VTU Notes

The Complete 21MAT11 | Calculus and Differential Equations - Maths Notes

  • 4.9
  • 2021 Scheme | Physics Department


  • The goal of the course Calculus and Differential Equations - 21MAT11 is:  
  • To facilitate the students with a concrete foundation of differential calculus  
  • To solve the first and higher-order ordinary differential equations enabling them to acquire the knowledge of these mathematical tools.  
  • To develop the knowledge of matrices and linear algebra in a comprehensive manner.

What You’ll Learn

Module 1: Differential Calculus-1

Introduction to Polar curves. “Radius vector and the tangent, the angle between 2 curves. Pedal equations, Curvature, Cartesian, parametric, polar, and pedal forms, and Problems.”

Module 2: Differential Calculus – 2

Introduction to Taylor’s and Maclaurin’s series expansion for one variable (Statement only) – problems. “Indeterminate forms – L’Hospital’s rule. Partial differentiation, total derivative-differentiation of composite functions, Jacobian and problems. Maxima and minima for a function of two variables and Problems.”

Module 3: Integral Calculus

Evaluation of double and triple integrals. “Evaluation of double integrals-change of the order of integration, changing into polar coordinates. Application to find area and volume and Problems. Definition of Beta and Gamma functions.” Relation between Beta and Gamma functions, and problems.

Module 4: Ordinary Differential Equations (ODE’s) of the first order

Linear and Bernoulli’s differential equations. “Exact and reducible to exact differential equations. Applications of ODE’s-Orthogonal trajectories, Newton’s law of cooling. Nonlinear differential equations: Introduction to general and singular solutions; Solvable for p only; Clairaut’s equations, reducible to Clairaut’s equations and Problems.”

Module 5: Ordinary Differential Equations (ODE’s) of higher-order

“Higher-order linear ODE with the constant coefficients-Inverse differential operator, method of variation of parameters, Cauchy’s and Legendre homogeneous differential equations and Problems.”


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