Basic Mathematics: Part II

Basic Mathematics: Part II

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  • ISBN : 9789358707977
  • Pages : 640
  • Binding : Paperback
  • Language : English
  • Imprint : S Chand Publishing
  • © year : 2024
  • Size : 6.50*9.25

Price : 650.00 520.00

"Basic Mathematics Part II" serves as a comprehensive guide through essential topics in calculus, integration, and vectors, making it an indispensable resource for students and professors alike. In Unit I: Calculus 1, readers delve into foundational concepts such as continuity, differentiability and second-order derivatives, laying the groundwork for advanced mathematical exploration. The exploration of Rolle's Theorem and the Mean Value Theorem offers insight into the fundamental principles of calculus, while discussions on the rate of change of quantities tangents and normals provide practical applications. Moreover, the unit explores differentials, errors, and approximations, crucial for understanding real-world problems and scientific analysis. The unit concludes with a thorough examination of increasing and decreasing functions, maxima, and minima, providing tools for optimizing mathematical models. 
In Unit II: Calculus 2, the focus shifts to integration techniques, including indefinite integrals, integration by substitution, partial fractions, and integration of rational and irrational functions. The study of definite integrals and techniques like integration by parts enriches readers' understanding of mathematical analysis and problem-solving. Additionally, the unit covers sketching of simple curves and the calculation of bounded regions' areas, enhancing geometric intuition and visualization skills. The inclusion of differential equations and their applications further extends the reader's mathematical toolkit, with topics ranging from separable variables to homogeneous equations and their practical implications. 
Finally, Unit III: Vectors and Three-Dimensional Geometry introduces algebraic operations with vectors, scalar and vector products, and their applications in probability theory. The exploration of probability distributions, including binomial distribution, offers a bridge between calculus and statistics, enabling readers to tackle a diverse range of mathematical challenges with confidence. 
With its clear explanations, worked examples, and comprehensive coverage, "Basic Mathematics Part II" empowers learners to master essential mathematical concepts and apply them across various disciplines.

Unit I: Calculus 1

1. Continuity

2. Differentiability

3. Second Order Derivatives

4. Rolle's Theorem and Mean Value Theorem

5. Rate of Change of Quantitives

6. Tangents and Normals

7. Differentials, Errors and Approximations

8. Increasing and Decreasing Functions

9. Maxima and Minima

Unit II: Calculus 2

10. Indefinite Integrals

11. Integration by Substitution

12. Integration by Using Partial Fractions

13. Integration of Rational and Irrational Functions

14. Integration by Parts

15. Definite Integrals

16. Sketching of Simple Curves

17. Area of Bounded Regions

18. Differential Equations

19. Differential Equations with Variables Separable

20. Homogeneous Differential Equations

21. Applications of Differential Equations

Unit III: Vectors and Three-Dimensional Geometry

22. Algebra of Vectors

23. Scalar Product of two Vectors

24. Vector Product of Two Vectors

25. Probability

26. Probability Distribution

27. Binomial Distribution

The book has been designed as a comprehensive guide through essential topics in Calculus, Integration and Vectors for all Engineering students and faculties.

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