Engineering

Support for Future Engineers of India

Mathematics-I

University

Kakatiya University

Department

Information Technology

Semester

1 Year I Semester

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UNIT I Sequences & Series 37

UNIT-II Calculus61

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

Unit-III Multivariable Differential Calculus45

  1. Limits of function and its derivatives
  2. Limits of function and its derivatives
  3. Continuity and its problems
  4. Continuity and its problems
  5. Partial derivatives and its problems
  6. Partial derivatives and its problems
  7. Total derivative and its problems
  8. Total derivative and its problems
  9. Chain rule of differentiation
  10. Chain rule of differentiation
  11. Homogeneous Function, Eulers Theorem and its Problems
  12. Homogeneous Function, Eulers Theorem and its Problems
  13. Homogeneous Function, Eulers Theorem and its Problems-part2
  14. Homogeneous Function, Eulers Theorem and its Problems-part 2
  15. Jacobian and its problems
  16. Jacobian and its problems
  17. Jacobin and its problems - 2
  18. Jacobin and its problems - 2
  19. Functional Dependence and its Problem
  20. Functional Dependence and its Problem
  21. Taylor Series for Function of Two Variable and its Problems
  22. Taylor Series for Function of Two Variable and its Problems
  23. Taylor Series for a Function of Two Variables and its Problems - 2
  24. Taylor Series for a Function of Two Variables and its Problems - 2
  25. Maximum and Minimum for Function of Two Variables
  26. Maximum and Minimum for Function of Two Variables
  27. Problems based on Maximum and Minimum - 1
  28. Problems based on Maximum and Minimum - 1
  29. Problems based on Maximum and Minimum - 2
  30. Problems based on Maximum and Minimum - 2
  31. Lagrange Method of Multipliers and Its Problems - 1
  32. Lagrange Method of Multipliers and Its Problems - 1
  33. Scalar And Vector Point Functions
  34. Scalar And Vector Point Functions
  35. Divergence of a Vector and its Problems
  36. Divergence of a Vector and its Problems
  37. Problems on Gradient
  38. Problems on Gradient
  39. Curl of a vector
  40. Curl of a vector
  41. Curl of a vector and its problems
  42. Curl of a vector and its problems
  43. Multiple Choice Questions
  44. Unit-V Short answer questions
  45. Unit-V Long answer question

UNIT– IV : Multivariable Calculus (Integration)41

  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 Differential Equations48

  1. Introduction to Differential Equation
  2. Introduction to Differential Equation
  3. First Order First Degree Differential Equations
  4. First Order First Degree Differential Equations
  5. Linear Differential Equations
  6. Linear Differential Equations
  7. Bernouli's Equation
  8. Bernouli's Equation
  9. Exact Differential Equations
  10. Exact Differential Equations
  11. Non Exact Differential Equations
  12. Non Exact Differential Equations
  13. Problems Related to Non Exact Differential Equations
  14. Problems Related to Non Exact Differential Equations
  15. Applications of 1st order and First Degree Differential equations
  16. Applications of 1st order and First Degree Differential equations
  17. Procedure to find Orthogonal Trajectory in polar coordinate system
  18. Procedure to find Orthogonal Trajectory in polar coordinate system
  19. Newtons Laws of Cooling
  20. Newtons Laws of Cooling
  21. Problems related to Newtons laws of cooling
  22. Problems related to Newtons laws of cooling
  23. Law of Natural Growth and Decay
  24. Law of Natural Growth and Decay
  25. Problems related to Newtons Laws of decay and growth
  26. Problems related to Newtons Laws of decay and growth
  27. Problems based on Newtons Law of Growth and Decay -1
  28. Problems based on Newtons Law of Growth and Decay-1
  29. Linear Differential Equation of 2nd and Higher Order
  30. Linear Differential Equation of 2nd and Higher Order
  31. Linear Differential Equation of 2nd and higher order-1
  32. Linear Differential Equation of 2nd and higher Order-1
  33. General Formula to Find Particular Integral
  34. General Formula to Find Particular Integral
  35. Rules to find PI in Some Special Cases
  36. Rules to find PI in Some Special Cases
  37. Method of Variation of Parameters
  38. Method of Variation of Parameters
  39. Rules for finding particular integrals I
  40. Rules for finding particular integrals I
  41. Finding particular integrals II
  42. Finding particular integrals II
  43. Finding particular integrals III
  44. Finding particular integrals III
  45. Electrical Circuits
  46. Electrical Circuits
  47. Unit-1 Short answer questions
  48. Unit-1 long answer question
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