Free online courseEngineering Mathematics

Conteúdo do Curso

• Video class: Engineering Mathematics 01 | Single Variable Calculus 2.0 | All Branches #gate #gate2025

  1h33m

• Exercise: Consider the function f(x) = x^3 - 3x^2 + 4. Determine the nature of the critical points of the function.

• Video class: Engineering Mathematics 02 | Fundamentals Theorems of Integration 2.0 | All Branches #gate2025

  1h33m

• Exercise: For real values of x greater than zero, what is the best approximation for the minimum value attained by the function f(x) = e^(-x) * sin(100x)?

• Video class: Engineering Mathematics 03 | Properties of Definite Integrals 2.0 | All Branches #gate #gate2025

  1h33m

• Exercise: For real values of x, the minimum value of the function e^x + e^-x is ___.

• Video class: Engineering Mathematics 04 | Applications of Definite Integrals (Part 01) 2.0 | All Branches

  1h35m

• Exercise: What is the integral of the function f(x) = x^2 - 3 with respect to x from 0 to 2?

• Video class: Engineering Mathematics 05 | Applications of Definite Integrals (Part 02) 2.0 | All Branches

  1h41m

• Exercise: What is the area enclosed by the curves y = sin(x), y = cos(x), x = 0, and x = π/2?

• Video class: Engineering Mathematics 06 | Limits, Continuity and Partial derivatives 2.0 | All Branches

  1h31m

• Exercise: What is the surface area of a solid obtained by revolving the line segment joining the points (0, 0) and (a, b) around the x-axis?

• Video class: Engineering Mathematics 07 | Eulers Theorem, Taylor series in 2 variables 2.0 | All Branches

  1h19m

• Exercise: What is the limit of the function f(x, y) = (2xy - y^2) / (x^2 + y^2) as (x, y) approaches (0, 0)?

• Video class: Engineering Mathematics 08 | Maxima and Minima (Constrained and Unconstrained) 2.0 | All Branches

  1h29m

• Exercise: Consider the function f(x, y) = x^2 + y^2. Which of the following represents the second partial derivative of f with respect to x, evaluated at the point (1, 2)?

• Video class: Engineering Mathematics 09 | Multiple Integrals 2.0 (Part 01) | All Branches

  1h33m

• Exercise: Consider the function f(x, y) = x^4 + y^4 + 4xy - 2x^2 - 2y^2. How many stationary points does this function have?

• Video class: Engineering Mathematics 10 | Multiple Integrals 2.0 (Part 02) | All Branches

  1h39m

• Exercise: What is the minimum value of the product XYZ if the constraint x + y + z = 3 is applied, and each of x, y, z are positive real numbers?

• Video class: Engineering Mathematics 11 | Multiple Integrals 2.0 (Part 03) | All Branches

  1h36m

• Exercise: In the context of multiple integrals, what is the result of ∫∫_A y² dy dx, where A is the region in the first quadrant bounded by the circle x² + y² = a²?

• Video class: Engineering Mathematics 12 | Order, Degree and Formation of ODEs 2.0 | All Branches

  1h46m

• Exercise: What is the degree of the differential equation given by the expression \( (d^3 y/dx^3)^2 + 3(d^2 y/dx^2)^5 - 7(dy/dx)^4 + y = 0 \)?

• Video class: Engineering Mathematics 13 | Solving Methods of 1st order Equations 2.0 | All Branches

  1h31m

• Exercise: What is the general form of a first-order differential equation, commonly used to begin solving physical system models involving differential equations?

• Video class: Engineering Mathematics 14 | Exact Equations and Integrating factors, Linear Equations 2.0 Part 01

  0h19m

• Exercise: What is the purpose of performing a coordinate transformation in solving non-homogeneous first-order differential equations?

• Video class: Engineering Mathematics 15 | Exact Equations and Integrating factors, Linear Equations 2.0 Part-2

  1h32m

• Exercise: In the context of first-order linear differential equations of the form dy/dx + P(x)*y = Q(x), what is the integrating factor?

• Video class: Engineering Mathematics 17 | Higher order Differential Equations 2.0 | All Branches

  1h25m

• Exercise: What is the general form of a linear differential equation of an nth order with constant coefficients?

• Video class: Engineering Mathematics 18 | Particular Integrals, Wronskian and Euler - Cauchy Equations 2.0

  1h37m

• Exercise: In the context of solving linear differential equations using the method of undetermined coefficients, which function on the right-hand side of the differential equation requires you to multiply the assumed particular integral by the least power of x such that no term in the particular integral is also a solution of the corresponding homogeneous equation?