LPUNEST 2025 BTech Syllabus: Mathematics
Check the LPUNEST 2025 BTech Syllabus for Mathematics here.
Unit 1: Mathematical Reasoning
Understanding statements, logical operations (and, or, implies), tautology, contradiction, converse, and contrapositive.
Unit 2: Vectors
Addition of vectors, components in two and three dimensions, scalar and vector products, and the scalar and vector triple product.
Unit 3: Functions and Limits
One-one, into, and onto functions; composition of functions; types of real-valued functions, including polynomials and trigonometric functions. Concepts of limits, continuity, and differentiability.
Unit 4: Quadratic Equations
Solving quadratic equations within real and complex number systems, understanding the relationships between roots and coefficients, and forming equations with specified roots.
Unit 5: Sequences and Series
Various types of progressions, including arithmetic and geometric. Insertion of means and relations between them, along with summation formulas for special series.
Unit 6: Matrices
Introduction to matrices, their algebra, types, and properties. Solutions involving matrices of order two and three, including adjoint and transpose.
Unit 7: Sets
Fundamental definitions of sets, visual representations, operations such as union, intersection, and complement, and the algebraic properties of these operations.
Unit 8: Relations
Types of relations, including equivalence relations and their properties.
Unit 9: Integral Calculus (Part 1)
Understanding integrals as anti-derivatives, fundamental integrals, and methods of integration including substitution and parts.
Unit 10: Derivatives
Calculating derivatives of various functions including trigonometric, logarithmic, and inverse functions, examining the properties of these derivatives.
Unit 11: Determinants
Properties of determinants, evaluation methods, and applications in finding areas and solving simultaneous equations.
Unit 12: Complex Numbers
Representation of complex numbers in the form a + ib, their algebraic properties, and graphical representation using the Argand diagram.
Unit 13: Application of Derivatives
Exploring rates of change, identifying maxima and minima, and determining tangents and normals to curves.
Unit 14: Binomial Theorem
Understanding the binomial expansion for positive integral indices and its application, including properties of binomial coefficients.
Unit 15: Permutations and Combinations
Basic counting principles, definitions of permutations and combinations, and their applications in selection and arrangements.
Unit 16: Differential Equations
Introduction to ordinary differential equations, including order and degree. Methods of solution include the separation of variables.
Unit 17: Coordinate Geometry
Overview of the Cartesian coordinate system, distance, and section formulas, slopes of lines, and equations of various geometric configurations.
Unit 18: Circles and Conic Sections
Understanding equations of circles and conic sections, including standard forms and key properties related to intersections and tangents.
Unit 19: Integral Calculus (Part 2)
Further exploration of integral calculus techniques and evaluation of complex integrals.
Unit 20: Properties of Determinants
Evaluating determinants and their application in geometric problems, including areas of triangles.
Unit 21: Straight Lines
Different forms of line equations, intersections, angles between lines, and calculations for concurrency of lines.
Unit 22: Algebra of Functions
Exploration of function types, including exponential and logarithmic functions, and their graphical representations.
Unit 23: Sequences and Arithmetic Progression
Discussion of sequences, including the arithmetic and geometric progressions, their sums, and other properties.
Unit 24: Mathematical Induction
Principles of mathematical induction and its applications in proving various statements.