Numerical Methods & Analysis

Numerical Methods is a free engineering mathematics handbook covering important course topics, detailed notes, diagrams, equations, formulas and study materials. Download this digital book and reference guide for Diploma, BE, BTech, BSc, BCA, MCA and related degree courses.

Explore 77 topics across 5 chapters on numerical analysis, root-finding, linear equations, eigenvalues, interpolation, differentiation, numerical integration and ordinary differential equations. Useful for university exams, GATE revision, viva, interviews, assignments, projects and quick reference.

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57 LISTED TOPICS FROM 77

ROOT-FINDING & ITERATIVE METHODS

1. Solving Algebraic and Transcendental Equations

2. Methods for Finding Roots of Polynomial Equations

3. Initial Approximation for Iterative Procedures

4. False Position Method (Regula Falsi)

5. Newton-Raphson Method

6. General Iteration Method

7. Convergence of Iterative Methods

LINEAR SYSTEMS & EIGENVALUES

8. Systems of Linear Algebraic Equations

9. Direct Methods for Solving Linear Systems

10. Gaussian Elimination Method

11. Gauss-Jordan Method

12. Iterative Methods

13. Gauss-Jacobi Iteration Method

14. Gauss-Seidel Iteration Method

15. Eigenvalue Problems

16. Power Method

INTERPOLATION & NUMERICAL DIFFERENTIATION

17. Interpolation

18. Lagrange Interpolation

19. Linear Interpolation

20. Quadratic Interpolation

21. Interpolation Error

22. Divided Differences

23. Newton's Divided Difference Interpolation

24. Interpolation with Equally Spaced Points

25. Relations Between Differences and Derivatives

26. Newton's Forward Difference Formula

27. Newton's Backward Difference Interpolation Formula

28. Spline Functions

29. Cubic Interpolation

30. Numerical Differentiation

31. Derivatives Using Newton's Forward Difference Formula

32. Derivatives Using Newton's Backward Difference Formula

33. Derivatives Using Divided Difference Formula

NUMERICAL INTEGRATION

34. Numerical Integration with Uniform Mesh Spacing

35. Trapezoidal Rule

36. Error in the Trapezoidal Rule

37. Composite Trapezoidal Rule

38. Simpson's 1/3 Rule

39. Error in Simpson's 1/3 Rule

40. Composite Simpson's 1/3 Rule

41. Simpson's 3/8 Rule

42. Romberg Method

43. Romberg Method with the Trapezoidal Rule

44. Romberg Method with Simpson's 1/3 Rule

45. Gauss-Legendre Integration Rules

46. Gauss-Legendre One-Point Rule

47. Gauss-Legendre Two-Point Rule

48. Gauss-Legendre Three-Point Rule

49. Double Integrals Using the Trapezoidal Rule

50. Double Integrals Using Simpson's Rule

ORDINARY DIFFERENTIAL EQUATIONS

51. Initial Value Problems for Ordinary Differential Equations (ODEs)

52. Reducing Second-Order ODEs to First-Order Systems

53. Single-Step Methods

54. Multistep Methods

55. Taylor Series Method

56. Modified Euler (Heun's) Methods

57. Runge-Kutta Methods

Use this free Numerical Methods and Analysis ebook to revise numerical calculations, approximation methods and engineering mathematics.