This article will be very helpful for those students who have taken admission in BSc. Come let's know. Let us tell you that the government has released NEP 2020 according to which the duration of this degree will remain 3 years but it will be divided into semesters, there will be two semesters in a year and the total will be six semesters.
And we will know the syllabus of BSc 1st yesr maths which based on NEP 2020. Students like I told that there are two semesters in a year and in your 1st semester you have to read two books, 1st book differential calculus which has 4 units and 2nd book integral calculus which has 4 units which you have to read. For your convenience, I have provided niche units and topics in the form of a table.
The most important subject in mathematics is Calculus, it is also important for all universities because every year many questions come from it in the examinations.
Table of Syllabus:
| Unit No. | Topic | Subtopics |
|---|---|---|
| 1 | Functions and Continuity |
- Limit, continuity, and differentiability of a function of a single variable - Cauchy's definition - Uniform continuity - Boundedness theorem - Intermediate value theorem - Extreme value theorem - Darboux's intermediate value theorem for derivatives - Chain rule |
| 2 | Mean Value Theorems and Series Expansion |
- Rolle's theorem - Lagrange and Cauchy Mean value theorems - Taylor's theorem with various forms of remainders - Successive differentiation - Leibnitz theorem - Maclaurin's and Taylor's series - Partial differentiation - Euler's theorem on homogeneous functions |
| 3 | Curve Sketching and Geometry |
- Tangent and Normal - Asymptotes - Curvature - Envelopes and evolutes - Tests for concavity and convexity - Points of inflexion - Multiple points - Parametric representation of curves - Tracing of parametric curves - Tracing of curves in Cartesian and Polar forms |
| 4 | Sequences and Series |
- Definition of a sequence - Theorems on limits of sequences - Bounded and monotonic sequences - Cauchy's convergence criterion - Cauchy sequence - Limit superior and limit inferior of a sequence - Subsequence - Series of non-negative terms - Convergence and divergence - Comparison tests - Cauchy's integral test - Ratio tests, Root test - Raabe's logarithmic test - De Morgan and Bertrand's tests - Alternating series - Leibnitz's theorem - Absolute and conditional convergence |
| 5 | Definite Integrals and Riemann Integral |
- Definite integrals as the limit of the sum - Riemann integral - Integrability of continuous and monotonic functions - Fundamental theorem of integral calculus - Mean value theorems of integral calculus - Differentiation under the sign of integration |
| 6 | Improper Integrals and Special Tests |
- Classification and convergence of improper integrals - Comparison test, u-test, Abel's test, Dirichlet's test, quotient test - Beta and Gamma functions |
| 7 | Geometry and Multiple Integrals |
- Rectification, volumes, and surfaces of solids of revolution - Pappus theorem - Multiple integrals and change of order of double integration - Dirichlet's theorem, Liouville's theorem for multiple integrals |
| 8 | Vector Calculus |
- Vector differentiation: Gradient, Divergence, and Curl - Normal on a surface, Directional Derivative - Vector integration - Theorems of Gauss, Green, Stokes, and related problems |
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