Applied Numerical Methods for Chemical Engineers emphasizes the derivation of a variety of numerical methods and their application to the solution of engineering problems, with special attention to problems in the chemical engineering field. These algorithms encompass linear and nonlinear algebraic equations, eigenvalue problems, finite difference methods, interpolation, differentiation and integration, ordinary differential equations, boundary value problems, partial differential equations, and linear and nonlinear regression analysis. MATLAB is adopted as the calculation environment throughout the book because of its ability to perform all the calculations in matrix form, its large library of built-in functions, its strong structural language, and its rich graphical visualization tools. Through this book, students and other users will learn about the basic features, advantages and disadvantages of various numerical methods, learn and practice many useful m-files developed for different numerical methods in addition to the MATLAB built-in solvers, develop and set up mathematical models for problems commonly encountered in chemical engineering, and solve chemical engineering related problems through examples and after-chapter problems with MATLAB by creating application m-files.
1. 2.1 Introduction - p. 64 2. 2.2 Review of selected matrix and vector operations - p. 68 3. 2.3 Consistency of equations and existence of solutions - p. 78 4. 2.4 Cramer’s rule - p. 79 5. 2.5 Gauss elimination method - p. 80 6. Calculation of determinants by the Gauss method - p. 88 7. 2.6 Gauss-Jordan Reduction Method - p. 91 8. 2.7 Gauss-Seidel substitution method - p. 99 9. 2.8 Jacobi method - p. 105 10. 2.9 Homogeneous algebraic equations and the characteristic-value problem - p. 113 11. 2.10 Using built-in MATLAB® and Excel functions - p. 124 12. 2.11 Summary - p. 125 13. Problems - p. 125 14. References - p. 134 15. Chapter 3. Finite difference methods and interpolation - p. 137 16. Chapter 4. Differentiation and integration - p. 179 17. Chapter 5. Ordinary differential equations: initial value problems - p. 225 18. Abstract: - p. 225 19. Chapter Outline - p. 225 20. Motivation - p. 225 21. 5.1 Introduction - p. 226 22. 5.2 Classifications of ordinary differential equations - p. 229 23. 5.3 Transformation to canonical form - p. 230 24. 5.4 Linear ordinary differential equations - p. 235 25. 5.5 Nonlinear ordinary differential equations - p. 241 26. 5.6 Using built-in MATLAB® functions - p. 263 27. 5.7 Difference equations and their solutions - p. 263 28. 5.8 Propagation, stability, and convergence - p. 267 29. 5.9 Step size control - p. 276 30. 5.10 Stiff differential equations - p. 277 31. 5.11 Summary - p. 279 32. Problems - p. 279 33. References - p. 291 34. Chapter 6. Ordinary differential equations: boundary value problems - p. 293 35. Chapter 7. Partial differential equations - p. 327 36. Abstract - p. 327 37. Chapter Outline - p. 327 38. Motivation - p. 327 39. 7.1 Introduction - p. 328 40. 7.2 Classification of partial differential equations - p. 329 41. 7.3 Initial and boundary conditions - p. 330 42. 7.4 Solution of partial differential equations using finite differences - p. 332 43. 7.5 Using built-in MATLAB® functions - p. 387 44. 7.6 Stability analysis - p. 387 45. 7.7 Summary - p. 390 46. Problems - p. 391 47. References - p. 400 48. Chapter 8. Linear and nonlinear regression analysis - p. 403 49. Abstract - p. 403 50. Chapter Outline - p. 403 51. Motivation - p. 403 52. 8.1 Process analysis, mathematical modeling, and regression analysis - p. 404 53. 8.2 Review of statistical terminology used in regression analysis - p. 407 54. 8.3 Linear regression analysis - p. 427 55. 8.4 Nonlinear regression analysis - p. 437 56. 8.5 Analysis of variance and other statistical tests of the regression results - p. 447 57. 8.6 Using built-in MATLAB® and Excel functions - p. 465 58. 8.7 Summary - p. 466 59. Problems - p. 468 60. References - p. 475 61. Appendix. Orthogonal Polynomials - p. 477 62. Index - p. 483
Applied Numerical Methods for Chemical Engineers emphasizes the derivation of a variety of numerical methods and their application to the solution of engineering problems, with special attention to problems in the chemical engineering field. These algorithms encompass linear and nonlinear algebraic equations, eigenvalue problems, finite difference methods, interpolation, differentiation and integration, ordinary differential equations, boundary value problems, partial differential equations, and linear and nonlinear regression analysis. MATLAB is adopted as the calculation environment throughout the book because of its ability to perform all the calculations in matrix form, its large library of built-in functions, its strong structural language, and its rich graphical visualization tools. Through this book, students and other users will learn about the basic features, advantages and disadvantages of various numerical methods, learn and practice many useful m-files developed for different numerical methods in addition to the MATLAB built-in solvers, develop and set up mathematical models for problems commonly encountered in chemical engineering, and solve chemical engineering related problems through examples and after-chapter problems with MATLAB by creating application m-files.
