Author(s): Catherine Quinn et al
Mathematics HL (Option): Calculus has been written as a companion book to the Mathematics HL (Core) textbook. Together, they aim to provide students and teachers with appropriate coverage of the two-year Mathematics HL Course, first examined in 2014.
This book covers all sub-topics set out in Mathematics HL Option Topic 9 and Further Mathematics HL Topic 5, Calculus.
The aim of this topic is to introduce students to the basic concepts, theory and techniques concerning differential and integral calculus and their applications.
Detailed explanations and key facts are highlighted throughout the text. Each sub-topic contains numerous Worked Examples, highlighting each step necessary to reach the answer for that example.
In this changing world of mathematics education, we believe that the contextual approach shown in this book, with associated use of technology, will enhance the student's understanding, knowledge and appreciation of mathematics and its universal applications.
This product has been developed independently from and is not endorsed by the International Baccalaureate Organization. International Baccalaureate, Baccalaureát International, Bachillerato Internacional and IB are registered trademarks owned by the International Baccalaureate Organisation.
Mathematics HL (Option): Calculus
SYMBOLS AND NOTATION USED IN THIS BOOK 6
A Number properties 9
B Limits 12
C Continuity of functions 20
D Differentiable functions 25
E l'Hôpital's Rule 29
F Rolle's theorem and the Mean Value Theorem (MVT) 34
G Riemann sums 38
H The Fundamental Theorem of Calculus 44
I Improper integrals of the form (integral from a to infinity of f(x) dx) 50
J Sequences 57
K Infinite series 66
L Taylor and Maclaurin series 89
M Differential equations 105
N Separable differential equations 112
O The integrating factor method 117
P Taylor or Maclaurin series developed from a differential equation 120
Review set A 123
Review set B 124
Review set C 125
Review set D 126
THEORY OF KNOWLEDGE (Torricelli's trumpet) 129
APPENDIX A (Methods of proof) 131
THEORY OF KNOWLEDGE (Axioms and Occam's razor) 140
APPENDIX B (Formal definition of a limit) 141
WORKED SOLUTIONS 145