Approximately calculus / Shahriar Shahriari.

Author/creator Shahriari, Shahriar
Format Book
Publication InfoProvidence, R.I. : American Mathematical Society, ©2006.
Descriptionxvii, 292 pages : illustrations ; 27 cm
Subjects
Calculus--Problems, exercises, etc.
Approximation theory--Problems, exercises, etc.

Contents Preface -- ch. 1. Patterns and induction -- Goals -- 1.1. Mathematics, patterns, and computers -- Problems -- 1.2. Writing mathematical sentences and proof by induction -- Problems -- 1.3. Additional problems -- Problems -- ch. 2. Divisibility -- Goals -- 2.1. The division algorithm and strange properties of positive integers -- Problems -- 2.2. Writing mathematics in paragraphs, proof by contradiction, and irrational numbers -- Problems -- 2.3. Introducing the planet mod n -- Problems -- 2.4. Additional problems -- Problems -- ch. 3. Primes -- Goals -- 3.1. Prime numbers -- Problems -- 3.2. Formulas for primes -- Problems -- 3.3. Fermat's theorem, pseudo-primes, and Carmichael numbers -- Problems -- 3.4. Dynamical systems and a proof of Fermat's theorem -- Problems -- 3.5. Public key cryptography -- Problems -- 3.6. Open conjectures about primes -- ch. 4. Derivatives and approximations of functions -- Goals -- 4.1. A quick review of derivatives -- Problems -- 4.2. Continuous functions and differentiability -- Problems -- 4.3. Linearization and approximation of functions -- Problems -- 4.4. Taylor polynomials -- Problems -- 4.5. Additional problems -- Problems --
Contents ch. 5. Antiderivatives and integration -- Goals -- 5.1. Why can areas be found using antiderivatives? A quick review of integration -- Problems -- 5.2. Approximating integrals : inscribed and circumscribed rectangles -- Problems -- 5.3. Functions defined by integrals -- Problems -- 5.4. What if F'(x) = G'(x)? -- Problems -- ch. 6. Distribution of primes -- Goals -- 6.1. Approximating x/[pi](x) -- Problems -- 6.2. The sieve of Eratosthenes -- Problems -- ch. 7. Log, exponential, and the inverse trigonometric functions -- Goals -- 7.1. The natural log function and the distribution of primes -- problems -- 7.2. Properties of the log function -- Problems -- 7.3. The exponential function -- Problems -- 7.4. Inverse trigonometric functions -- Problems -- 7.5. Additional problems -- Problems -- ch. 8. The mean value theorem and approximations -- Goals -- 8.1. Real numbers and properties of continuous functions -- Problems -- 8.2. The mean value theorem for integrals -- Problems -- 8.3. The mean value theorem -- Problems -- 8.4. The error in a Taylor polynomial approximation -- Problems--
Contents ch. 9. Linearization topics -- Goals -- 9.1. L'Hospital's rule -- Problems -- 9.2. Newton's method -- Problems -- ch. 10. Defining integrals, areas, and arclengths -- Goals -- 10.1. Going beyond an intuitive notion of area -- Problems -- 10.2. Arc length -- Problems -- ch. 11. Improper integrals and techniques of integration -- Goals -- 11.1. Improper integrals -- Problems -- 11.2. Integration methods -- Problems -- ch. 12. The prime number theorem -- Goals -- 12.1. The prime number theorem -- Problems -- 12.2. Prime between n and 2n -- Problems -- 12.3. Logarithmic integral -- Problems -- 12.4. Where approximately is the nth prime? -- Problems -- 12.5. Primes and the Riemann hypothesis -- ch. 13. Local approximation of functions and integral estimations -- Goals -- 13.1. Taylor polynomials and approximations of integrals. Are they related? -- Problems -- 13.2. Approximating integrals : rectangles, trapezoids, and parabolas -- Problems -- 13.3. Curvature -- Problems -- 13.4. Padé approximants -- Problems --
Contents ch. 14. Sequences and series -- Goals -- 14.1. Sequences, convergence, and mathematical rigor -- Problems -- 14.2. SEries -- Problems -- 14.3. Monotone bounded sequences and limit properties -- Problems -- 14.4. The nth term test and the comparison test -- Problems -- 14.5. Euler's constant and the alternating harmonic series -- Problems -- 14.6. The integral test and p-series -- Problems -- 14.7. Additional problems -- Problems -- ch. 15. Power series and Taylor series -- Goals -- 15.1. Taylor polynomials and series -- Problems -- 15.2. Power series and the ratio test -- Problems -- 15.3. Analytic functions and convergence of Taylor series -- Problems -- 15.4. The interval of convergence of a power series -- Problems -- 15.5. New power series form old -- Problems -- ch. 16. More on series -- Goals -- 16.1. The limit comparison test -- Problems -- 16.2. Leibniz's alternating series test -- Problems -- 16.3. Additional problems -- Problems -- ch. 17. Limits of functions -- Goals -- Introduction -- 17.1. The precise definition of limits -- Problems --
Contents ch. 18. Differential equations -- Goals -- 18.1. Differential equations and modeling -- Problems -- 18.2. Qualitative analysis of differential equations -- Problems -- 18.3. Additional problems -- Problems -- ch. 19. Logical arguments -- Goals -- 19.1. Logical reasoning through puzzles -- Problems -- Hints for selected problems -- Bibliography -- Index.
Bibliography noteIncludes bibliographical references (p. 283-286) and index.
LCCN 2006048370
ISBN0821837508 (alk. paper)
ISBN9780821837504 (hbk.)

Availability

Library Location Call Number Status Item Actions
Joyner General Stacks QA301 .S49 2006 ✔ Available Place Hold