To be eligible for admission to a 3-year Bachelor of Science (B.sc) degree program in colleges affiliated with Sant Gadge Baba Amravati University, a student typically needs to have successfully completed their Higher Secondary Certificate (HSC) in either the science or Science field and maintained a consistent academic record throughout their educational career.
Program: B.Sc. – I (Mathematics)
Semester: I
Course Code / Subject: 126200 / Mathematics
Course Name: Algebra and Calculus
Syllabus
Unit I
Rank of a Matrix, Row Rank, Column Rank, Eigen Values, Eigen Vectors and the Characteristic Equation of a Matrix, Cayley–Hamilton Theorem, Inverse by Cayley–Hamilton Theorem.
Unit II
De Moivre’s Theorem, Roots of Complex Numbers, Circular Functions, Hyperbolic Functions, Inverse Hyperbolic Functions, Relation between Circular and Hyperbolic Functions.
Unit III
Limit of a Function, ε–δ Definition, Basic Properties of Limits, Some Standard Limits, Continuous and Discontinuous Functions, Types of Discontinuity.
Unit IV
Rolle’s Theorem, Lagrange’s Mean Value Theorem, Cauchy’s Mean Value Theorem, Maclaurin’s and Taylor’s Series Expansions.
After successful completion of this course, students will be able to:
CO1: Evaluate the characteristic equation, eigenvalues, and corresponding eigenvectors of a given matrix.
CO2: Apply and interpret De Moivre’s Theorem in various mathematical problems.
CO3: Understand and analyze the concepts of limits and continuity along with their basic properties.
CO4: Explain and apply the significance of mean value theorems in calculus.
S1107 - BSC 1 SEMESTER 1 -MATHEMATICS PAPER 1(NEP)
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