MTH166: Differential Equations And Vector Calculus Notes & Study Material
This course focuses on the definitions, distinctions, and solution methods for various differential equations, including partial differential equations like heat, wave, and Laplace equations. Additionally, it covers vector calculus concepts such as derivatives of vector fields, gradient, divergence, curl, and the computation of line, surface, and volume integrals.
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Available Study Materials
Handwritten Notes & Slides
Unit-by-unit lecture summaries and handwritten notes from class toppers.
Previous Year Papers (PYQs)
LPU Mid-Term (MTE) and End-Term (ETE) questions with solutions.
Official Syllabus & CA Pattern
Course structure, credits, weightage, and continuous evaluation criteria.
Course Overview & Evaluation Scheme
MTH166 Unit-Wise Detailed Syllabus
Unit 1: Ordinary differential equations
exact equations, equations reducible to exact equations, equations of the first order and higher degree, Clairaut's equation
Unit 2: Differential equations of higher order
introduction to linear differential equation, Solution of linear differential equation, linear dependence and linear independence of solution, method of solution of linear differential equation- Differential operator, solution of second order homogeneous linear differential equation with constant coefficient, solution of higher order homogeneous linear differential equations with constant coefficient
Unit 3: Linear differential equation
solution of non-homogeneous linear differential equations with constant coefficients using operator method, method of variation of parameters, method of undetermined coefficient, solution of Euler-Cauchy equation, simultaneous differential equations by operator method
Unit 4: Partial differential equation
introduction to partial differential equation, method of Separation of Variables, solution of wave equation, solution of heat equation, solution of Laplace equation
Unit 5: Vector calculus I
limit, continuity and differentiability of vector functions, length of space curve, motion of a body or particle on a curve, gradient of a scalar field and directional derivatives, divergence and curl of vector field
Unit 6: Vector calculus II
line integral, Greens' theorem, surface area and Surface integral, Stokes' theorem, Gauss's divergence theorem
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Passing criteria follow LPU academic regulations with combined evaluation across Continuous Assessments, Attendance, and End-Term Examination.