1. 2.1 Introduction - p. 64 2. 2.2 Review of selected matrix and vector operations - p. 68 3. 2.3 Consistency of equations and existence of solutions - p. 78 4. 2.4 Cramer’s rule - p. 79 5. 2.5 Gauss elimination method - p. 80 6. Calculation of determinants by the Gauss method - p. 88 7. 2.6 Gauss-Jordan Reduction Method - p. 91 8. 2.7 Gauss-Seidel substitution method - p. 99 9. 2.8 Jacobi method - p. 105 10. 2.9 Homogeneous algebraic equations and the characteristic-value problem - p. 113 11. 2.10 Using built-in MATLAB® and Excel functions - p. 124 12. 2.11 Summary - p. 125 13. Problems - p. 125 14. References - p. 134 15. Chapter 3. Finite difference methods and interpolation - p. 137 16. Chapter 4. Differentiation and integration - p. 179 17. Chapter 5. Ordinary differential equations: initial value problems - p. 225 18. Abstract: - p. 225 19. Chapter Outline - p. 225 20. Motivation - p. 225 21. 5.1 Introduction - p. 226 22. 5.2 Classifications of ordinary differential equations - p. 229 23. 5.3 Transformation to canonical form - p. 230 24. 5.4 Linear ordinary differential equations - p. 235 25. 5.5 Nonlinear ordinary differential equations - p. 241 26. 5.6 Using built-in MATLAB® functions - p. 263 27. 5.7 Difference equations and their solutions - p. 263 28. 5.8 Propagation, stability, and convergence - p. 267 29. 5.9 Step size control - p. 276 30. 5.10 Stiff differential equations - p. 277 31. 5.11 Summary - p. 279 32. Problems - p. 279 33. References - p. 291 34. Chapter 6. Ordinary differential equations: boundary value problems - p. 293 35. Chapter 7. Partial differential equations - p. 327 36. Abstract - p. 327 37. Chapter Outline - p. 327 38. Motivation - p. 327 39. 7.1 Introduction - p. 328 40. 7.2 Classification of partial differential equations - p. 329 41. 7.3 Initial and boundary conditions - p. 330 42. 7.4 Solution of partial differential equations using finite differences - p. 332 43. 7.5 Using built-in MATLAB® functions - p. 387 44. 7.6 Stability analysis - p. 387 45. 7.7 Summary - p. 390 46. Problems - p. 391 47. References - p. 400 48. Chapter 8. Linear and nonlinear regression analysis - p. 403 49. Abstract - p. 403 50. Chapter Outline - p. 403 51. Motivation - p. 403 52. 8.1 Process analysis, mathematical modeling, and regression analysis - p. 404 53. 8.2 Review of statistical terminology used in regression analysis - p. 407 54. 8.3 Linear regression analysis - p. 427 55. 8.4 Nonlinear regression analysis - p. 437 56. 8.5 Analysis of variance and other statistical tests of the regression results - p. 447 57. 8.6 Using built-in MATLAB® and Excel functions - p. 465 58. 8.7 Summary - p. 466 59. Problems - p. 468 60. References - p. 475 61. Appendix. Orthogonal Polynomials - p. 477 62. Index - p. 483
