatives
- 4.8E: AntiDerivative & Indefinite Integral Exercises

- Chapter 5: Integration
- 5.0: Prelude to Integration
- 5.0E: Exercises
- 5.1: Approximating Areas
- 5.1 Approximating Area (Riemann Sum) Exercises
- 5.2: The Definite Integral
- 5.2 E: Definite Integral Intro Exercises
- 5.3: The Fundamental Theorem of Calculus Basics
- 5.3 E: FTOC Exercises
- 5.4: Average Value of a Function
- 5.4E: Average Value of a Function Exercises
- 5.5: U-Substitution
- 5.5E & 5.6E U-Substitution Exercises
- 5.6: More U-Substitution - Exponential and Logarithmic Functions
- 5.6 Notes
- 5.7: Net Change
- 5.7E: Net Change Exercises
- Xtra full 5.3: includes Proof of The Fundamental Theorem of Calculus

- professor playground
- 0.0 Special Symbols
- 2.E: Limits (Exercises)
- 3.2: The Derivative as a Function
- 3.3: Differentiation Rules
- 3.4: Product & Quotient Rules
- 3.9: Derivatives of Exponential and Logarithmic Functions
- 3.E: Derivatives (ALL Chapter 3 Exercises)
- 4.6: Limits at Infinity and Asymptotes
- 4.E: Applications of Derivatives (ALL Chap 4 Exercises)
- 4.E: Open Stax 4.1 - 4.5 Exercises
- 5.2: originalThe Definite Integral
- 5.3: original The Fundamental Theorem of Calculus
- 5.4: Original Integration Formulas and the Net Change Theorem
- 5.E: Integration (Exercises)

- MTH 211 Calculus II
- Calculus I Review
- Chapter 5: Integration
- 4.8: Antiderivatives
- 4.8E: Antiderivative and Indefinite Integral Exercises
- 5.0: Prelude to Integration
- 5.1: Approximating Areas
- 5.1E: Approximating Areas (Exercises)
- 5.2: The Definite Integral
- 5.3: The Fundamental Theorem of Calculus
- 5.4: Integration Formulas and the Net Change Theorem
- 5.5: Substitution
- 5.5E and 5.6E U-Substitution Exercises
- 5.6: Integrals Involving Exponential and Logarithmic Functions
- 5.7: Integrals Resulting in Inverse Trigonometric Functions and Related Integration Techniques
- 5.7E: Exercises for Integrals Resulting in Inverse Trigonometric Functions
- 5.E: Integration (Exercises)
- Chapter 5 Exercises

- Chapter 6: Applications of Integration
- 6.0: Prelude to Applications of Integration
- 6.1: Areas between Curves
- 6.1E: Exercises for Section 6.1
- 6.2: Determining Volumes by Slicing
- 6.2E: Exercises for Volumes of Common Cross-Section and Disk/Washer Method
- 6.3: Volumes of Revolution: Cylindrical Shells OS
- 6.3: Volumes of Revolution: The Shell Method
- 6.3E: Exercises for the Shell Method
- 6.4: Arc Length and Surface Area
- 6.4: Arc Length of a Curve and Surface Area
- 6.5: Using Integration to Determine Work
- 6.5b: More Physical Applications of Integration
- 6.5E: Exercises on Work
- 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)

- Chapter 7: Techniques of Integration
- 7.0: Prelude to Techniques of Integration
- 7.1: Integration by Parts
- 7.1E: Exercises for Integration by Parts
- 7.2: Trigonometric Integrals
- 7.2E: Exercises for Trigonometric Integrals
- 7.3: Trigonometric Substitution
- 7.3E: Exercises for Trigonometric Substitution
- 7.4: Partial Fractions
- 7.4E: Exercises for Integration by Partial Fractions
- 7.5: Other Strategies for Integration
- 7.6: Numerical Integration
- 7.7: L'Hôpital's Rule
- 7.7E: Exercises for L'Hôpital's Rule
- 7.8: Improper Integrals
- 7.8E: Exercises for Improper Integrals
- 7.E: Techniques of Integration (Exercises)

