Engineering

Support for Future Engineers of India

Engineering Mathematics I

University

Osmania University

Department

Bio-Medical Engineering

Semester

1 Year I Semester

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UNIT-I Sequences and Series36

UNIT-II Differential Calculus61

  1. Curvatures ,Evolutes and Envelopes
  2. Curvatures ,Evolutes and Envelopes
  3. Radius of Curvatures
  4. Radius of Curvatures
  5. Problems on the Radius of curvatures
  6. Problems on the Radius of curvatures
  7. Problems on Radius of Curvatures 1
  8. Problems on Radius of Curvatures 1
  9. Problem on Radius of Curvatures 2
  10. Problem on Radius of Curvatures 2
  11. Radius of curvature at the origin
  12. Radius of curvature at the origin
  13. Center of the curvature
  14. Center of the curvature
  15. Evolutes and its problems
  16. Evolutes and its problems
  17. Problems related to Evolutes
  18. Problems related to Evolutes
  19. Problem related to Evolute
  20. Problem related to Evolute
  21. Envelope and its related problems
  22. Envelope and its related problems
  23. Problems Related to Envelope
  24. Problems Related to Envelope
  25. Problems related to envelope 1
  26. Problems related to envelope 1
  27. Problems related to curves
  28. Problems related to curves
  29. Problems related to curves 1
  30. Problems related to curves 1
  31. Problem related to curves 2
  32. Problem related to curves 2
  33. Problem related to traces
  34. Problem related to traces
  35. Mean value theorem and its problems
  36. Mean value theorem and its problems
  37. Rolles Theorem and its Releted problems
  38. Rolles Theorem and its Releted problems
  39. Introduction to curve sketching
  40. Introduction to curve sketching
  41. Tracing or sketching of curves in Cartesian coordinate system
  42. Tracing or sketching of curves in Cartesian coordinate system
  43. Lagrange's Mean Value theorem and its related problems
  44. Lagrange's Mean Value theorem and its related problems
  45. Lagrange's Mean Value theorem and its related problems 1
  46. Lagrange's Mean Value theorem and its related problems 1
  47. Lagrange’s Mean Value theorem and its related problems 2
  48. Lagrange’s Mean Value theorem and its related problems 2
  49. Lagrange’s Mean Value theorem and its related problems 3
  50. Lagrange’s Mean Value theorem and its related problems 3
  51. Cauchy’s Mean Value theorem and its related problems
  52. Cauchy’s Mean Value theorem and its related problems
  53. Cauchy’s Mean Value theorem and its related problems 1
  54. Cauchy’s Mean Value theorem and its related problems 1
  55. Taylor's theorem and its related problems
  56. Taylor's theorem and its related problems
  57. Taylor's theorem and its related problems 1
  58. Taylor's theorem and its related problems 1
  59. Long Answer Questions
  60. Short Answer Questions
  61. Multiple Choice Questions

Unit-334

UNIT–IV Multiple Integrals41

  1. Double And Triple Integrals
  2. Double And Triple Integrals
  3. Evaluation of Double Integrals in Cartesian Co Ordinates when limits are given
  4. Evaluation of Double Integrals in Cartesian Co Ordinates when limits are given
  5. Evaluation of Double Integrals in Cartesian Co Ordinates when Region is given 1
  6. Evaluation of Double Integrals in Cartesian Co Ordinates when Region is given 1
  7. Evaluation of Double Integrals in Polar Co Ordinates when Limits are given 1
  8. Evaluation of Double Integrals in Polar Co Ordinates when Limits are given 1
  9. Evaluation of Double Integrals in Polar co ordinates when limits are given 2
  10. Evaluation of Double Integrals in Polar co ordinates when limits are given 2
  11. Evaluation of Double Integrals in Polar Co Ordinates when Region is given 1
  12. Evaluation of Double Integrals in Polar Co Ordinates when Region is given 1
  13. Evaluation of Double Integrals in polar co ordinates when region is given 2
  14. Evaluation of Double Integrals in polar co ordinates when region is given 2
  15. Change Of  Variable And Its Problems 1
  16. Change Of  Variable And Its Problems 1
  17. Change Of Variable And Its Problems 2
  18. Change Of Variable And Its Problems 2
  19. Change Of Order Of Integration
  20. Change Of Order Of Integration
  21. Change Of Order Of Integration and Its Problems - 1
  22. Change Of Order Of Integration And Its Problems - 1
  23. Change By Order Of Integration and Its Problem - 2
  24. Change By Order Of Integration and Its Problem - 2
  25. Triple Integral
  26. Triple Integral
  27. Triple Integrals And Its Problems 1
  28. Triple Integrals And Its Problems 1
  29. Triple Integral And Its Problems 2
  30. Triple Integral And Its Problems 2
  31. Finding Areas of 'R' Represented Through Cartesian Coordinates
  32. Finding Areas of 'R' Represented Through Cartesian Coordinates
  33. Finding Areas Of 'R' Represented Through Polar Coordinates
  34. Finding Areas Of 'R' Represented Through Polar Coordinates
  35. Volume As Double Integral
  36. Volume As Double Integral
  37. Volume Of Triple Integral
  38. Volume Of Triple Integral
  39. Unit – 4 Long Question and Answers
  40. Unit – 4 Short Question and Answers
  41. Multiple Choice Questions

UNIT–V Vector Calculus 48

  1. Introduction to Vector Differentiation
  2. Introduction to Vector Differentiation
  3. Scalar And Vector Point Functions
  4. Scalar And Vector Point Functions
  5. Directional Derivatives And Its Problems 1
  6. Directional Derivatives And Its Problems 1
  7. Directional Derivatives And Its Problem 2
  8. Directional Derivatives And Its Problem 2
  9. Angle Between The Surfaces And Normal And Its Problem
  10. Angle Between The Surfaces And Normal And Its Problem
  11. Divergence of a Vector and its Problems
  12. Divergence of a Vector and its Problems
  13. Problems on Gradient
  14. Problems on Gradient
  15. Curl of a vector
  16. Curl of a vector
  17. Curl of a vector and its problems
  18. Curl of a vector and its problems
  19. Laplacian Operators
  20. Laplacian Operators
  21. Laplacian Operator and its Problem 1
  22. Laplacian Operator and its Problem 1
  23. Laplacian operator and its problem 2
  24. Laplacian operator and its problem 2
  25. Laplacian operator and its problem 3
  26. Laplacian operator and its problem 3
  27. Laplacian operator and its problem 4
  28. Laplacian operator and its problem 4
  29. Introduction to vector integration and integral theorem
  30. Introduction to vector integration and integral theorem
  31. Problems on line integral 1
  32. Problems on line integral 1
  33. Problems on line integral 2
  34. Problems on line integral 2
  35. Problems on line Integral 3
  36. Problems on line Integral 3
  37. Problems on line Integral 4
  38. Problems on line Integral 4
  39. Surface Integral
  40. Surface Integral
  41. Problems On Surface Integrals - 1
  42. Problems On Surface Integrals - 1
  43. Problems On Surface Integrals - 2
  44. Problems On Surface Integrals - 2
  45. Green's Theorem and its problems - 1
  46. Green's Theorem and its problems - 1
  47. Multiple Choice Questions
  48. Short Answer Questions
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