# BTech Engineering Preparatory Unit (BEPU) in Introductory Engineering Mathematics

## Syllabus

- 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.