- Chapter 8: Introduction to Differential Equations
- 8.0: Prelude to Differential Equations
- 8.1: Basics of Differential Equations
- 8.1E: Exercises for Basics of Differential Equations
- 8.2: Direction Fields and Numerical Methods
- 8.2E: Exercises for Direction Fields and Numerical Methods
- 8.3: Separable Differential Equations
- 8.3E: Exercises for Separable Differential Equations
- 8.4: The Logistic Equation
- 8.4E: Exercises for the Logistic Equation
- 8.5: First-order Linear Equations
- 8.E: Introduction to Differential Equations (Exercises)

- Chapter 9: Sequences and Series
- 9.0: Prelude to Sequence and Series
- 9.1: Sequences
- 9.1E: Exercises for Sequences
- 9.2: Infinite Series
- 9.2E: Exercises for Infinite Series
- 9.3: The Divergence and Integral Tests
- 9.3E: Exercises for Divergence and Integral Tests
- 9.4: Comparison Tests
- 9.4E: Exercises for Comparison Test
- 9.5: Alternating Series
- 9.5E: Exercises for Alternating Series
- 9.6: Ratio and Root Tests
- 9.6E: Exercises for Ratio and Root Tests
- 9.E: Sequences and Series (Exercises)

- Chapter 10: Power Series
- Appendices

- MTH 212 Calculus III
- Chapter 11: Vectors and the Geometry of Space
- Chapter 12: Vector-valued Functions
- Chapter 13: Functions of Multiple Variables and Partial Derivatives
- 13.0: Introduction to Functions of Multiple Variables
- 13.1: Functions of Multiple Variables
- 13.2: Limits and Continuity
- 13.3: Partial Derivatives
- 13.4: Tangent Planes, Linear Approximations, and the Total Differential
- 13.5: The Chain Rule for Functions of Multiple Variables
- 13.6: Directional Derivatives and the Gradient
- 13.7: Taylor Polynomials of Functions of Two Variables
- 13.8: Optimization of Functions of Several Variables
- 13.9: Constrained Optimization
- 13.10: Lagrange Multipliers
- 13.E: Differentiation of Functions of Several Variables (Exercise)

- Chapter 14: Multiple Integration
- 14.1: Iterated Integrals and Area
- 14.2a: Double Integrals Over Rectangular Regions
- 14.2b: Double Integrals Over General Regions
- 14.3: Double Integration with Polar Coordinates
- 14.4: Triple Integrals
- 14.5: Triple Integrals in Cylindrical and Spherical Coordinates
- 14.6: Calculating Centers of Mass and Moments of Inertia
- 14.7: Change of Variables in Multiple Integrals (Jacobians)
- 14.E: Multiple Integration (Exercises)
- 14E: Exercises for Chapter 14

- Chapter 15: Vector Fields, Line Integrals, and Vector Theorems
- Table of Contents: MTH 212 Calculus III
- Appendices

- Montana State University
- M273: Multivariable Calculus
- 1: Chapter 1
- 2: Chapter 2
- 3: Chapter 3
- 4: Chapter 4
- 5: Chapter 5
- 6: New Page
- 7: New Page
- 8: New Page
- 9: New Page
- 10: New Page
- 11: New Page
- 12: Vectors and the Geometry of Space
- 13: Vector-valued Functions
- 14: Functions of Multiple Variables and Partial Derivatives
- Constrained Optimization
- Differentiation of Functions of Several Variables (Exercise)
- Directional Derivatives and the Gradient
- Functions of Multiple Variables
- Introduction to Functions of Multiple Variables
- Lagrange Multipliers
- Limits and Continuity
- Optimization of Functions of Several Variables
- Partial Derivatives
- Tangent Planes, Linear Approximations, and the Total Differential
- Taylor Polynomials of Functions of Two Variables
- The Chain Rule for Functions of Multiple Variables

