Mathematics higher level : calculus, course companion /
Written by experienced IB workshop leaders, this book covers all the course content and essential practice needed for success in the Calculus Option for Higher Level. Enabling a truly IB approach to mathematics, real-world context is thoroughly blended with mathematical applications, supporting deep...
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| Main Authors: | , , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford :
Oxford University Press,
2014.
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| Series: | Oxford IB Diploma Programme
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| Subjects: | |
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| 008 | 150501s2014 enka 000 0 eng | ||
| 020 | |a 9780198304845 (pbk.) | ||
| 020 | |a 0198304846 | ||
| 040 | |a rda |b English |c MSULIB |e rda | ||
| 050 | 0 | 0 | |a QA301 MAT |
| 100 | 1 | |a Harcet, Josip. |e author. | |
| 245 | 1 | 0 | |a Mathematics higher level : |b calculus, course companion / |c created by Josip Harcet, Lorraine Heinrichs, Palmira Mariz Seiler, Marlene Torres Skoumal. |
| 264 | 1 | |a Oxford : |b Oxford University Press, |c 2014. | |
| 264 | 4 | |c ©2014. | |
| 300 | |a vi, 186 pages : |b illustrations ; |c 26 cm. | ||
| 336 | |a text |2 rdacontent | ||
| 337 | |a unmediated |b n |2 rdamedia | ||
| 338 | |a volume |b nc |2 rdacarrier | ||
| 490 | 0 | |a Oxford IB Diploma Programme | |
| 504 | |a Includes index | ||
| 505 | |a 1. Patterns to infinity ; 1.1 From limits of sequences to limits of functions ; 1.2 Squeeze theorem and the algebra of limits of convergent sequences ; 1.3 Divergent sequences: indeterminate forms and evaluation of limits ; 1.4 From limits of sequences to limits of functions ; 2. Smoothness in mathematics ; 2.1 Continuity and differentiability on an interval ; 2.2 Theorems about continuous functions ; 2.3 Differentiable functions: Rolle's Theorem and Mean Value Theorem ; 2.4 Limits at a point, indeterminate forms, and L'Hopital's rule ; 2.5 What are smooth graphs of functions? ; 2.6 Limits of functions and limits of sequences ; 3. Modeling dynamic phenomena ; 3.1 Classifications of differential equations and their solutions ; 3.2 Differential Equations with separated variables ; 3.3 Separable variables differential Separable variables differential ; 3.4 Modeling of growth and decay phenomena ; 3.5 First order exact equations and integrating factors ; 3.6 Homogeneous differential equations and substitution methods ; 3.7 Euler Method for first order differential equations ; 4. The finite in the infinite ; 4.1 Series and convergence ; 4.2 Introduction to convergence tests for series ; 4.3 Improper Integrals ; 4.4 Integral test for convergence ; 4.5 The p-series test ; 4.6 Comparison test for convergence ; 4.7 Limit comparison test for convergence ; 4.8 Ratio test for convergence ; 4.9 Absolute convergence of series ; 4.10 Conditional convergence of series ; 5. Everything polynomic ; 5.1 Representing Functions by Power Series 1 ; 5.2 Representing Power Series as Functions ; 5.3 Representing Functions by Power Series 2 ; 5.4 Taylor Polynomials ; 5.5 Taylor and Maclaurin Series ; 5.6 Using Taylor Series to approximate functions ; 5.7 Useful applications of power series ; 6. Answers | ||
| 520 | |a Written by experienced IB workshop leaders, this book covers all the course content and essential practice needed for success in the Calculus Option for Higher Level. Enabling a truly IB approach to mathematics, real-world context is thoroughly blended with mathematical applications, supporting deep understanding and confident thinking skills. | ||
| 650 | 0 | |a Calculus |x Study and teaching (Secondary) | |
| 650 | 0 | |a Calculus |x Examinations |x Study guides. | |
| 700 | 1 | |a Heinrichs, Lorraine. |e author. | |
| 700 | 1 | |a Seiler, Palmira Mariz. |e author. | |
| 700 | 1 | |a Torres Skoumal, Marlene. |e author. | |
| 830 | |a Oxford IB Diploma Programme | ||
| 942 | |2 lcc |c B | ||
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| 999 | |c 161181 |d 161181 | ||