A free on-line calculus text
Many of these materials were developed for the Open Course Library Project of the Washington State Colleges as part of a Gates Foundation grant.
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Chapter 0 -- Review and Preview
- Chapter 0 Learning Outcomes
- 0.1 Preview
- 0.2 Lines
- 0.3 Functions
- 0.4 Combinations of Functions
- 0.5 Mathematical Language
- Chapter 0 Odd Answers
Chapter 1 -- Functions, Graphs, Limits and Continuity
- Chapter 1 Learning Outcomes
- 1.0 Slopes & Velocities
- 1.1 Limit of a Function
- 1.2 Limit Properties
- 1.3 Continuous Functions
- 1.4 Formal Definition of Limit
- Chapter 1 Odd Answers
Chapter 2 -- The Derivative
- Chapter 2 Learning Outcomes
- 2.0 Slope of a Tangent Line
- 2.1 Definition of Derivative
- 2.2 Differentiation Formulas
- 2.3 More Differentiation Patterns
- 2.4 Chain Rule (!!!)
- 2.5 Using the Chain Rule
- 2.6 Related Rates
- 2.7 Newton's Method
- 2.8 Linear Approximation
- 2.9 Implicit Differentiation
- Chapter 2 Odd Answers
Chapter 3 -- Derivatives and Graphs
- Chapter 3 Learning Outcomes
- 3.1 Introduction to Maximums & Minimums
- 3.2 Mean Value Theorem
- 3.3 f' and the Shape of f
- 3.4 f'' and the Shape of f
- 3.5 Applied Maximums & Minimums
- 3.6 Asymptotes
- 3.7 L'Hospital's Rule
- Chapter 3 Odd Answers
Chapter 4 -- The Integral
- Chapter 4 Learning Outcomes
- 4.0 Introduction to Integrals
- 4.1 Sigma Notation & Riemann Sums
- 4.2 The Definite Integral
- 4.3 Properties of the Definite Integral
- 4.4 Areas, Integrals and Antiderivatives
- 4.5 The Fundamental Theorem of Calculus
- 4.6 Finding Antiderivatives
- 4.7 First Applications of Definite Integrals
- 4.8 Using Tables to Find Antiderivatives
- 4.9 Approximating Definite Integrals
- Chapter 4 Odd Answers
Chapter 5 -- Applications of Definite Integrals
- Chapter 5 Learning Outcomes
- 5.0 Introduction to Applications
- 5.1 Volumes
- 5.2 Arc Lengths & Surface Areas
- 5.3 More Work
- 5.4 Moments & Centers of Mass
- 5.5 Additional Applications
- Chapter 5 Odd Answers
Chapter 6 -- Introduction to Differential Equations
- Chapter 6 Learning Outcomes
- 6.0 Introduction to Differential Equations
- 6.1 Differential Equation y'=f(x)
- 6.2 Separable Differential Equations
- 6.3 Exponential Growth, Decay & Cooling
- Chapter 6 Odd Answers
Chapter 7 -- Inverse Trigonometric Functions
- Chapter 7 Learning Outcomes
- 7.0 Introduction to Transcendential Functions
- 7.1 Inverse Functions
- 7,2 Inverse Trigonometric Functions
- 7.3 Calculus with Inverse Trigonometric Functions
- Chapter 7 Odd Answers
Chapter 8 -- Improper Integrals and Integration Techniques
- Chapter 8 Learning Outcomes
- 8.0 Introduction Improper Integrals & Integration Techniques
- 8.1 Improper Integrals
- 8.2 Integration Review
- 8.3 Integration by Parts
- 8.4 Partial Fraction Decomposition
- 8.5 Trigonometric Substitution
- 8.6 Trigonometric Integrals
- Chapter 8 Odd Answers
- Chapter 9 Learning Outcomes
- 9.1 Polar Coordinates
- 9.2 Calculus with Polar Coordinates
- 9.3 Parametric Equations
- 9.4 Calculus with Parametric Equations
- 9.4.5 Bezier Curves
- 9.5 Conic Sections
- 9.6 Properties of the Conic Sections
- Chapter 9 Odd Answers
- Chapter 10 Learning Outcomes
- 10.0 Introduction to Sequences & Series
- 10.1 Sequences
- 10.2 Infinite Series
- 10.3 Geometric and Harmonic Series
- 10.3.5 An Interlude and Introduction
- 10.4 Positive Term Series: Integral & P-Tests
- 10.5 Positive Term Series: Comparison Tests
- 10.6 Alternating Sign Series
- 10.7 Absolute Convergence and the Ratio Test
- 10.8 Power Series
- 10.9 RepresentingFunctions with Power Series
- 10.10 Taylor and Maclaurin Series
- 10.11 Approximation Using Taylor Polynomials
- 10.12 Fourier Series
- Chapter 10 Odd Answers
- Chapter 11 Learning Outcomes
- 11.0 Moving Beyond Two Dimensions
- 11.1 Vectors in the Plane
- 11.2 Rectangular Coordinates in Three Dimensions
- 11.3 Vectors in Three Dimensions
- 11.4 Dot Product
- 11.5 Cross Product
- 11.6 Lines and Planes inThree Dimensions
- 11.7 Vector Reflections
- Appendix -- Sketching in 3D
- Chapter 11 Odd Answers
- 12.0 Introduction to Vector-Valued Functions
- 12.1 Vector-Valued Functions and Curves in Space
- 12.2 Derivatives & Antiderivatives of Vector-Valued Functions
- 12.3 Arc Length and Curvature of Space Curves
- 12.4 Cylindrical & Spherical Coordinate Systems in 3D
- Chapter 12 Odd Answers
- 13.0 Introduction to Functions of Several Variables
- 13.1 Functions of Two or More Variables
- 13.2 Limits and Continuity
- 13.3 Partial Derivatives
- 13.4 Tangent Planes and Differentials
- 13.5 Directional Derivatives and the Gradient
- 13.6 Maximums and Minimums
- 13.7 Lagrange Multiplier Method
- 13.8 Chain Rule
- Chapter 13 Odd Answers
- 14.0 Introduction to Double Integrals
- 14.1 Double Integrals over Rectangular Domains
- 14.2 Double Integrals over General Domains
- 14.3 Double Integrals in Polar Coordinates
- 14.4 Applications of Double Integrals
- 14.5 Surface Area
- 14.6 Triple Integrals and Applications
- 14.7 Triple Integrals in Cylindrical and Spherical Coordinates
- 14.8 Changing Variables in Double and Triple Integrals
- Chapter 14 Odd Answers
- 15.0 Introduction to Vector Calculus
- 15.1 Vector Fields
- 15.2 Divergence, Curl and Del in 2D
- 15.3 Line Integrals
- A Message
- 15.4 Fundamental Theorem of Line Integrals and Potential Functions
- 15.4.5 Theorems of Green, Stokes and Gauss: Discrete Introdutions
- 15.5 Green's Theorem
- 15.6 Divergence and Curl in 3D
- 15.7 Parametric Surfaces
- 15.8 Surface Integrals
- 15.9 Stokes' Theorem
- 15.10 Gauss/Divergence Theorem
- Chapter 15 Odd Answers
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