European University Institute Library

Maths, a student's survival guide, Jenny Olive

eng

index present

non fiction

Maths

electronic resource

dictionaries

57419676

Jenny Olive

Cambridge University Press - Higher Education Textbooks

a student's survival guide

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.--, Provided by publisher

1. Basic algebra: some reminders of how it works -- Handling unknown quantities -- Multiplications and factorising: the next stage -- Using fractions -- The three rules of working with powers -- The different kinds of numbers -- Working with different kinds of number: some examples -- 2. Graphs and equations -- Solving simple equations -- Introducing graphs -- Relating equations to graphs: simultaneous equations -- Quadratic equations and the graphs which show them -- Further equations -- the Remainder and Factor Theorems -- 3. Relations and functions -- Two special kinds of relationship -- An introduction to functions -- Exponential and log functions -- Unveiling secrets-logs and linear forms -- 4. Some trigonometry and geometry of triangles and circles -- Trigonometry in right-angled triangles -- Widening the field in trigonometry -- Circles -- Using radians -- Tidying up-some thinking points returned to -- 5. Extending trigonometry to angles of any size -- Giving meaning to trig functions af any size of angle -- The trig reciprocal functions -- Building more trig functions from the simplest ones -- Finding rules for combining trig functions -- Solving trig equations -- 6. Sequences and series -- Patterns and formulas -- Arithmetic progressions (APs) -- Geometric Progressions (GPs) -- A compact way of writing sums -- Practical fractions7. Binominal series and proof by induction -- Binominal series for positive whole numbers -- Some applications of binominal series and selections -- Binominal expansions when n is not a positive whole number -- Mathematical induction -- 8. Differentiation -- Some problems answered and difficulties solved -- Natural growth and decay -- Differentiating more complicated functions -- The hyperbolic functions of sinh x and cosh x -- Some uses for differentiation -- Implicit differentiation -- Writing functions in an alternative form using series -- 9. Integration -- Doing the opposite of differentiating -- Techniques of integration -- Solving some more differential equations -- 10. Complex numbers -- A new sort of number -- Doing arithmetic with complex numbers -- How e connects with complex numbers -- Using complex numbers to solve more equations -- Finding where z can be if it must fit particular rules -- 11. Working with vectors -- Basic rules for handling vectors -- Multiplying vectors -- Finding equations for lines and planes -- Finding angles and distances involving lines and planes