राजकीय महाविद्यालय, कण्डाघाट
Mathematics is a vast and fascinating field that encompasses various branches, including:
| Month | Week | Topic | Teaching Method | Student Activity |
|---|---|---|---|---|
| August | 1st | Differential Calculus: Limit and Continuity (epsilon and delta definition), Types of discontinuities. | Lecture Method, Blackboard | Discussion |
| 2nd | Differentiability of functions, Successive differentiation, Leibnitz’s theorem, Indeterminate forms. | Lecture Method, Blackboard | Discussion | |
| 3rd | Differential Equations: First order exact differential equations. Integrating factors, rules to find an integrating factor. | Lecture Method, Blackboard | Discussion | |
| 4th | First order higher degree equations solvable for x, y, p. Methods for solving higher-order differential equations. | Lecture Method, Blackboard | Discussion | |
| September | 1st | Differential Calculus: Rolle’s theorem, Lagrange’s & Cauchy Mean Value theorems, Taylor’s theorem with Lagrange’s. | Lecture Method, Blackboard | Discussion |
| 2nd | Cauchy’s forms of remainder, Taylor’s series. Maclaurin’s series of sin x, cos x, ex, log(1+x), (1+x)m. | Lecture Method, Blackboard | Discussion | |
| 3rd | Differential Equations: Basic theory of linear differential equations, Wronskian, and its properties. Solving a differential equation by reducing its order. | Lecture Method, Blackboard | Discussion | |
| 4th | Linear homogeneous equations with constant coefficients, Linear non-homogeneous equations, The method of variation of parameters. | Lecture Method, Blackboard | Discussion | |
| October | 1st | Differential Calculus: Concavity, Convexity & Points of Inflexion, Curvature, Asymptotes, Singular points. | Lecture Method, Blackboard | Discussion |
| 2nd | Parametric representation of curves and tracing of curves in parametric form, Polar coordinates and tracing of curves in polar coordinates. | Lecture Method, Blackboard | Discussion | |
| 3rd | Differential Equations: The Cauchy-Euler equation, Simultaneous differential equations. | Lecture Method, Blackboard | Discussion | |
| 4th | Total differential equations. Order and degree of partial differential equations. | Lecture Method, Blackboard | Discussion | |
| November | 1st | Concept of linear and non-linear partial differential equations. | Lecture Method, Blackboard | Discussion |
| 2nd | Formation of first-order partial differential equations (PDE), Linear partial differential equation of first order. | Lecture Method, Blackboard | Discussion | |
| 3rd | Linear partial differential equation by using Lagrange’s method. | Lecture Method, Blackboard | Discussion | |
| 4th | Differential Calculus: Functions of several variables (up to three variables): Limit of these functions, Partial differentiation. | Lecture Method, Blackboard | Discussion | |
| December | 1st | Differential Calculus: Functions of several variables (up to three variables): Continuity of these functions, Partial differentiation. | Lecture Method, Blackboard | Discussion |
| 2nd | Euler’s theorem on homogeneous functions. | Lecture Method, Blackboard | Discussion | |
| 3rd | MID TERM EXAM | |||
| 4th | MID TERM EXAM | |||
| February | 1st | Maxima and Minima | Lecture Method, Blackboard | Discussion |
| 2nd | Maxima and Minima with Lagrange Multipliers Method | Lecture Method, Blackboard | Discussion | |
| 3rd | Jacobian | Lecture Method, Blackboard | Discussion | |
| 4th | Differential Equations: Charpit’s method for solving PDE. | Lecture Method, Blackboard | Discussion | |
| March | 1st | Classification of second-order partial differential equations into elliptic, parabolic, and hyperbolic through illustrations only. | Lecture Method, Blackboard | Discussion |
| 2nd | Final Practical | |||
| August | 1st | Real Analysis: Finite and infinite sets, examples of countable and uncountable sets. Integral Calculus: Integration by Partial fractions, integration of rational and irrational functions. Properties of definite integrals. | Lecture Method, Blackboard | Discussion |
| 2nd | Real Analysis: Real line, bounded sets, suprema and infima, completeness property of R. Vector Calculus: Scalar and vector product of three vectors. Product of four vectors. Reciprocal vectors. | Lecture Method, Blackboard | Discussion | |