- 15: Multiple Integration
- Calculating Centers of Mass and Moments of Inertia
- Change of Variables in Multiple Integrals (Jacobians)
- Double Integrals Over General Regions
- Double Integrals Over Rectangular Regions
- Double Integration with Polar Coordinates
- Exercises for Chapter 14
- Iterated Integrals and Area
- Multiple Integration (Exercises)
- Triple Integrals
- Triple Integrals in Cylindrical and Spherical Coordinates

- 16: Vector Fields, Line Integrals, and Vector Theorems

- M273: Multivariable Calculus
- Mount Royal University
- MATH 1150: Mathematical Reasoning
- Preface
- 1: Basic Language of Mathematics
- 2: Basic Concepts of Sets
- 3: Number Patterns
- 4: Basic Concepts of Euclidean Geometry
- 5: Basic Concepts of Probability
- 6: Introduction to Statistics
- 6.1: Qualitative Data and Quantitative Data
- 6.2: Descriptive Statitics:Measures of Center, Measures of Variation and the Five -Number Summary
- 6.3: Introduction to Statistical Calculations using Microsoft EXCEL
- 6.4: Binomial distribution and Normal Distribution
- 6.E: Introduction to Statistics (Exercises)

- 7: Dimensional Analysis
- Suggested readings

- MATH 2150: Higher Arithmetic
- Preface
- 0: Preliminaries
- 1 Binary operations
- 2 Binary relations
- 3 Modular Arithmetic
- 4 Greatest Common Divisor, least common multiple and Euclidean Algorithm
- 5 Diophantine Equations
- 6 Prime numbers
- 7 Number Bases
- 8 Number systems
- 9 Rational numbers, Irrational Numbers, and Continued fractions
- Notations
- Mock exams

- MATH 1200: Calculus for Scientists I
- Preface
- 0: Pre-Calculus Refresher
- 1: Limit and Continuity of Functions
- 1.0: Library of functions
- 1.1: Introduction to concept of a limit
- 1.2: One sided Limits and Vertical Asymptotes
- 1.3: Limit calculations for algebraic expressions
- 1.4: Limits at Infinity and Horizontal Asymptotes
- 1.5: Formal Definition of a Limit (optional)
- 1.6: Continuity and the Intermediate Value Theorem
- 1.7: Limit of Trigonometric functions
- 1.8: Limits and continuity of Inverse Trigonometric functions
- 1.9: Limit of Exponential Functions and Logarithmic Functions
- Chapter 1 Review Exercises

- 2: Derivatives
- 2.0: Tangent lines and Rates of change
- 2.1: Derivative as a Function
- 2.2: Techniques of differentiation
- 2.3: Derivative as a rate of Change
- 2.4: Derivatives of Trigonometric functions
- 2.5: Chain Rule
- 2.6: Implicit Differentiation
- 2.7: Derivatives of Inverse Trigonometric Functions
- 2.8: Derivatives of Exponential and Logarithmic functions
- 2.9: L'Hôpital's Rule
- 2E Exercises

- 3: Applications of Derivatives
- 3.0 Introduction to applications of Derivative
- 3.1: Related Rates
- 3.2 Linear approximations and Differentials
- 3.3: Extremas
- 3.4 The Mean Value Theorem
- 3.5 Derivative tests
- 3.6 Applied Optimization Problems
- 3.7 Curve skectching
- 3.8: Newton's Method
- 3.9 Anti derivatives and Rectilinear Motion
- 3E Chapter Exercises

- 4 Integral Calculus
- 4.0 Antidervatives and Indefinite Integration (Revisited)
- 4.1 Integration by Substitution
- 4.2 Definite Integral- An Introduction
- 4.3 Approximating Areas
- 4.4 The Definite Integral
- 4.5 : The Fundamental Theorem of Calculus
- 4.6 Integration Formulas and the Net Change Theorem
- 4.7 Definite integrals by substitution.
- 4.8 Area between two curves
- 4.9 Applications of definite integrals
- 4E Exercises

