DDU Basic of mathematics first semester bsc 1st year pdf notes 2024

DDU BSc 1st semester Mathematics PDF Notes: Basic of Mathematics(First Paper).

Are you searching for Complete PDF notes on "Basic of Mathematics" of BSc 1st year Mathematics? Are you searching for fundamental questions and concepts in the "Basic of Mathematics" BSc Mathematics 1st semester? If so, you are at the right place to easily get all these study materials.

In this PDF note, we discussed the first paper of the first semester of BSc mathematics "Basic Of Mathematics". All the basic concepts of mathematics are explained by our experts. This PDF is loved by thousands of students of nearby colleges. 

Here, we provide a complete syllabus of the first paper of DDU BSc 1st Year, you can easily understand each topic of your syllabus. It is just like checklists of your syllabus to check before your examinations.

DDU BSc 1st Year Mathematics Complete Syllabus 2024-2025.

The syllabus of the 1st paper of BSc 1st year is divided into two sections. Differential Calculus in section (A) and  Integral Calculus in section (B). We explore the 1st paper syllabus "Differential Calculus"  topic of each unit in tabular form. In this paper, a total of 8 units are given. 

Paper/Course Code: MAT 101
Paper/Course Title: Basics Of Mathematics
Basics Of Mathematics
Units	Topics
1	Set theory: Definition of sets, representation of sets, universal sets, empty set, singleton set, finite and infinite set, equal set, the cardinal number of a finite set, equivalent set, set of a set, subsets, proper subset, superset, power set, improper set, comparability of sets, union, and intersection of sets, Complement of sets, de Morgan’s law, disjoint sets, difference and symmetric difference, algebra of sets, duality, counting principle, Venn diagram, and its applications.
2	Ordered pair, Cartesian product of two sets, relations, domain, co-domain, and range of a relation, types of relations: identity relation, inverse relation, empty relation, universal relation, reflexive relation, symmetric relation, anti-symmetric relation, transitive relation, equivalence relation. Functions or mapping, domain, co-domain, and range of a function, the composition of functions, types of function: one-one function, many–one function, onto function, into function, one-one into function, one-one onto function, many-one into function, many-one onto function, and invertible functions.
3	Differentiation of functions, the geometrical significance of derivatives, a derivative of the product of functions, a derivative of the quotient of two functions, a derivative of a function of function, Maxima, and a minima of a function of one variable. Integration of functions, properties of indefinite integrals, integration by substitution, integration by parts, integration of rational functions, integration using partial fractions. Definite integrals and their properties.
4	Principle of mathematical induction, Polynomials, Linear polynomials, quadratic polynomials, cubic polynomials, roots of polynomials, Quadratic equations, Factorization, Determinants, and their applications, matrix theory, types of matrices: Horizontal matrix, vertical matrix, square matrix, row matrix, column matrix, null matrix, identity matrix, diagonal matrix, scalar matrix, submatrix, triangular matrix, comparable matrix, Operation on matrices: Matrix addition, subtraction, a product of matrices, a difference of two matrices, transpose of a matrix, inverse of a matrix by adjoin method.
Paper/Course Code: MAT 102 (B030101T)
Paper/Course Title: Differential Calculus and Integral Calculus
Part-A Differential Calculus
Units	Topics
1	Definition of sequences, Theorems of limits of sequences, Bounded and Monotonic Sequences, Convergent Sequences, Cauchy's convergence criterion, BalzanoWeierstrass Theorem for sequences, Cauchy's sequence, Cauchy's first and second theorems on limits, Limits superior and limits inferior of a sequence, Cantor's theorem on nested intervals, Subsequence.
2	Limit, Continuity, variable, and Differentiability the function of a single variable, Cauchy's definition, Heine's definition, Equivalence of definition of Cauchy and Heine, Uniform continuity, Borel's theorem, Bolzano's theorem, Intermediate value theorem, Extreme value theorem, Darboux's intermediate value theorem for derivates, Chain rule.
3	Rolle's Theorem, Lagrange and Cauchy Mean value theorems, mean value theorems of higher order, Taylor's theorem with various forms of remainders, successive differentiation, Leibnitz theorem, Maclaurin's and Taylor's series expression.
4	Partial differentiation, Euler's theorem on homogeneous function, Jacobians and its properties, Asymptotes, Curvature, Envelops, and evolutes, Test for concavity and convexity.
Part-B Integral Calculus
5	Lower and upper bounds, Supremum and infimum of the subsets of R and its basic properties, Completeness of R.Riemann integral and its properties, Integrability of continuous and monotonic functions, Fundamental theorem of integral calculus, Mean value theorems of integral calculus, Differentiation under the sign of Integration.
