Advanced Engineering Mathematics

Course Curriculum

Chapter 1: First order differential equations

Lecture 1: Introduction to Linear differential equation

Lecture 2: Solving linear 1st order differential equation using integrating factor

Lecture 3: Separable differential equations

Lecture 4: Homogeneous differential equations

Lecture 5: Bernoulli equation

Lecture 6: Riccati equation

Lecture 7: Exact equations- part 1- 1st order homogeneous differential equations

Lecture 8: Exact equations- part 2- 1st order homogeneous differential equations

Chapter 2: Second order differential equations

Lecture 1: Reduction of order- 2nd order homogeneous differential equations

Lecture 2: Exponential guess- Repeated roots- 2nd order homogeneous differential equations

Lecture 3: Exponential guess- Distinct roots- 2nd order homogeneous differential equations

Lecture 4: Exponential guess- complex roots- 2nd order homogeneous differential equations

Lecture 5: Euler – Cauchy equation

Lecture 6: Euler – Cauchy equation – repeated and complex roots

Lecture 7: Variation of parameters -2nd order NON-homogeneous differential equations

Lecture 8: Undetermined coefficients-2nd order NON-homogeneous differential equations

Lecture 9: Super position method-2nd order NON-homogeneous differential equations

Chapter 3: The Laplace Transform

Lecture 1: Introduction to the Laplace transform

Lecture 2: Initial value problem – Laplace transform

Lecture 3: Using partial fraction expansion in the Laplace transform

Lecture 4: Repeated roots- partial fraction expansion- Laplace transform

Lecture 5: The convolution theorem

Lecture 6: Impulse and delta function transformation

Lecture 7: Solving system of equations