Engineering Mathematics Syllabus: EM I

In this page, the syllabus of Engineering Mathematics I is provided.

MIDTERM Syllabus (EM-I-MTH11501): For 20 Marks Differential Calculus (10 Marks): Introduction to limits, continuity, derivatives for functions of one variable, Successive differentiation, Leibnitz’s theorem, Indeterminate forms, Rolle’s theorem, Lagrange’s mean value theorem Integral Calculus (5 Marks): Review of definite integrals, Reduction formulae Linear Algebra (5 Marks): Basics of real and complex matrices, Hermitian and skew-Hermitian matrices, Determinant and its properties, Elementary row and column operations on a matrix, Echelon form, Rank

Some Study Material:

1. nth Derivative
2. Rolle’s Theorem
3. Characteristic Equation of a Matrix
4. Cayley-Hamilton Theorem

Engineering Mathematics I: Best Books, Practice Problems

Engineering Mathematics I Syllabus

Unit I: Differential Calculus

Introduction to limit, continuity, derivative for function of one variable; Successive
differentiation, Leibnitz’s theorem; Rolle’s theorem, Lagrange’s mean value theorem, Taylor’
and Maclaurin’s theorems with remainders; Indeterminate forms; Concavity and convexity of
a curve, Points of inflexion, Maxima and Minima

Limit, continuity, and differentiability of a functions of several variables; partial derivatives
and their geometrical interpretation; chain rule, total derivative, derivatives of composite and
implicit functions; homogeneous function, Euler’s theorem on homogeneous functions;
Jacobian of variable transformation; maxima and minima of functions of several variables,
Lagrange’s method of multipliers.

Unit II: Integral Calculus

Review of definite integrals, Reduction formulae, Improper integral, Beta and Gamma
functions, elementary properties, Rectification, double and triple integrals, computations of
area, surfaces and volumes, change of variables in double integrals, applications.

Unit III: Linear Algebra

Basics of real and complex matrices, Determinant and its properties, Orthogonal matrices, Hermitian and skew-Hermitian matrices, Unitary matrices, Elementary row and column operations on a matrix, Rank, echelon form, Inverse of a matrix using elementary operations, Solution of system of linear equations, Consistency, Characteristic equation, Caley-Hamillton theorem, eigenvalues and eigenvectors, algebraic and geometric multiplicity, diagonalization.

Unit IV: Vector Algebra

Scalar and vector fields, Vector product, Scalar triple product and their interpretation, directional derivative, gradient, Curl, divergence.

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