## Course Objectives:

To make the students familiarize with Mathematical Modeling of physical systems using differential equations advanced techniques of integration, tracing of curve, multiple integrals and their applications. The aim is to equip them with the techniques to understand advanced level mathematics and its applications that would enhance thinking power, useful in their disciplines.

## Examination Scheme:

In Semester : 30 Marks

End Semester: 70 Marks

PR: 25 Marks

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**Syllabus**

### Unit I: First Order Ordinary differential Equations

Exact differential equations, Equations reducible to exact form. Linear differential equations, Equations reducible to linear form, Bernoulli’s equation.

### Unit 2: Applications of Differential Equations

Applications of Differential Equations to Orthogonal Trajectories, Newton’s Law of Cooling,

Kirchhoff’s Law of Electrical Circuits, Rectilinear Motion, Simple Harmonic Motion, One dimensional Conduction of Heat.

### Unit 3: Integral Calculus

Reduction Formulae, Beta and Gamma functions, Differentiation Under Integral Sign and Error functions.

### Unit 4: Curve Tracing

Tracing of Curves – Cartesian, Polar and Parametric curves, Rectification of curves.

### Unit 5: Solid Geometry

Cartesian, Spherical polar and Cylindrical coordinate systems, Sphere, Cone and Cylinder.

### Unit 6: Multiple Integrals and their Applications

Double and Triple integrations, Change of order of integration, Applications to find Area, Volume, Mass, Centre of Gravity and Moment of Inertia.