1.1: Table of Contents
- Page ID
- 111139
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The text guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them
1: Functions and Graphs
- 1.1: Prelude to Functions and Graphs
- 1.2: Review of Functions
- 1.2E: Exercises for Section 1.1
- 1.3: Basic Classes of Functions
- 1.3E: Exercises for Section 1.2
- 1.4: Trigonometric Functions
- 1.4E: Exercises for Section 1.3
- 1.5: Inverse Functions
- 1.5E: Exercises for Section 1.4
- 1.6: Exponential and Logarithmic Functions
- 1.6E: Exercises for Section 1.5
- 1.7: Chapter 1 Review Exercises
2: Limits
- 2.1: Prelude to Limits
- 2.2: A Preview of Calculus
- 2.2E: Exercises for Section 2.1
- 2.3: The Limit of a Function
- 2.3E: Exercises for Section 2.2
- 2.4: The Limit Laws
- 2.4E: Exercises for Section 2.3
- 2.5: Continuity
- 2.5E: Exercises for Section 2.4
- 2.6: The Precise Definition of a Limit
- 2.6E: Exercises for Section 2.5
- 2.7: Chapter 2 Review Exercises
3: Derivatives
- 3.1: Prelude to Derivatives
- 3.2: Defining the Derivative
- 3.2E: Exercises for Section 3.1
- 3.3: The Derivative as a Function
- 3.3E: Exercises for Section 3.2
- 3.4: Differentiation Rules
- 3.4E: Exercises for Section 3.3
- 3.5: Derivatives as Rates of Change
- 3.5E: Exercises for Section 3.4
- 3.6: Derivatives of Trigonometric Functions
- 3.6E: Exercises for Section 3.5
- 3.7: The Chain Rule
- 3.7E: Exercises for Section 3.6
- 3.8: Derivatives of Inverse Functions
- 3.8E: Exercises for Section 3.7
- 3.9: Implicit Differentiation
- 3.9E: Exercises for Section 3.8
- 3.10: Derivatives of Exponential and Logarithmic Functions
- 3.10E: Exercises for Section 3.9
- 3.11: Chapter 3 Review Exercises
4: Applications of Derivatives
- 4.1: Prelude to Applications of Derivatives
- 4.2: Related Rates
- 4.2E: Exercises for Section 4.1
- 4.3: Linear Approximations and Differentials
- 4.3E: Exercises for Section 4.2
- 4.4: Maxima and Minima
- 4.4E: Exercises for Section 4.3
- 4.5: The Mean Value Theorem
- 4.5E: Exercises for Section 4.4
- 4.6: Derivatives and the Shape of a Graph
- 4.6E: Exercises for Section 4.5
- 4.7: Limits at Infinity and Asymptotes
- 4.7E: Exercises for Section 4.6
- 4.8: Applied Optimization Problems
- 4.8E: Exercises for Section 4.7
- 4.9: L’Hôpital’s Rule
- 4.9E: Exercises for Section 4.8
- 4.10: Newton’s Method
- 4.10E: Exercises for Section 4.9
- 4.11: Antiderivatives
- 4.11E: Exercises for Section 4.10
- 4.12: Chapter 4 Review Exercises
5: Integration
- 5.1: Approximating Areas
- 5.1E: Exercises for Section 5.1
- 5.2: The Definite Integral
- 5.2E: Exercises for Section 5.2
- 5.3: The Fundamental Theorem of Calculus
- 5.3E: Exercises for Section 5.3
- 5.4: Integration Formulas and the Net Change Theorem
- 5.4E: Exercises for Section 5.4
- 5.5: Substitution
- 1.5E: Exercises for Section 5.5
- 5.6: Integrals Involving Exponential and Logarithmic Functions
- 1.6E: Exercises for Section 5.6
- 5.7: Integrals Resulting in Inverse Trigonometric Functions
- 5.7E: Exercises for Section 5.7
- 5.8: Chapter 5 Review Exercises
6: Appendicies
- 6.1: A- Table of Derivatives