Civil Engineering & Surveying ( PMB )

MATHEMATICS C completes the math course done in the diploma.The course material consists of Inverse trig and Inverse hyperbolic derivatives, Partial differentiation, Techniques of Integration, Applications of Integration and Differential equations.

Inverse function derivatives

Differentiation of the inverse trig and inverse hyperbolic functions

Partial differentiation:

The derivative of a function of two or more independent variables, applications of partial derivatives, small changes and related rates of change problems

Techniques of Integration:

Substitution method, Integration by parts, Integration by partial fractions, Trig integrals, t-substitutions, Table integrals, Splitting type integrals.

Applications of definite integrals:

Area between curves, volumes of solid of revolution, length of plane curves, centre of mass of a lamina of uniform density, area of surface of revolution

Differential equations

Seperable, Homogenous, Linear and Bernoulli equations are solved

The MATHEMATICS B course of the trio of math courses in the diploma is an important one. It is an important prerequisite for the final math course which is  MATHEMATICS C . The course material is split into four sections: Differentiation, Introduction to Integration, Matrix theory and Statistics. Of these , differentiation is the most important section. The whole of the first major test is based on differentiation, including the first two minor tests. This section is also key to the techniques of integration and partial differentiation in the MATHS C course.The course content is:

Differentiation:

All methods of differentiation and rules of differentiation are covered. After this, the applications of differentiation are done. These include: min/max problems, curve sketching, Maclaurin  series, rates of change.

Integration:

Basics in integration, standard integration, Integration as a sum, area between curves,

Matrix theory:

Matrix algebra, determinants of (2x2) and (3x3) matrices, finding inverses of (2x2) and (3x3) matrices, solving a system of equations using Gaussian elimination, Cramers Rule, Inverse matrix method

Statistics:

Basic definitions, grouping a raw data set into a frequency table, graphical representation of frequency tables, Histograms and Ogives. Calculating percentiles and measures of central location for raw and grouped data sets.