Advanced Engineering Mathematics (2130002)   Old Code : 130002

5
Credit
3 + 2 + 0
Lect + Tuto + Pract
Teaching Scheme
70 + 20 + 10
ESE + PA + ALA
Theory Marks
30 + 0 + 20
ESE + OEP + PA
Practical Marks
ESE - End Semester Examination, PA - Progress Assessment, ALA - Active Learning Assignments, OEP -Open Ended Problem


Prerequisite

The course follows from Calculus, Linear algebra

Rationale

Mathematics is a language of Science and Engineering

Course Outcome

After learning the course the students should be able to

  1. Fourier Series and Fourier Integral
    • Identify functions that are periodic. Determine their periods.
    • Find the Fourier series for a function defined on a closed interval.
    • Find the Fourier series for a periodic function.
    • Recall and apply the convergence theorem for Fourierseries.
    • Determine whether a given function is even, odd or neither.
    • Sketch the even and odd extensions of a function defined on the interval [0,L].
    • Find the Fourier sine and cosine series for the function defined on [0,L]
  2. Ordinary Differential Equations and Their Applications
    • Model physical processes using differential equations.
    • Solve basic initial value problems, obtain explicit solutions if possible.
    • Characterize the solutions of a differential equation with respect to initial values.
    • Use the solution of an initial value problem to answer questions about a physicalsystem.
    • Determine the order of an ordinary differential equation. Classify an ordinary differential equation as linear or nonlinear.
    • Verify solutions to ordinary differential equations.
    • Identify and solve first order linear equations.
    • Analyze the behavior of solutions.
    • Analyze the models to answer questions about the physical system modeled.
    • Recall and apply the existence and uniqueness theorem for first order linear differential equations.
    • Identify whether or not a differential equation is exact.
    • Use integrating factors to convert a differential equation to an exact equation and then solve.
    • Solve second order linear differential equations with constant coefficients that have a characteristic equation with real and distinct roots.
    • Describe the behavior of solutions.
    • Recall and verify the principal of superposition

Active Learning

Preparation of power-point slides, which include videos, animations, pictures, graphics for better understanding theory and practical work – The faculty will allocate chapters/ parts of chapters to groups of students so that the entire syllabus to be covered. The power-point slides should be put up on the web-site of the College/ Institute, along with the names of the students of the group, the name of the faculty, Department and College on the first slide. The best three works should submit to GTU.