Mathematics - I Semester-I: (RTM) Nagpur University

"Mathematics - I" is as per the latest prescribed Syllabus RTMNU Nagpur with a major focus on Differential and Multivariable Calculus, Matrices, First Order and Higher Order Ordinary Differential Equations. The text is lucid and brimming with examples for further ease of students. The practice quotient is high as well so that the reader further understands the topics which have been deftly explained.

• A comprehensive explanation of all topics is provided with 21 chapters.

• Over 500 solved examples for better understanding.

• More than 800 practice exercise questions from examination papers of various Technical Universities.

UNIT 1: Differential Calculus

1. Successive Differentiation: Leibniz Rule

2. Taylor and Maclaurin Series

3. Indeterminate Forms and L'Hôpital Rule

4. Maxima and Minima for Function of One Variable

 UNIT 2: Multivariable Calculus (Differentiation)

5. Partial Derivatives

6. Total Differentiation

7. Jacobians

8. Maxima and Minima for Function of Two Variables

9. Lagrange Method of Undetermined Multipliers

 UNIT 3: Matrices

10. Inverse of Matrix by Partitioning

11. Rank of Matrix

12. Consistency of Linear System of Equations

13. Linear and Orthogonal Transformations

14. Cayley - Hamilton Theorem

 UNIT 4: First Order Ordinary Differential Equations

15. First Order Differential Equations

16. Applications of First Order Differential Equations

 UNIT 5: Higher Order Ordinary Differential Equations

17. Higher Order Linear Differential Equations with Constant Coefficients

18. Method of Variation of Parameters

19. Cauchy and Legendre's Homogeneous Differential Equations

20. Simultaneous Differential Equations

21. Applications of Higher Order Differential Equations

• Questions from Latest RTMNU Examination Papers Mathematics-I

This book is designed for B.Tech. (First Semester) students of RTM Nagpur University.