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.

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