Algebra and Trigonometry
The complete syllabus for Algebra and Trigonometry, the first Major (core) mathematics paper for B.Sc / B.A. First Year at Madhya Pradesh state universities under NEP 2020 — a 6-credit, 90-hour course. Six modules span the Indian Knowledge System and Vedic algebra, matrices (rank, eigenvalues, Cayley–Hamilton), theory of equations, and trigonometry (De Moivre's theorem, circular and hyperbolic functions), closing with a case study on industrial applications. Available in English and Hindi editions.
Algebra and Trigonometry · English
by Dr. H.K. Pathak · ₹300 — covers this full syllabus.
Bijganit aur Trikonmiti (बीजगणित और त्रिकोणमिति) · Hindi
by Dr. H.K. Pathak · ₹300 — covers this full syllabus.
Course contents — unit by unit
Unit 1 · Indian Knowledge System & Vedic Algebra
Contributions of Indian mathematicians to algebra and matrices — Bhaskaracharya II, Brahmagupta, Mahaviracharya and Narayana Pandit. Vedic algebra — algebraic multiplication and algebraic division.
Unit 2 · Algebra – I: Matrices
Rank of a matrix; echelon and normal form of a matrix; eigenvalues and eigenvectors.
Unit 3 · Algebra – II: Characteristic Equation & Cayley–Hamilton
Characteristic equation of a matrix; Cayley–Hamilton theorem and its application to finding the inverse of a matrix; application of matrices to solve systems of linear equations; theorems on consistency and inconsistency; solving linear equations in up to three unknowns.
Unit 4 · Algebra – III: Theory of Equations
Root of an equation; synthetic division; relation between the roots and coefficients of an equation; Descartes' rule of signs.
Unit 5 · Trigonometry – I: De Moivre's Theorem
De Moivre's theorem; extraction of the roots of a complex quantity; expansions of sin nθ, cos nθ and tan nθ.
Unit 6 · Trigonometry – II: Circular & Hyperbolic Functions
Circular functions; hyperbolic functions; inverse circular functions; inverse hyperbolic functions.
Unit 7 · Industrial Applications (Case Study)
Applications of matrices to problems in industry, business and economics; applications of trigonometry to industrial and real-world problems.