| 3rd | Real Analysis: Archimedean property of R, intervals. Concept of cluster points and statement of Bolzano-Weierstrass theorem. Vector Calculus: Vector differentiation, Scalar valued point functions, vector valued point functions. Derivative along a curve, directional derivatives. | Lecture Method, Blackboard | Discussion | |
| 4th | Algebra: Definition and examples of groups, examples of abelian and non-abelian groups. Integral Calculus: Integration by Partial fractions, integration of rational and irrational functions. Properties of definite integrals. | Lecture Method, Blackboard | Discussion | |
| September | 1st |
ALGEBRA: The group Zn of integers under addition modulo n and the group U(n) of units under multiplication modulo n. Cyclic groups from number systems, complex roots of unity. INTEGRAL CALCULUS: Reduction Formulae, ∫Sinⁿx, ∫cosⁿx, ∫eᵃˣⁿ, ∫xⁿ(log x)ⁿ. |
Lecture Method, Blackboard | Discussion |
| 2nd |
ALGEBRA: Vector valued point functions, the general linear group GLn (n,R), groups of symmetries of (i) an isosceles triangle, (ii) an equilateral triangle, (iii) a rectangle, and (iv) a square, the permutation group Sym(n). INTEGRAL CALCULUS: ∫xⁿsin x dx, ∫xⁿcos x dx. ∫Sinⁿx cosⁿx dx and indefinite integrals with limit 0 to π/2: ∫Sinⁿx dx, ∫cosⁿx dx, ∫Sinⁿx cosⁿx dx. |
Lecture Method, Blackboard | Discussion | |
| 3rd |
REAL ANALYSIS: Real Sequence, Bounded sequence, Cauchy convergence criterion for sequences. Cauchy’s theorem on limits. INTEGRAL CALCULUS: Reduction by connecting two integrals (Smaller Index + 1 Method). |
Lecture Method, Blackboard | Discussion | |
| 4th |
REAL ANALYSIS: Order preservation and squeeze theorem, monotone sequences and their convergence (monotone convergence theorem without proof). VECTOR CALCULUS: Gradient of a scalar point function, geometrical interpretation of gradient of a scalar point function (grad φ). Divergence and curl of a vector point function, character of divergence. |
Lecture Method, Blackboard | Discussion | |
| October | 1st |
ALGEBRA: Subgroups, cyclic subgroups, the concept of a subgroup generated by a subset and the commutator subgroup of group. VECTOR CALCULUS: Curl of a vector point function, Gradient, Divergence and Curl of sums and products and their related vector identities. Laplacian operator. |
Lecture Method, Blackboard | Discussion |
| 2nd |
ALGEBRA: Examples of subgroups including the centre of a group. Cosets, Index of subgroup, Lagrange’s theorem, order of an element. INTEGRAL CALCULUS: Areas and lengths of curves in the plane. |
Lecture Method, Blackboard | Discussion | |
| 3rd |
REAL ANALYSIS: Geometric series, comparison test. Convergence of p-series, Root test, Ratio test. INTEGRAL CALCULUS: Volumes and surfaces of solids of revolution. |
Lecture Method, Blackboard | Discussion | |
| 4th |
REAL ANALYSIS: Infinite series, Cauchy convergence criterion for series, positive term series. VECTOR CALCULUS: Orthogonal curvilinear coordinates. Conditions for orthogonality. |
Lecture Method, Blackboard | Discussion | |
| February | 1st | Maxima and Minima | Lecture Method, Blackboard | Discussion |
| 2nd | Maxima and Minima with Lagrange Multipliers Method | Lecture Method, Blackboard | Discussion | |
| 3rd | Jacobian | Lecture Method, Blackboard | Discussion | |
| 4th | Differential Equations: Charpit’s method for solving PDE. | Lecture Method, Blackboard | Discussion | |
| March | 1st | Classification of second-order partial differential equations into elliptic, parabolic, and hyperbolic through illustrations only. | Lecture Method, Blackboard | Discussion |
| 2nd | Final Practical | - | - | |
| August | 1st |
Real Analysis: Finite and infinite sets, examples of countable and uncountable sets. Integral Calculus: Integration by Partial fractions, integration of rational and irrational functions. Properties of definite integrals. |
Lecture Method, Blackboard | Discussion |
| 2nd |
Real Analysis: Real line, bounded sets, suprema and infima, completeness property of R. Vector Calculus: Scalar and vector product of three vectors. Product of four vectors. Reciprocal vectors. |
Lecture Method, Blackboard | Discussion | |
| 3rd |
Real Analysis: Archimedean property of R, intervals. Concept of cluster points and statement of Bolzano-Weierstrass theorem. Vector Calculus: Vector differentiation, Scalar valued point functions, vector valued point functions. Derivative along a curve, directional derivatives. |
Lecture Method, Blackboard | Discussion | |
| 4th |