- Mock Exams (Celebration of Learning)
- Additional Resources

- MATH 2200: Calculus for Scientists II
- Preface
- 1: Applications of Integration
- 1.1: Volumes of solids of revolution -cross-sections
- 1.2: Volumes of solids of revolution - cylindrical shells
- 1.3: Surface area (surfaces of revolution)
- 1.4: Other applications: Work, centroid, and center of mass
- 1.5: Moments and Centers of Mass
- 1.7: Calculus of the Hyperbolic Functions
- 1E: Chapter Exercises

- 2: Techniques of Integration
- 3 Introduction to Differential Equations
- 3.1: Some Applications Leading to Differential Equation
- 3.2: Basic Concepts
- 3.3: First order linear equations
- 3.4: Direction Fields for First Order Equations
- 3.5: Separable Differential Equations
- 3.6 : Existence and Uniqueness of Solutions of Nonlinear Equations
- 3.7: First Order Equations: Transformation of Nonlinear Equations into Separable Equations

- 4 Parametric Equations and Polar Coordinates
- 4.0: Prelude to Parametric Equations and Polar Coordinates
- 4.1: Parametric equations - Tangent lines and arc length
- 4.2: Calculus of Parametric Curves
- 4.3: Polar coordinates: definitions, arc length, and area for polar curves
- 4.4: Area and Arc Length in Polar Coordinates
- 4.5: Conic Sections
- 4E: Chapter Exercises

- 5 Vector Spaces
- 6 Mulitvariable Calculus
- 7: Multiple Integration
- 7.1 Double Integrals over Rectangular Regions
- 7.2: Double Integrals over General Regions
- 7.3: Double Integrals in Polar Coordinates
- 7.4: Triple Integrals
- 7.5: Triple Integrals in Cylindrical and Spherical Coordinates
- 7.6: Calculating Centers of Mass and Moments of Inertia
- 7.7: Change of Variables in Multiple Integrals

- 8: Sequences and Series

- MATH 3200: Mathematical Methods
- 1: Power Series
- 2: Ordinary differential equations
- 3: Series Solutions of Linear Second order Equations
- 4: Linear Systems of Ordinary Differential Equations (LSODE)
- 4.1: Introduction to Systems of Differential Equations
- 4.2: Linear Systems of Differential Equations
- 4.3: Basic Theory of Homogeneous Linear System
- 4.4: Constant Coefficient Homogeneous Systems I
- 4.5: Constant Coefficient Homogeneous Systems II
- 4.6: Constant Coefficient Homogeneous Systems III
- 4.7: Variation of Parameters for Nonhomogeneous Linear Systems

- 5: Vector-Valued Functions
- 6: Differentiation of Functions of Several Variables
- 7: Multiple Integration
- 7.1 :Double Integrals over Rectangular Regions
- 7.2: Double Integrals over General Regions
- 7.3: Double Integrals in Polar Coordinates
- 7.4: Triple Integrals
- 7.5: Triple Integrals in Cylindrical and Spherical Coordinates
- 7.6: Calculating Centers of Mass and Moments of Inertia
- 7.7: Change of Variables in Multiple Integrals

- 8: Partial Differential Equations
- 9: Vector Calculus
- Summary Tables

- Mathematics Activities: Instructions and instructional videos for Elementary education
- Calculus Projects
- FK Draft-testing

