Engineering Mathematics I
Syllabus for Engineering Degree Course – Revision 2017
F.E. Semester – I: 107001 – Engineering Mathematics – I
Teaching Scheme: Examination Scheme:
Lectures – 4 Hrs./Week Paper – 100 Marks\(3 Hrs. Duration)
Unit 1 (09 Hrs.)
Matrices: Rank, Normal form, System of Linear Equations, Linear Dependence and Independence, Linear and Orthogonal Transformations. Eigen values, Eigen Vectors, Cayley – Hamilton Theorem. Application to problems in Engineering (Translation and Rotation of Matrix).
Unit 2 (09 Hrs.)
Complex Numbers & Applications: Argand’s Diagram, De’Moivre’s theorem and its application to find roots of algebraic equations. Hyperbolic Functions, Inverse Hyperbolic Functions, Logarithm of Complex Numbers, Separation into Real and Imaginary parts, Application to problems in Engineering.
Unit 3 (09 Hrs.)
Infinite Series: Infinite Sequences, Infinite Series, Alternating Series, Tests for Convergence, Absolute and Conditional Convergence, Range of Convergence. Differential Calculus: Successive Differentiation, Leibnitz Theorem.
Unit 4 (09 Hrs.)
Expansion of Functions: Taylor’s Series and Maclaurin’s Series. Differential Calculus: Indeterminate Forms, L’ Hospital’s Rule, Evaluation of Limits.
Unit 5 (09 Hrs.)
Partial Differentiation and Applications: Partial Derivatives, Euler’s Theorem on Homogeneous Functions, Implicit functions, Total Derivatives, Change of Independent Variables.
Unit 6 (09 Hrs.)
Jacobian: Jacobians and their applications. Errors and Approximations. Maxima and Minima: Maxima and Minima of Functions of two variables, Lagrange’s method of undetermined multipliers.
- Lectures 0
- Quizzes 0
- Skill level All levels
- Language English
- Students 0
- Assessments Yes
Engg. Maths 1 Overview Engg. Maths 1 is fundamentals of mathematics. Comparatively simpler than Maths 2 & 3 and is a applied mathematics. The syllabus is time consuming Multiple concepts that require consistent practice. Tricks and tips are crucial to remember methods and procedures Understanding concepts and then rigorous practice is essential