Advanced Calculus Detailed Syllabus for B.Tech first year first sem is covered here. This gives the details about credits, number of hours and other details along with reference books for the course.

The detailed syllabus for Mathematics II: Advanced Calculus B.Tech 2016-2017 (R16) first year fristsem is as follows.

B.Tech. I Year I Sem. L T/P/D C

Course Code: MA102BS/MA202BS 4 1/0/0 4

Prerequisites: Foundation course (No prerequisites).

**Course Objectives: To learn**

- concepts & properties of Laplace Transforms
- solving differential equations using Laplace transform techniques
- evaluation of integrals using Beta and Gamma Functions
- evaluation of multiple integrals and applying them to compute the volume and areas of regions
- the physical quantities involved in engineering field related to the vector valued functions.
- the basic properties of vector valued functions and their applications to line, surface and volume integrals.

**Course Outcomes:**

After learning the contents of this course the student must be able to

- use Laplace transform techniques for solving DE’s
- evaluate integrals using Beta and Gamma functions
- evaluate the multiple integrals and can apply these concepts to find areas, volumes, moment of inertia etc of regions on a plane or in space
- evaluate the line, surface and volume integrals and converting them from one to another

**UNIT–I**

**Laplace Transforms**: Laplace transforms of standard functions, Shifting theorems,derivatives and integrals, properties- Unit step function, Dirac’s delta function, Periodic function, Inverse Laplace transforms, Convolution theorem (without proof).**Applications**: Solving ordinary differential equations (initial value problems) using Laplace transforms.

**UNIT-II**

**Beta and Gamma Functions:**Beta and Gamma functions, properties, relation between Beta and Gamma functions, evaluation of integrals using Beta and Gamma functions.**Applications**: Evaluation of integrals.

**UNIT–III**

**Multiple Integrals**: Double and triple integrals, Change of variables, Change of order of integration.**Applications:**Finding areas, volumes& Center of gravity (evaluation using Beta and Gamma functions).

**Text Books:**

- Advanced Engineering Mathematics by R K Jain & S R K Iyengar, Narosa Publishers
- Engineering Mathematics by Srimanthapal and Subodh C. Bhunia, Oxford Publishers

**References:**

- Advanced Engineering Mathematics by Peter V. O. Neil, Cengage Learning Publishers.
- Advanced Engineering Mathematics by Lawrence Turyn, CRC Press

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