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## Book Description

This friendly self-help workbook covers mathematics essential to first-year undergraduate scientists and engineers. In the second edition of this highly successful textbook the author has completely revised the existing text and added a totally new chapter on vectors. Mathematics underpins all science and engineering degrees, and this may cause problems for students whose understanding of the subject is weak. In this book Jenny Olive uses her extensive experience of teaching and helping students by giving a clear and confident presentation of the core mathematics needed by students starting science or engineering courses. The book contains almost 800 exercises, with detailed solutions given in the back to allow students who get stuck to see exactly where they have gone wrong. Topics covered include trigonometry and hyperbolic functions, sequences and series (with detailed coverage of binomial series), differentiation and integration, complex numbers, and vectors.

1. Cover
2. Title Page
4. Contents
5. Acknowledgements
6. Dedication Page
7. Introduction
8. Introduction to the second edition
9. 1 Basic algebra: some reminders of how it works
1. 1.A Handling unknown quantities
2. l.B Multiplications and factorising: the next stage
3. l.C Using fractions
4. l.D The three rules for working with powers
5. l.E The different kinds of numbers
6. l.F Working with different kinds of number: some examples
10. 2 Graphs and equations
1. 2.A Solving simple equations
2. 2.B Introducing graphs
3. 2.C Relating equations to graphs: simultaneous equations
4. 2.D Quadratic equations and the graphs which show them
5. 2.E Further equations – the Remainder and Factor Theorems
11. 3 Relations and functions
1. 3.A Two special kinds of relationship
2. 3.B An introduction to functions
3. 3.C Exponential and log functions
4. 3.D Unveiling secrets - logs and linear forms
12. 4 Some trigonometry and geometry of triangles and circles
1. 4.A Trigonometry in right-angled triangles
2. 4.B Widening the field in trigonometry
3. 4.C Circles
5. 4.E Tidying up - some thinking points returned to
13. 5 Extending trigonometry to angles of any size
1. 5.A Giving meaning to trig functions of any size of angle
2. 5.B The trig reciprocal functions
3. 5.C Building more trig functions from the simplest ones
4. 5.D Finding rules for combining trig functions
5. 5.E Solving trig equations
14. 6 Sequences and series
1. 6.A Patterns and formulas
2. 6.B Arithmetic progressions (APs)
3. 6.C Geometric progressions (GPs)
4. 6.D A compact way of writing sums: the ? notation
5. 6.E Partial fractions
6. 6.F The fate of the frog down the well
15. 7 Binomial series and proof by induction
1. 7.A Binomial series for positive whole numbers
2. 7.B Some applications of binomial series and selections 272
3. 7.C Binomial expansions when n is not a positive whole number 275
4. 7.D Mathematical induction 279
16. 8 Differentiation
1. 8.A Some problems answered and difficulties solved
2. 8.B Natural growth and decay – the number e
3. 8.C Differentiating more complicated functions
4. 8.D The hyperbolic functions of sinh x and cosh x
5. 8.E Some uses for differentiation
6. 8.F Implicit differentiation
7. 8.G Writing functions in an alternative form using series
17. 9 Integration
1. 9.A Doing the opposite of differentiating
2. 9.B Techniques of integration
3. 9.C Solving some more differential equations
18. 10 Complex numbers
1. 10.A A new sort of number
2. 10.B Doing arithmetic with complex numbers
3. 10.C How e connects with complex numbers
4. 10.D Using complex numbers to solve more equations
5. 10.E Finding where z can be if it must fit particular rules
19. 11 Working with vectors
1. ll.A Basic rules for handling vectors
2. 11.B Multiplying vectors
3. 11.C Finding equations for lines and planes
4. 11.D Finding angles and distances involving lines and planes