__Course Syllabi:
UMA003 Mathematics - I (L : T : P :: 3 : 1 : 0)__

**1. ****Course
number and name**: UMA003 Mathematics – I

**2. ****Credits
and contact hours**: 3.5 and 4

**3. ****Text
book, title, author, and year**

**Text Books / Reference Books**

·
*Thomas, G.B. and Finney, R.L., Calculus and Analytic Geometry,
Pearson Education (2007), 9 ^{th}ed.*

·
*Stewart James, Essential Calculus; Thomson Publishers (2007),
6 ^{th}ed.*

·
*Wider David V, Advanced Calculus: Early Transcendentals,
Cengage Learning (2007).*

·
*Apostol Tom M, Calculus, Vol I and II, John Wiley (2003).*

*a. **Other
supplemental materials*

·
*Nil*

**4. ****Specific
course information**

a. Brief description of the content of the course (catalog description)

**Applications
of Derivatives:** Mean value theorems and their geometrical interpretation,
Cartesian graphing using first and second order derivatives, Asymptotes and dominant
terms, Graphing of polar curves, Applied minimum and maximum problems.

**Sequences and
Series:** Introduction to sequences and Infinite series, Tests for convergence/divergence,
Limit comparison test, Ratio test, Root test, Cauchy integral test, Alternating
series, Absolute convergence and conditional convergence.

**Series
Expansions:** Power series, Taylor series, Convergence of Taylor series,
Error estimates, Term by term differentiation and integration.

**Partial
Differentiation:** Functions of several variables, Limits and continuity,
Chain rule, Change of variables, Partial differentiation of implicit functions,
Directional derivatives and its properties, Maxima and minima by using second
order derivatives.

**Multiple
Integrals:** Change of order of integration, Change of variables,
Applications of multiple integrals.

** **

**5. ****Specific
goals for the course**

After the completion of the course, the students will be able to:

· Apply the knowledge of calculus to plot graphs of functions and solve the problem of maxima and minima.

· Determine the convergence/divergence of infinite series, approximation of functions using power and Taylor’s series expansion and error estimation.

· Evaluate multiple integrals and their applications to engineering problems.

· Examine functions of several variables, define and compute partial derivatives, directional derivatives and their use in finding maxima and minima.

· Analyze some mathematical problems encountered in engineering applications.

**6. ****Brief
list of topics to be covered**

· Applications of Derivatives

· Sequences and Series

· Series Expansions

· Partial Differentiation

· Multiple Integrals