A Basic Course in Mathematics for Polytechnic – Volume III by Prof. Bishwa Ram Sharma is a comprehensive textbook designed strictly according to the newly revised syllabus for 3rd Semester Polytechnic courses. The book presents fundamental and applied mathematical concepts in a clear, systematic, and student-friendly manner, making it ideal for diploma engineering students across various branches.

The content covers essential areas of mathematics such as calculus, matrices, differential equations, numerical methods, vector algebra, and complex numbers, with a strong focus on practical application in engineering and technology. Each chapter includes clear explanations, solved examples, practice exercises, and problem sets that help students strengthen analytical skills and prepare effectively for examinations.

Published by Mahaveer Publications, this volume serves as a reliable and updated resource for polytechnic institutions and students seeking a strong foundation in mathematics for technical education.

Chapter 1: Partial Differentiation (Pages 1–17)

• Function of two or more variables

• Definition and meaning of partial derivatives (First order)

Chapter 2: Differential Equation (Pages 18–31)

• Definition, classification, order and degree of a differential equation

• Formation of ordinary differential equations

Chapter 3: Ordinary Differential Equations of First Order and First Degree (Pages 32–88)

• Separation of variables

• Homogeneous equations

• Equations reducible to homogeneous form

• Linear equations

• Bernoulli’s equations

• Applications of differential equations

  • Laws of voltage

  • Current related to EC, RC, LRC Circuits

Chapter 4: Differential Equations of First Order and Higher Degree (Pages 89–116)

• Left-hand side resolved into factors

• Equations solvable for x

• Equations solvable for y

• Clairaut’s equations

Chapter 5: Differential Equations of Second Order (Pages 117–153)

• Second-order differential equations with constant coefficients and RHS zero

• Operator D, auxiliary equation

• Rules for real and equal, real and unequal, and complex roots

• Complete solution

• Second-order differential equations with constant coefficients and RHS a simple function of x

• Exponential, trigonometric, and algebraic functions

Chapter 6: Measures of Central Tendency (Pages ~154–176)

• Mean

• Median

• Mode

Chapter 7: Measures of Dispersion (Pages ~177–196)

• Range, quartile deviation

• Mean deviation (from mean, median, mode)

• Standard deviation, variance, coefficient of variation

Chapter 8: Correlation (Pages 197–216)

• Definition of bivariate distribution

• Scatter diagram

• Karl Pearson’s coefficient of correlation

Chapter 9: Probability (Pages 217–231)

• Classical definition of probability

• Addition and multiplication laws

• Related solved examples (simple cases)

Chapter 10: Graphics (Pages 231–259)

• Graphs of trigonometric functions

Chapter 11: Matrix (Pages 260–282)

• Transpose of a matrix

• Adjoint of a square matrix

• Inverse of a matrix

• Solution of simultaneous linear equations

• Characteristic equations

Chapter 12: Linear Programming Problems (Basics) (Pages 283–315)

• Introduction to system of linear inequalities in two variables

• Graphical solution of the system

• Mathematical formulation of LPP (two variables)

• Unique optimal feasible solution of LPP (two variables) by graphical method