http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
I. Real Number System -- 1. Familiar Number Systems -- 2. Intervals -- 3. Suprema and Infima -- 4. Exact Arithmetic in R -- 5. Topics for Further Study -- II. Continuous Functions -- 1. Functions in Mathematics -- 2. Continuity of Numerical Functions -- 3. Intermediate Value Theorem -- 4. More Ways to Form Continuous Functions -- 5. Extreme Values -- III. Limits -- 1. Sequences and Limits -- 2. Limits and Removing Discontinuities -- 3. Limits Involving [infinity] -- IV. Derivative -- 1. Differentiability -- 2. Combining Differentiable Functions -- 3. Mean Values -- 4. Second Derivatives and Approximations -- 5. Higher Derivatives -- 6. Inverse Functions -- 7. Implicit Functions and Implicit Differentiation -- V. Riemann Integral -- 1. Areas and Riemann Sums -- 2. Simplifying the Conditions for Integrability -- 3. Recognizing Integrability -- 4. Functions Defined by Integrals -- 5. Fundamental Theorem of Calculus -- 6. Topics for Further Study -- VI. Exponential and Logarithmic Functions -- 1. Exponents and Ligarithms -- 2. Algebraic Laws as Definitions -- 3. Natural Logarithm -- 4. Natural Exponential Function -- 5. Important Limit -- VII. Curves and Arc Length -- 1. Concept of Arc Length -- 2. Arc Length and Integration -- 3. Arc Length as a Parameter -- 4. Arctangent and Arcsine Functions -- 5. Fundamental Trigonometric Limit -- VIII. Sequences and Series of Functions -- 1. Functions Defined by Limits -- 2. Continuity and Uniform Convergence -- 3. Integrals and Derivatives -- 4. Taylor's Theorem -- 5. Power Series -- 6. Topics for Further Study -- IX. Additional Computational Methods -- 1. L'Hopital's Rule -- 2. Newton's Method -- 3. Simpson's Rule -- 4. Substitution Rule for Integrals.
Includes bibliographical references (page 197) and index.