Mathematics - 1 Syllabus (BTAM101-23)

Course Objectives

The objective of the Engineering Mathematics-I course is to enable students to understand concepts of basic mathematical methods for sequences & series, improper integrals, and multivariable calculus. These techniques are vital for solving engineering problems.

Course Outcomes

• CO1: Verify theoretical concepts in the course.
• CO2: Train students to visualize and conceptualize engineering problems.
• CO3: Model engineering problems mathematically using calculus.
• CO4: Draw conclusions from data and develop industrial problem-solving skills.
• CO5: Apply solutions from the studied engineering problems.

Detailed Syllabus

Part A

• Unit I: Sequences and Series - Infinite series, convergence tests, alternating series, power series, and radius of convergence.
• Unit II: Integral Calculus - Length of curves, volumes, surface areas of revolution, improper integrals, Beta and Gamma functions.

Part B

• Unit III: Functions of Several Variables - Continuity, partial derivatives, total derivatives, Lagrange's multipliers, maxima and minima.
• Unit IV: Multiple Integral - Double and triple integrals, change of order, and applications to area and volume.

Suggested Books

• Calculus by Maurice D. Weir, Pearson Education
• Advanced Engineering Mathematics by E. Kreyszig
• Higher Engineering Mathematics by B.V. Ramana