MASTERING SELECTED TOPICS IN MATHEMATICS

This book, MASTERING SELECTED TOPICS IN MATHEMATICS: Including Differential Calculus, is a useful book for high school students and students in higher institutions. It serves as a useful tool for students who are preparing for entrance examinations into colleges and universities. Students with poor mathematical foundation will find this text very valuable in improving their problem solving skills in mathematics. The step by step explanations presented in the worked examples are easy to understand since care was taken to sufficiently explain salient points and mathematical ideas. Efforts have been made to achieve a complete and simplified explanation of every worked example given in this eBook. Many worked examples have been included in each topic in order to fully cover every complexity the topic might contain. Numerous exercises at the end of each chapter are added to test students' understanding of the topic. Therefore students are thus presented with an effective means of self-assessment whereby they can determine their individual strengths and revision needs. Solutions to the exercises are provided at the end of the book.

The topics covered in this book include:

• Number bases
• Standard forms and approximations
• Laws and theories of logarithms
• Modular arithmetic
• Percentage error
• Arithmetic progression/Linear Sequence
• Geometric progression/Exponential Sequence
• Surds, including square root of surds
• LIMIT OF A FUNCTION
• DIFFERENTIATION FROM FIRST PRINCIPLE
• GENERAL RULE OF DIFFERENTIATION AND COMPOSITE FUNCTIONS
• PRODUCT RULE OF DERIVATIVE
• QUOTIENT RULE OF DERIVATIVE
• DERIVATIVE OF PARAMETRIC EQATIONS
• DERIVATIVE OF IMPLICIT FUNCTIONS
• DERIVATIVE OF TRIGONOMETRIC FUNCTIONS
• DERIVATIVE OF INVERSE FUNCTIONS
• DERIVATIVES OF INVERSE TRIGONOMETRIC FUNCTIONS
• DERIVATIVES OF HYPERBOLIC FUNCTIONS