- MATH 1150: Mathematical Reasoning
- Prince George's Community College
- Pre Calc 1
- 1: Functions
- 2: Linear and Quadratic Functions
- 3: Polynomial and Rational Functions
- 3.1: Prelude to Polynomial and Rational Functions
- 3.2: Complex Numbers
- 3.3: Quadratic Functions
- 3.4: Power Functions and Polynomial Functions
- 3.5: Graphs of Polynomial Functions
- 3.6: Dividing Polynomials
- 3.7: Zeros of Polynomial Functions
- 3.8: Rational Functions
- 3.9: Inverses and Radical Functions
- 3.10: Modeling Using Variation
- 3.11: Polynomial and Rational Functions(Exercises)
- 3.12: Polynomial and Rational Functions(Review)

- 4: Extras

- Pre Calc 1
- Saint Mary's College, Notre Dame, IN
- SMC: MATH 339 - Discrete Mathematics (Rohatgi)
- Text
- Front Matter
- 0: Introduction and Preliminaries
- 1: Counting
- 2: Sequences
- 3: Symbolic Logic and Proofs
- 4: Algorithms
- 5: Graph Theory
- 5.10: Spanning Tree Algorithms
- 5.11: Transportation Networks and Flows
- 5.1: Prelude to Graph Theory
- 5.2: Definitions
- 5.3: Planar Graphs
- 5.4: Coloring
- 5.5: Euler Paths and Circuits
- 5.6: Matching in Bipartite Graphs
- 5.7: Weighted Graphs and Dijkstra's Algorithm
- 5.8: Trees
- 5.9: Tree Traversal
- 5.E: Graph Theory (Exercises)
- 5.S: Graph Theory (Summary)

- 6: Additional Topics

- Text

- SMC: MATH 339 - Discrete Mathematics (Rohatgi)
- Truckee Meadows Community College
- TMCC: Precalculus I and II
- 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

- testing new category

- TMCC: Precalculus I and II
- University of Arkansas Little Rock
- University of California, Davis
- UCD Mat 21A: Differential Calculus
- 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

- UCD Mat 21B: Integral Calculus
- 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

- UCD Mat 21C: Multivariate Calculus
- UCD Mat 21D: Vector Analysis
- Multiple Integrals
- 15.1: Double and Iterated Integrals over Rectangles
- 15.2: Double Integrals over General Regions
- 15.3: Area by Double Integration
- 15.4: Double Integrals in Polar Form
- 15.5: Triple Integrals in Rectangular Coordinates
- 15.6: Moments and Centers of Mass
- 15.7: Triple Integrals in Cylindrical and Spherical Coordinates
- 15.8: Substitutions in Multiple Integrals

- Vector-Valued Functions and Motion in Space
- Integration in Vector Fields
- 16.1: Line Integrals
- 16.2: Vector Fields and Line Integrals: Work, Circulation, and Flux
- 16.3: Path Independence, Conservative Fields, and Potential Functions
- 16.4: Green's Theorem in the Plane
- 16.5: Surfaces and Area
- 16.6: Surface Integrals
- 16.7: Stokes' Theorem
- 16.8: The Divergence Theorem and a Unified Theory

- Multiple Integrals
- UCD Mat 67: Linear Algebra
- UCD MAT 235A: Probability Theory
- Notes
- 01 Introduction
- 02 Probability spaces
- 03 Random variables
- 04 Random vectors and independence
- 05 The Borel-Cantelli Lemmas
- 06 A brief excursion into measure theory
- 07 Expected values
- 08 Special distributions and their properties
- 9: Laws of Large Numbers
- 10 Applications and further examples
- 11 The Central Limit Theorem, Stirling's formula and the de Moivre-Laplace theorem
- 12 Convergence in distribution
- 13 Characteristic functions
- 14 Central limit theorems
- 15 Random number generation

- Notes
- UCD MAT 280: Macdonald Polynomials and Crystal Bases

- UCD Mat 21A: Differential Calculus

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\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

Here are custom designed online **Libretexts **that are developed for individual instructors/classes and schools. The MathWiki maintains all **Modules **(pages of chemistry information) in the primary sections collectively referred to as the **Core**; the LibreTexts below contain only class organization, which may or may not be reproduced in the organization of the core.

- Remixer University
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