# 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.