Calculus and Linear Algebra: CSE Stream 11BMATS101
Module-wise notes, PYQs, and a built-in resource explorer — everything you need to crack 1BMATS101 in one focused page.
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Module 1: Detailed Syllabus
Calculus (8Hours Theory + 4Hours Tutorial) Partial differentiation, total derivative, differentiation of composite functions, Jacobian, Statement of Taylor’s and Maclaurin’s series expansion for two variables. Maxima and minima for the function of two variables. Textbook-1: Chapter 5: Sections 5.1- 5.11
Module 2: Detailed Syllabus
Vector Calculus (8Hours Theory + 4Hours Tutorial) Scalar and vector fields, Gradient, directional derivatives, divergence and curl - physical interpretation, solenoidal vector fields, irrotational vector fields and scalar potential. Introduction to polar coordinates and polar curves. Curvilinear coordinates: Scale factors, base vectors, Cylindrical polar coordinates, Spherical polar coordinates, transformation between cartesian and curvilinear systems, orthogonality. Textbook-1: Chapter 5: Sections 5.4 – 5.21
Module 3: Detailed Syllabus
System of Linear Equations, Eigenvalues and Eigenvectors (8Hours Theory + 4Hours Tutorial) Elementary row transformation of a matrix, Echelon form, rank of a matrix. Consistency and solution of system of linear equations : Gauss elimination method, Gauss Jordan method. Applications: Traffic flow. Eigenvalues and Eigenvectors, diagonalization of the matrix, modal matrix. Textbook-1: Chapter 2: Sections 2.7-2.16, Chapter 28: Sections 28.6 and 28.7 Textbook-2: Chapter-7
Module 4: Vector Space (8Hours Theory + 4Hours Tutorial) Vector spaces
definition and examples, subspace: definition and examples . Linear Combinations, linear span, linearly independent and dependent sets, basis and dimension, row space and column space of a matrix, Coordinates vector, inner products and orthogonality. Textbook-3: Chapter 4: Sections 4.1 to 4.9 and 4.11
Module 5: Detailed Syllabus
Linear Transformation (8Hours Theory + 4Hours Tutorial) Definition and examples, algebra of linear transformations, matrix of a linear transformation. Singular, non-singular linear transformations and invertible linear transformations. Rank and nullity of linear transformations, Rank-Nullity theorem. Textbook-3: Chapter 5: Sections 5.3- 5.7 Chapter 6: Sections-6.1-6.2
Textbooks & Resources
- B. S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 44th Ed., 2021.
- E. Kreyszig, Advanced Engineering Mathematics, John Wiley&Sons,10th Ed.,2018.
- Seymour Lipschutz and Marc Lipson, Linear Algebra, Schaum’s outlines series, 4 th Ed., 2008.
Resource Explorer
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Frequently Asked Questions
What is 1BMATS101 (Calculus and Linear Algebra: CSE Stream)?
Calculus and Linear Algebra: CSE Stream (1BMATS101) is a VTU course covered through module-wise syllabus, notes, and PYQ-driven exam practice available on this page.
How many credits is 1BMATS101?
Credits for 1BMATS101: 04.
Are notes and previous year question papers available for 1BMATS101?
Yes. You can access organized notes, PDFs, and PYQ material from the file explorer/resources section on this page.
How should I prepare Mathematics-I 1BMATS101 for VTU exams?
Start with module summaries, solve recent PYQs unit-wise, and finish with complete paper practice under time constraints for SEE readiness.
Is this 1BMATS101 page updated for current VTU scheme?
Yes, this page is maintained with current scheme-oriented materials and practical exam-focused resource curation.
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About Mathematics-I (1BMATS101)
Mathematics-I (1BMATS101) is a critical course in the VTU curriculum, essential for any student looking to master the foundations of engineering. It covers key theoretical frameworks and practical concepts that are widely used in the industry today, ensuring students are well-prepared for both exams and their future careers.
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