UNIT 1

Multivariable Calculus And First-Order Differential Equations

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21 topics arranged for quick revision.

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Differential calculus of functions of several variables, partial derivatives, chain rule, implicit functions, exact differentials, Jacobians, Taylor series, maxima/minima, Lagrange multipliers, Leibniz integral rule, and first-order ODEs with applications.

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Differential Calculus of Several Variables

Functions of several variables

Concepts and study notes for Functions of several variables under Differential Calculus of Several Variables.

10 MIN

Partial derivatives

Concepts and study notes for Partial derivatives under Differential Calculus of Several Variables.

5 MIN

Chain rule

Concepts and study notes for Chain rule under Differential Calculus of Several Variables.

Differentiation of implicit functions

Concepts and study notes for Differentiation of implicit functions under Differential Calculus of Several Variables.

Exact differentials

Concepts and study notes for Exact differentials under Differential Calculus of Several Variables.

Jacobians and transformation of coordinates

Concepts and study notes for Jacobians and transformation of coordinates under Differential Calculus of Several Variables.

Taylor's and Maclaurin's series

Concepts and study notes for Taylor's and Maclaurin's series under Differential Calculus of Several Variables.

10 MIN

Maxima, minima and saddle points

Concepts and study notes for Maxima, minima and saddle points under Differential Calculus of Several Variables.

Method of Lagrange multipliers

Concepts and study notes for Method of Lagrange multipliers under Differential Calculus of Several Variables.

Differentiation under the integral sign

Concepts and study notes for Differentiation under the integral sign under Differential Calculus of Several Variables.

First-Order Ordinary Differential Equations

Basic concepts of ordinary differential equations

Concepts and study notes for Basic concepts of ordinary differential equations under First-Order Ordinary Differential Equations.

Geometrical interpretation of first-order differential equations

Concepts and study notes for Geometrical interpretation of first-order differential equations under First-Order Ordinary Differential Equations.

Direction fields

Concepts and study notes for Direction fields under First-Order Ordinary Differential Equations.

Euler's method

Concepts and study notes for Euler's method under First-Order Ordinary Differential Equations.

Separable differential equations

Concepts and study notes for Separable differential equations under First-Order Ordinary Differential Equations.

Exact differential equations

Concepts and study notes for Exact differential equations under First-Order Ordinary Differential Equations.

Integrating factors

Concepts and study notes for Integrating factors under First-Order Ordinary Differential Equations.

Linear differential equations

Concepts and study notes for Linear differential equations under First-Order Ordinary Differential Equations.

Bernoulli equation

Concepts and study notes for Bernoulli equation under First-Order Ordinary Differential Equations.

Orthogonal trajectories

Concepts and study notes for Orthogonal trajectories under First-Order Ordinary Differential Equations.

Applications of first-order differential equations

Concepts and study notes for Applications of first-order differential equations under First-Order Ordinary Differential Equations.