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), 9thed.
· Stewart James, Essential Calculus; Thomson Publishers (2007), 6thed.
· 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
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