Mathematics II notes KNEC

INTRODUCTION

This module unit is designed to equip the trainee with the relevant mathematical knowledge, skills, techniques and attitudes necessary to enhance better understanding and application of mathematics in the respective trade.

TOPICS COVERED:

Probability

• Definition of probability
• Laws of probability
• Expectation variance and S.D.
• Types of distributions
• Mean, variance and SD of probability distributions
• Application of probability distributions

Statistics

• Definition of statistics
• Measures of centre tendency
• Measures of dispersion

Sequence and Series

• Sequence and series
• Simple and compound interest
• Arithmetic and geometric progressions

Vectors

• Operation of vectors
• Resolution of vectors into vertical and horizontal components
• Relative velocity

Mensurations

• Units of measurements
• Perimeters, areas, volumes of regular figures and solids
• Area of irregular figures

Integral Calculus

• Definition of integration
• Indefinite and definite integrals
• Methods of integration
• Application of integration

Differential Calculus

• Definition of derivative of a function
• Differentiation from first principle
• Tables of some common derivatives
• Rules of differentiation
• Higher order derivatives
• Definition of partial derivative
• Partial differentiation for function of two variables
• Application of partial differentiation to small changes, stationary points, curve sketching and rates of change

Power Series

• Definition of the term power series
• Taylor’s theorem
• Deduction of Maclaurin’s theorem from Taylor’s theorem
• Use Taylor’s theorem to obtain power series
• Use Maclaurin’s theorem to obtain power series
• Application of Taylor’s theorem and Maclaurin’s theorems in numerical work