6	Beta and Gamma functions, Tracing of curves in Cartesian and Polar forms, Improper Integrals, Their classification, and Convergence, Comparison test,μ-test Abel's test, Dirichlet's test, and quotient test.
7	Areas of Curve, Lengths of curve, Volumes of solid of revolution, Multiple integrals: Double and Triple integrals, Change of order of double integration, Area as a double integral in Cartesian form, Dirichlet’s theorem, and Liouville’s theorem for multiple integrals.
8	Vector Differentiation, Point function, Vector differential operator, Gradient, Divergence and Curl, Normal on a surface, Directional Derivative, Second order differential operator, Laplacian operator. Vector Integration, Line integral, Circulation, Work done by a force, Surface integral, Volume integral, Gauss, Green, Stokes theorems with proof and related problems.
Paper/Course Code: MAT 104 (B030201T)
Paper/Course Title: Matrices And Differential Equations
Matrices And Differential Equations
Units	Topics
1	Elementary operations on Matrices, Rank of a Matrix, Echelon form of a matrix, Normal form or canonical form of a matrix, Inverse of a matrix by elementary operations.complex matrix, conjugates of the matrix, Transpose of Conjugate of the matrix, Hermitian matrix and skew, Hermitian matrix, Period matrix, idempotent matrix, unitary matrix, the system of linear homogeneous and non-homogenous equations, consistency and Inconsistency of system of linear equation theorems on the consistency of a system of linear equations, Crammer’s Rule.
2	Vector, Linear Dependence and Independence of vectors, Dependence and Independence of vectors of vectors by rank method. Eigen values, Eigen vectors and characteristic equation of a matrix, Orthogonal Vectors. Algebraic Multiplicity, Geometric Multiplicity, Regular eigenvalue, Caley Hamilton theorem and its use in finding the inverse of a matrix, Diagonalisation of a square matrix, Power of matrix by Diagonalisation.
3	Order and Degree of a Differential Equations, Formation of differential equations, General Solution, Particular Solution, Geometrical meaning of a differential equation, Equation of first order and first degree, Equation in which the variables are separable, Equation Reducible to Variable separable form, Homogeneous differential equations, Equations Reducible to Homogeneous form.
4	Exact differential equations and equations reducible to the exact form, Linear differential equations, Equations Reducible to Linear form; First order higher degree differential equations solvable for p, y, x. Clairaut’s differential equation, Singular Solutions, Determination of singular solution, Orthogonal Trajectories, Trajectories in Cartesian form and Polar form.
Paper/Course Code: MAT 105 (B030201T)
Paper/Course Title: Geometry
Geometry
Units	Topics
1	Three-dimensional coordinates in space, Distance between two points, Direction cosines and direction ratios, Projection of a segment on a straight line, Projection of the joining of two points on a straight line, Angle between two lines, Distance of a point from a line.
2	Plane, General equation of plane, Equation of the plane in various forms, Equation of a plane through given points, Straight line in three dimensions, Coplanar lines, The image of a point in a plane, and Shortest distance between two lines.
3	Sphere, Equation of a sphere whose centre is given, Intersection of two spheres, Intersection of the sphere and a straight line, Cone, Equation of cone, Equation of right circular cone, enveloping cone.
4	Cylinder, Right circular cylinder, Enveloping cylinder, Central conicoid, properties of the central conicoid in standard form, the ellipsoid, the hyperboloid one sheet, the hyperboloid of two sheets, intersection of a line and a central conicoid, tangent plane, condition of tangency, director sphere, normal to a conicoid, polar plane, diametral plane.
Paper/Course Code: MAT 103 (B030103P)
Paper/Course Title: Practical
Practical
Units	Topics
1	Plotting the graphs of the following functions: I. 𝑎𝑥 II. [𝑥] (greatest integer function) III. 𝑥2𝑛; 𝑛𝜖𝑁 IV. 𝑥2𝑛−1; 𝑛𝜖𝑁 V. 1; 𝑛𝜖𝑁 𝑋2𝑛−1 VI. 1; 𝑛𝜖𝑁 𝑋2𝑛 VII. √𝑎𝑥 + 𝑏,|𝑎𝑥 +𝑏| VIII. |𝑥| 𝑓𝑜𝑟𝑥 ≠0 IX. 𝑒𝑥𝑓𝑜𝑟𝑥 ≠0 X. 𝑒−𝑥𝑓𝑜𝑟𝑥 ≠0
2	Plotting the graph of the following functions: log𝑒𝑥, sin x, cos x, tan x, sin hx, cos hx, tan hx.
3	Sketching parametric curves: Trochoid, Cycloid, and Epicycloid.
4	By plotting the graph find the solution of the equation: x = ex, x2 + 1 = ex, 1 − x2 = ex, x = log10 (x), cos (x) = x, sin(x) = x, cos(y) = cos(x), sin(y) = sin(x).
5	Plotting the graphs of polynomials of degrees 2, 3, 4 and 5.
6	Find numbers between two real numbers and plot finite and infinite subsets of R
7	Matrix operations: I. Addition, II. Multiplication, III. Inverse, IV. Transpose.
8	Complex numbers and their representations: I. Addition, II. Multiplication, III. Division, IV. Modulus.