# BTech Engineering Bridging Unit (BEBU) in Introductory Engineering Mathematics

### Objectives

- Introduce Matrices, Vectors and Complex Numbers with Engineering Applications.

- Introduce Limits, Differentiation and Integration with Engineering Applications.

### Description

- Fundamental topics – algebra, angles, trigonometric functions and identities, quadratic equations, inequality.

- Matrices – terminology, addition & subtraction, multiplication, inversion, types of matrices, simultaneous equations.

- Vectors – terminology, addition & subtraction, components of a vector, scalar product, vector product, vectors in coordinate geometry.

- Partial Fractions – quadratic denominators with distinct roots, quadratic denominators with repeated roots, cubic denominators.

- Complex Numbers – definition, addition, subtract, multiplication, division, Argand diagram, polar form, exponential form.

- Limits and continuity – Limits of functions and sequences, types of limits, the sandwich theorem, evaluation of limits, continuity of functions, property of continuous functions.

- Derivatives – Derivatives, differentiability, rules and properties. Differentiation of transcendental functions. Higher-order derivatives. Implicit differentiation. Indeterminate form, L'Hopital's rule. Curve sketching, extreme values and points of inflection. Curve tracing and function behavior.

- Integration – Integration as antidifferentiation. Fundamental theorem of calculus. Basic rules of integration, integration of polynomial, trigonometric, exponential and logarithmic functions. Inverse functions. Integration by substitution, integration by parts.

- Functions of Several Variables – Geometric interpretation, continuity, partial derivatives, chain rule.

- Engineering applications.

Assessment

- Four Assignments: 20%

- Final Examination: 80%