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Towards Higher Mathematics: A Companion [Hardback]

3.50/5 (2 ratings by Goodreads)
(University of Oxford)
  • Formāts: Hardback, 540 pages, height x width x depth: 253x178x34 mm, weight: 1100 g, Worked examples or Exercises; 35 Halftones, black and white; 65 Line drawings, black and white
  • Izdošanas datums: 07-Sep-2017
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1107162386
  • ISBN-13: 9781107162389
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  • Cena: 109,33 €
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Towards Higher Mathematics: A CompanionPalielināt
  • Formāts: Hardback, 540 pages, height x width x depth: 253x178x34 mm, weight: 1100 g, Worked examples or Exercises; 35 Halftones, black and white; 65 Line drawings, black and white
  • Izdošanas datums: 07-Sep-2017
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 1107162386
  • ISBN-13: 9781107162389
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781107162389.html
Keywords:
Containing a large and varied set of problems, this rich resource will allow students to stretch their mathematical abilities beyond the school syllabus, and bridge the gap to university-level mathematics. Many proofs are provided to better equip students for the transition to university. The author covers substantial extension material using the language of sixth form mathematics, thus enabling students to understand the more complex material. Exercises are carefully chosen to introduce students to some central ideas, without building up large amounts of abstract technology. There are over 1500 carefully graded exercises, with hints included in the text, and solutions available online. Historical and contextual asides highlight each area of mathematics and show how it has developed over time.

Containing a large and varied set of problems, this book allows students to stretch their mathematical abilities further to bridge the gap between school and university. Substantial extension material is covered using accessible language, offering students the chance to develop their understanding of mathematics without too much abstraction.

Recenzijas

'The text is quite reader friendly, with over 1,500 graded exercises (most with hints) presented throughout the text, not just at the ends of sections or chapters. As a result, readers are encouraged and motivated to take the time and make the effort to understand each concept as they proceed. Earl exerts a positive influence on beginning students as they decide whether to pursue a degree in mathematics. Perhaps best of all, students get a glimpse of the breadth of areas they can pursue within the mathematics realm - even at the early stages of their study. Summing Up: Recommended.' J. T. Zerger, Choice 'The biggest stumbling-block for many students about to go to university to study mathematics is not the lack of syllabus covered but the lethal attitude 'you don't need this for the exam'. This book will provide much of what they need It is also a good resource for school and college departments looking for questions on FM material that will stretch their best learners.' Owen Toller, Mathematical Gazette

Papildus informācija

This book allows students to stretch their mathematical abilities and bridges the gap between school and university.
Glossary ix
List of Symbols
xiii
General Notation xiii
Relating to Complex Numbers xiii
Relating to Vectors and Matrices xiii
Relating to Special Functions xv
Relating to Integration and Differential Equations xv
Abbreviations xv
Greek Alphabet xvi
1 Introduction
1(7)
1.1 Mathematics in Higher Education
1(3)
1.2 Using These Notes (Important to Read)
4(4)
1 Complex Numbers
8(60)
1.1 The Need for Complex Numbers
8(2)
1.2 Their Algebra
10(3)
1.3 The Argand Diagram
13(7)
1.4 Roots of Unity
20(8)
1.5 Solving Cubic Equations*
28(7)
1.6 Their Geometry
35(9)
1.7 Some Geometric Theory
44(7)
1.8 Further Exercises*
51(17)
2 Induction
68(60)
2.1 Introduction
68(5)
2.2 Examples
73(11)
2.3 The Binomial Theorem
84(16)
2.4 Fibonacci Numbers*
100(6)
2.5 Recurrence Relations*
106(10)
2.6 Further Exercises*
116(12)
3 Vectors and Matrices
128(154)
3.1 The Algebra of Vectors
128(5)
3.2 The Geometry of Vectors. The Scalar Product
133(13)
3.3 The Algebra of Matrices
146(16)
3.4 Simultaneous Equations Inverses
162(10)
3.5 Elementary Row Operations
172(23)
3.6 Dimension. Rank and Nullity*
195(16)
3.7 Matrices as Maps
211(12)
3.8 Determinants
223(15)
3.9 Permutation Matrices*
238(10)
3.10 The Vector Product
248(7)
3.11 Diagonalization
255(13)
3.12 Further Exercises*
268(14)
4 More on Matrices
282(59)
4.1 Changing Bases*
282(10)
4.2 Orthogonal Matrices and Isometries*
292(14)
4.3 Conics
306(13)
4.4 Spectral Theory for Symmetric Matrices*
319(13)
4.5 Further Exercises*
332(9)
5 Techniques of Integration
341(85)
5.1 History and Foundations*
341(20)
5.2 Standard Functions
361(11)
5.3 Integration by Parts. Reduction Formulae
372(11)
5.4 Substitution
383(13)
5.5 Rational and Algebraic Functions
396(8)
5.6 Numerical Methods
404(7)
5.7 A Miscellany of Definite Integrals
411(2)
5.8 Further Exercises*
413(13)
6 Differential Equations
426(64)
6.1 Introduction and History
426(9)
6.2 Separable Equations
435(7)
6.3 Integrating Factors
442(3)
6.4 Linear Differential Equations
445(5)
6.5 Linear Constant Coefficient Differential Equations
450(8)
6.6 Systems of Linear Differential Equations*
458(9)
6.7 Laplace Transform*
467(17)
6.8 Further Exercises*
484(6)
Hints to Selected Exercises 490(25)
Bibliography 515(2)
Index 517
Richard Earl is currently Director of Undergraduate Studies in the Mathematical Institute, University of Oxford, and a Tutor in Mathematics at Worcester College. From 200313, he was Admissions Coordinator and Schools Liaison Officer in the department and has over a decade's experience setting the MAT (Oxford's Mathematics Admissions Test). He has won several teaching awards within the University for his teaching and lecturing. This book grew out of a residential week he ran for several years in Oxford for new students who had not had the chance to study Further Mathematics at A-Level.