VTU Notes
The Complete 21MAT11  Calculus and Differential Equations  Maths Notes
 4.9

2021 Scheme  Physics Department
 Created by AcquireHowTo
 5 Modules
Description
 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 higherorder 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 Calculus1
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 derivativedifferentiation 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 integralschange 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’sOrthogonal 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 higherorder
“Higherorder linear ODE with the constant coefficientsInverse differential operator, method of variation of parameters, Cauchy’s and Legendre homogeneous differential equations and Problems.”
...Course Curriculum & Downloads Module Wise
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