MECH Dept Engineering Topics List

Worked Examples, Fundamental Theorem of Calculus

Subject and UNIT: Matrices and Calculus: Unit IV: Integral Calculus

Each of these sums is called a Riemann sum.

Introduction

Subject and UNIT: Matrices and Calculus: Unit IV: Integral Calculus

We have seen in chapter 1, that the problem of finding a tangent line at a point on a curve led to the concept of a derivative as a limit of difference quotient.

Solved Example Problems | Functions of Several Variables | Matrices and Calculus

Subject and UNIT: Matrices and Calculus: Unit III: Functions of Several Variables

Questions and Answers: Matrices and Calculus: Functions of Several Variables

Definition, Worked Examples, Exercise with Answers

Subject and UNIT: Matrices and Calculus: Unit III: Functions of Several Variables

A common name for relative maximum or relative minimum is extreme value.

Theorem, Worked Examples, Exercise with Answers

Subject and UNIT: Matrices and Calculus: Unit III: Functions of Several Variables

Taylor's formula gives polynomial approximation to a function of two variables about a given point.

Definition, Properties, Worked Examples, Exercise with Answers

Subject and UNIT: Matrices and Calculus: Unit III: Functions of Several Variables

Jacobians have many important applications such as functional dependence, transformation of variable in multiple integrals, problems in partial differentiation and in the study of existence of implicit functions determined by a system of functional equations.

Definition, Theorem, Worked Examples, Exercise with Answers

Subject and UNIT: Matrices and Calculus: Unit III: Functions of Several Variables

Functions of two or more independent variables appear in many practical problems more often than functions of one independent variable.

Definition, Worked Examples, Exercise with Answers

Subject and UNIT: Matrices and Calculus: Unit III: Functions of Several Variables

Let S be subset of R2. A function f: S→ R is a rule which assigns to every (x, y) ∈ S a unique real number in R, denoted by f(x, y).

Introduction | Calculus

Subject and UNIT: Matrices and Calculus: Unit III: Functions of Several Variables

There are many practical situations in which a quantity of interest depends on the values of two or more variables.

Solved Problems | Differential Calculus | Matrices and Calculus

Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus

QUESTIONS AND ANSWERS: Matrices and Calculus: Differential Calculus

Definition, Theorem, Worked Examples, Exercise with Answers | Differential Calculus

Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus

The sign of derivative of a function in an interval says where the graph of ƒ is increasing or decreasing, but it does not reveal the direction of bending of the curve.

Definition, Theorem, Geometrical Meaning, Tests, Worked Examples, Exercise with Answers | Differential Calculus

Subject and UNIT: Matrices and Calculus: Unit II: Differential Calculus

We have already seen the applications of derivative in problems of tangent and normal, in deciding increasing and decreasing nature of a function in an interval.