Algebra: Definition and examples of groups, examples of abelian and non-abelian groups. Integral Calculus: Integration by Partial fractions, integration of rational and irrational functions. Properties of definite integrals. |
Lecture Method, Blackboard | Discussion | |
| September | 1st |
Algebra: The group Zn of integers under addition modulo n and the group U(n) of units under multiplication modulo n. Cyclic groups from number systems, complex roots of unity. Integral Calculus: Reduction Formulae, ∫Sin x, ∫cos x, ∫e^x, ∫x(log x) |
Lectures, Group Discussion | Problem Solving, Group Discussions, Practice Problems |
| 2nd |
Algebra: Vector valued point functions, the general linear group GLn (n,R), groups of symmetries of (i) an isosceles triangle, (ii) an equilateral triangle, (iii) a rectangle, and (iv) a square, the permutation group Sym (n). Integral Calculus: ∫x sin x dx, ∫x cos x dx, ∫Sin x cos x dx, and indefinite integrals with limits 0 to π/2 ∫Sin x dx, ∫cos x dx, ∫Sin x cos x dx. |
Lectures, Problem-Solving Exercises | Practice Exercises, Solving Integration Problems | |
| 3rd |
Real Analysis: Real Sequence, Bounded sequence, Cauchy convergence criterion for sequences. Cauchy’s theorem on limits. Integral Calculus: Reduction by connecting two integrals (Smaller Index + 1 Method). |
Lectures, Discussion on Cauchy’s Theorem | Solving Problems on Sequences and Integration | |
| 4th |
Real Analysis: Order preservation and squeeze theorem, monotone sequences and their convergence (monotone convergence theorem without proof). Vector Calculus: Gradient of a scalar point function, geometrical interpretation of gradient of a scalar point function (grad φ). Divergence and curl of a vector point function, character of divergence. |
Lectures, Visualization of Vector Fields | Practice Problems, Visualization Activities Using Vector Fields | |
| October | 1st |
Algebra: Subgroups, cyclic subgroups, the concept of a subgroup generated by a subset and the commutator subgroup of group. Vector Calculus: Curl of a vector point function, Gradient, Divergence and Curl of sums and products and their related vector identities. Laplacian operator. |
Lecture Method, Blackboard | Discussion |
| 2nd |
Algebra: Examples of subgroups including the centre of a group. Cosets, Index of subgroup, Lagrange’s theorem, order of an element. Integral Calculus: Areas and lengths of curves in the plane. |
Lecture Method, Blackboard | Discussion | |
| 3rd |
Real Analysis: Geometric series, comparison test. Convergence of p-series, Root test, Ratio test. Integral Calculus: Volumes and surfaces of solids of revolution. |
Lecture Method, Blackboard | Discussion | |
| 4th |
Real Analysis: Infinite series, Cauchy convergence criterion for series, positive term series. Vector Calculus: Orthogonal curvilinear coordinates. Conditions for orthogonality. |
Lecture Method, Blackboard | Discussion | |
| November | 1st |
Real Analysis: Alternating series, Leibnitz’s test (Tests of Convergence without proof). Vector Calculus: Fundamental triads of mutually orthogonal unit vectors. Gradient, Divergence. |
Lecture Method, Blackboard | Discussion |
| 2nd |
Real Analysis: Definition and examples of absolute and conditional convergence. Vector Calculus: Curl operators in terms of orthogonal curvilinear coordinators. |
Lecture Method, Blackboard | Discussion | |
| 3rd |
Algebra: Quotient groups Fundamental theorem of Homomorphism. Vector Calculus: Laplacian operators in terms of orthogonal curvilinear coordinators. |
Lecture Method, Blackboard | Discussion | |
| 4th |
Algebra: Definition and examples of rings. Vector Calculus: Cylindrical and Spherical coordinates. |
Lecture Method, Blackboard | Discussion | |
| December | 1st |
Algebra: Examples of commutative and non-commutative rings. Vector Calculus: Relation between Cartesian and cylindrical or spherical coordinates. |
Lecture Method, Blackboard | Discussion |
| 2nd | Algebra: Rings from number systems, Zn the ring of integers modulo n. | Lecture Method, Blackboard | Discussion | |
| 3rd | Mid Term Examination | |||
| 4th | Mid Term Examination | |||
| February | 1st |
Algebra: Rings of matrices, polynomial rings. Integral Calculus: Double integrals. |
Lecture Method, Blackboard | Discussion |
| 2nd |
Algebra: Subrings and ideals, Integral domains and fields, examples of fields: Zp, Q, R, and C. Integral Calculus: Triple integrals. |
Lecture Method, Blackboard | Discussion | |
| 3rd |
