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

After learning the course the students should be able to

- 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]
- 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