Guide to Mathematical Methods
Palgrave Macmillan (Verlag)
978-0-333-49209-3 (ISBN)
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Like other books in the Macmillan Mathematical Guides series, this book is written for first year undergraduates on mathematics degree courses, and provides a carefully paced and readable introduction to its topic. Plenty of worked examples and exercises are provided. The book is based on the first year Mathematical Methods course in the Pure Maths department at Sheffield University - a course which has run successfully for many years in a self-paced learning mode.
Part 1 Functions: sets and intervals; functions; limits and continuity; polynomials; rational functions; trigonometric functions; exponential and logarithmic functions; hyperbolic functions; composite and inverse functions. Part 2 Differentiation: introduction; derivatives of combinations of functions; derivatives of trigonometric functions; derivatives of exponential and logarithmic functions; higher derivatives; power series expansion. Part 3 Integration: area and definite integrals; speed and distance, force and work; the fundamental theorem of calculus; standard integrals; integration of substitution; integration by parts; partial fractions; systematic integration of rational functions; rational trigonometric functions; improper integrals. Part 4 Linear equations, determinants and matrices: introduction; determinants; three or more simultaneous equations; matrices; square matrices; numerical solution of linear equations. Part 5 Vectors: introduction; coordinate systems; the algebra of vectors; unit vectors and direction cosines; scalar products; vector products; triple products; lines and planes; vector equation of curves in space; differentiation of vector functions; arclength. Part 6 Functions of two variables: introduction; the standard family of functions; graphical representation; functions of three or more variables; partial derivatives; chain rules; directional derivatives; higher partial derivatives; maxima and minima. Part 7 Line integrals and double integrals: vector fields; line integrals; properties of line integrals; conservative fields; double integrals; change of variables; Green's theorem. Part 8 Complex numbers: introduction; the algebra of complex numbers; solution of equations; equalities and inequalities; polar form of complex numbers; exponential form of complex numbers; trigonometric identities. Part 9 Differential equations: introduction; differential equations of type 1 (separable); differential equations of type 2; differential equations of type 3 (exact); differential equations of type 4 (linear); an alternative way of solving first order linear equations; solution of second order differential equations; complementary function of second order differential equations; general solution of non-homogeneous equation; initial and boundary conditions.
| Erscheint lt. Verlag | 4.2.1991 |
|---|---|
| Reihe/Serie | Mathematical Guides |
| Zusatzinfo | illustrations, index |
| Verlagsort | Basingstoke |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 551 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-10 | 0-333-49209-9 / 0333492099 |
| ISBN-13 | 978-0-333-49209-3 / 9780333492093 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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