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Differential Equations and Mechanics (B.Sc Mathematics)

Higher-order and partial differential equations, statics and dynamics of particles.

6 महीनेअवधि 5Chapters27टॉपिक
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सिलेबस · पाठ्यक्रम

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01Unit 1: Linear Differential Equations of Higher Order 5 टॉपिक
  1. Linear equations with constant coefficients
  2. Complementary function and particular integral
  3. Cauchy-Euler equation
  4. Method of variation of parameters
  5. Simultaneous differential equations
02Unit 2: Partial Differential Equations 6 टॉपिक
  1. Formation of PDEs
  2. Lagrange's linear equation
  3. Charpit's method
  4. Linear PDEs with constant coefficients
  5. Classification of second-order PDEs
  6. Separation of variables: heat and wave equations
03Unit 3: Statics 6 टॉपिक
  1. Resultant of coplanar forces
  2. Equilibrium and Lami's theorem
  3. Moments and couples
  4. Friction
  5. Virtual work
  6. Common catenary
04Unit 4: Dynamics of a Particle 5 टॉपिक
  1. Velocity and acceleration: tangential and normal components
  2. Radial and transverse components
  3. Simple harmonic motion
  4. Projectiles
  5. Motion in a resisting medium
05Unit 5: Central Orbits 5 टॉपिक
  1. Central forces
  2. Differential equation of a central orbit
  3. Pedal (p-r) equation
  4. Apses and apsidal distances
  5. Kepler's laws of planetary motion

परिचय

आप यह कर पाएँगे

  • Solve linear differential equations with constant coefficients and Cauchy-Euler equations
  • Solve first-order PDEs by Lagrange's and Charpit's methods and classify second-order PDEs
  • Find resultant and equilibrium of coplanar forces using Lami's theorem, moments and friction
  • Solve problems on motion in a straight line, simple harmonic motion and projectiles
  • Apply radial-transverse components and Kepler's laws to central orbits

यह किसके लिए है

  • B.Sc Mathematics students of Semester 4 (UP State Universities, NEP 2020)
  • Students preparing for end-semester theory papers of Mathematics

आपको क्या चाहिए

  • Differential equations of Semester 2
  • Class 12 physics (vectors, Newton's laws)

सवाल

Which syllabus does this subject follow?

It follows the B.Sc Mathematics Semester 4 syllabus of the UP State Universities (NEP 2020 common minimum syllabus). Where your own university's syllabus differs, the centre follows your university syllabus.

How are students assessed at the centre?

Through unit-wise multiple-choice tests, a final test paper and doubt-clearing sessions that follow the university examination pattern.

Will this help in the semester examination?

Yes. Units are taught in the university order with solved numericals and exam-pattern questions.

Download the syllabus (PDF)

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