Real Analysis: Sequences and series of functions, Pointwise and uniform convergence. Vector Calculus: Vector integration: line integral, surface integral. |
Lecture Method, Blackboard | Discussion | |
| 4th |
Real Analysis: Mn-test, M-test, Results about uniform convergence, integrability. Vector Calculus: Volume integral Theorems of Gauss, Green and Stokes (without proof). |
Lecture Method, Blackboard | Discussion | |
| March | 1st |
Real Analysis: Differentiability of functions (Statements only). Power series and radius of convergence. Vector Calculus: Problems based on Gauss, Green, and Stokes theorems. |
Lecture Method, Blackboard | Discussion |
| 2nd | Final Practicals |
| Name of the Course | Objectives | Course Outcome |
|---|---|---|
| Differential Calculus | Differential calculus is used to find the maximum and minimum values of a function and also to find out the approximate value of a small change in a quantity. | Students will be able to find out the maxima and minima of function and how to check the continuity of function. |
| Differential Equation | It helps to find out the solution of differential equation by using different methods, i.e., direct integration, separation of variables, and integrating factor method. | Students will be able to recognise differential equations that can be solved by each of three methods - direct integration, separation of variables, and integrating factor method. |
| Real Analysis | Real analysis is used to study the behavior of real numbers, functions, sequences, and series. | Students will be able to learn the fundamental properties of real numbers and the theory of sequences and series, including convergence. |
| Algebra | Algebra helps to understand the properties and operations of algebraic structures like groups, rings, and fields. | Students will be able to identify the groups, rings, and fields by using their properties. |
| Integral Calculus | Integral calculus helps to find out the area and volume under the curve by dividing it into infinite rectangles of very small width and adding up their areas. | Students will be able to find out the area and volume under the curves. |
| Vector Calculus | Vector calculus helps to learn how to compute dot and cross products, partial derivatives, and directional derivatives. | Students will be able to solve the cross and dot product problems and directional derivatives. |
| Matrices | Matrices help to find out the solution of equations with more than two or three variables. | Students will be able to solve the equations with more than two or three variables. |
| Numerical Method | Numerical methods help to design and analyse techniques to find approximate but accurate solutions to challenging problems. | Students will be able to solve the roots of equations by using different methods such as the bisection method, regula falsi method, etc. |
| Probability and Statistics | Probability is used to predict the likelihood of something happening, and statistics helps to represent complex data in a way that's easy to understand. | Students will be able to solve applied problems by using the concept of probability and statistics. |
| Transportation and Game Theory | Transportation problems are used to find the minimum cost of transportation of goods from m source to n destination, and the goal of game theory is to explain the strategic actions of two or more players in a given situation with set rules and outcomes. | Students will be able to manage to recognize and formulate precise questions about strategic situations and understand the theoretical tools to address these questions. |
| Year | DSC Name & Code | DSE Name & Code | SEC Name & Code |
|---|---|---|---|
| B.A. / B.Sc.-I | Differential Calculus & MATH101TH Differential Equation & MATH102TH |
||
| B.A. / B.Sc.-II | Real Analysis & MATH201TH Algebra & MATH202TH |
Integral Calculus & MATH309TH Vector Calculus & MATH310TH |
|
| B.A. / B.Sc.-III | Matrices & MATH301TH Numerical Method & MATH304TH |
Probability and Statistics & MATH313TH Transportation and Game Theory & MATH317TH |
| Topics | Subject |
|---|---|
| Area and lengths of curves in the plane, volumes and surfaces of solids of revolution. | Integral Calculus MATH309TH |
| Mathematical expectation, binomial expansion, exponential. | Probability and Statistics & MATH313TH |
| Lattices as ordered sets, properties of modular and distributive lattices, Boolean algebra and Boolean polynomial. | Boolean algebra MATH |