# 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%

02 October 2019