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Calculus Syllabus
unit 1: Derivatives for Graphing and Applications
The first-derivative test for relative extrema, Concavity and inflection points, Second-
derivative test for relative extrema, Curve sketching using first and second derivative tests;
Limits to infinity and infinite limits, Graphs with asymptotes, L’Hôpital’s rule; Applications
in Business, Economics and Life Sciences; Higher order derivatives, Leibniz rule.
Unit 2: Sketching and Tracing of Curves
Parametric representation of curves and tracing of parametric curves (except lines in3 ), Polar
coordinates and tracing of curves in polar coordinates; Techniques of sketching conics,
Reflection properties of conics, Rotation of axes and second degree equations, Classification
into conics using the discriminant.
Unit 3: Volume and Area of Surfaces
Volumes by slicing disks and method of washers, Volumes by cylindrical shells, Arc length,
Arc length of parametric curves, Area of surface of revolution; Hyperbolic functions;
Reduction formulae.
Unit 4: Vector Calculus and its Applications
Introduction to vector functions and their graphs, Operations with vector functions, Limits and
continuity of vector functions, Differentiation and integration of vector functions; Modeling
ballistics and planetary motion, Kepler’s second law; Unit tangent, Normal and binormal
vectors, Curvature.
Bsc Algebra Syllabus
Course Objectives: The primary objective of this course is to introduce the basic tools of
theory of equations, complex numbers, number theory and matrices to understand their linkage
to the real-world problems. Perform matrix algebra with applications to Computer Graphics.
Course Learning Outcomes: This course will enable the students to:
i) Employ De Moivre’s theorem in a number of applications to solve numerical problems.
ii) Apply Euclid’s algorithm and backwards substitution to find greatest common divisor.
iii) Recognize consistent and inconsistent systems of linear equations by the row echelon
form of the augmented matrix, using rank.
iv) Find eigenvalues and corresponding eigenvectors for a square matrix.
Course Contents:
Unit 1: Theory of Equations and Complex Numbers
Elementary theorems on the roots of an equation, Polynomials, The remainder and factor
theorem, Synthetic division, Factored form of a polynomial, The Fundamental theorem of
algebra, Relations between the roots and the coefficients of polynomial equations, Imaginary
roots occur in pairs, Integral and rational roots; Polar representation of complex numbers, The
nth roots of unity, De Moivre’s theorem for integer and rational indices and its applications(BSc Math Tutors in delhi)..
Unit 2: Equivalence Relations and Functions
Equivalence relations, Functions, Composition of functions, Invertibility and inverse of
functions, One-to-one correspondence and the cardinality of a set.
Unit 3: Basic Number Theory
The division algorithm, Divisibility and the Euclidean algorithm, The fundamental theorem
of arithmetic, Modular arithmetic and basic properties of congruences; Principles of
mathematical induction and well ordering principle.
Unit 4: Row Echelon Form of Matrices and Applications
Systems of linear equations, Row reduction and echelon forms, Vector equations, The matrix
equation Ax = b, Solution sets of linear systems, Linear independence, The rank of a matrix and
applications; Introduction to linear transformations, The matrix of a linear transformation;
Matrix operations, The inverse of a matrix, Characterizations of invertible matrices,
Applications to Computer Graphics, Eigenvectors and eigenvalues, The characteristic equation