FM-H8152.tex 19/7/2006 18: 59 Page xviii
xviii SYLLABUS GUIDANCEChapter Analytical Further Engineering
Methods Analytical Mathematics
for Methods for
Engineers Engineers- Total differential, rates of change and small changes ×
- Maxima, minima and saddle points for functions of two variables ×
- Standard integration ×
- Some applications of integration ×
- Integration using algebraic substitutions ×
- Integration using trigonometric and hyperbolic substitutions ×
- Integration using partial fractions ×
- Thet= tanθ/2 substitution
- Integration by parts ×
- Reduction formulae ×
- Numerical integration ×
- Solution of first order differential equations by ×
separation of variables - Homogeneous first order differential equations
- Linear first order differential equations ×
- Numerical methods for first order differential equations × ×
- Second order differential equations of the ×
formad^2 y
dx^2+bdy
dx+cy= 0- Second order differential equations of the ×
formad^2 y
dx^2+bdy
dx+cy=f(x)- Power series methods of solving ordinary ×
differential equations - An introduction to partial differential equations ×
- Presentation of statistical data ×
- Measures of central tendency and dispersion ×
- Probability ×
- The binomial and Poisson distributions ×
- The normal distribution ×
- Linear correlation ×
- Linear regression ×
- Sampling and estimation theories ×
- Significance testing ×
- Chi-square and distribution-free tests ×
- Introduction to Laplace transforms ×
- Properties of Laplace transforms ×
- Inverse Laplace transforms ×
- Solution of differential equations using Laplace transforms ×
- The solution of simultaneous differential equations using ×
Laplace transforms - Fourier series for periodic functions of period 2π ×
- Fourier series for non-periodic functions over range 2π ×
- Even and odd functions and half-range Fourier series ×
- Fourier series over any range ×
- A numerical method of harmonic analysis ×
- The complex or exponential form of a Fourier series ×