Differential Calculus And Linear Algebra: EEE stream 1BMATE101
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Module 1: Differential Calculus
(8 Hours Theory + 4 Hours Tutorial) Polar curves, angle between the radius vector and the tangent, angle between the polar curves, Pedal equations. Curvature and radius of curvature in cartesian, polar, parametric and Pedal forms. Textbook-1: Chapter- 4.7- 4.11
Module 2: Power series Expansions, indeterminate forms and multivariable calculus
(8 Hours Theory + 4 Hours Tutorial) Statement and problems on Taylorโs and Maclaurinโs series expansion for one variable. Indeterminate forms - LโHospitalโs rule. Partial Differentiation: Partial derivatives, total derivative, differentiation of composite functions, Jacobians. Maxima and minima for functions of two variables. Textbook-1: Chapter- 4.4(1,2,3),4.5(1,2,3), 5.1- 5.11.
Module 3: Ordinary Differential Equations (ODE) of first order and first degree and nonlinear ODE
(8 Hours Theory + 4 Hours Tutorial) Exact and reducible to exact differential equations- Integrating factors on 1 ๐ ( ๐๐ ๐๐ฆ โ ๐๐ ๐๐ฅ)and 1 ๐ ( ๐๐ ๐๐ฆ โ ๐๐ ๐๐ฅ) only. Linear and Bernoulliโs differential equations. Orthogonal trajectories, L-R and C-R circuits. Non-linear differential equations: Introduction to general and singular solutions, Solvable for p only, Clairautโs equations, reducible to Clairautโs equations. Textbook-1: Chapter-11.9-11.14- 12.3,12.5.
Module 4: Ordinary differential equations of higher Order
(8 Hours Theory + 4 Hours Tutorial) Higher-order linear ordinary differential equations with constant coefficients, homogeneous and non-homogeneous equations -๐๐๐ฅ, sin(๐๐ฅ + ๐), cos(๐๐ฅ + ๐), ๐ฅ๐only. Method of variation of parameters, Cauchyโs and Legendreโs homogeneous differential equations, L-C-R circuits. Textbook-1: Chapter-13.1-13.9, 14.5.
Module 5: Linear Algebra
(8 Hours Theory + 4 Hours Tutorial) Elementary transformations of a matrix, Echelon form, rank of a matrix, consistency of system of linear equations. Gauss elimination and Gauss โSeidel method to solve system of linear equations. Eigen values and eigen vectors of a matrix, Rayleighโs power method to determine the dominant eigen value and corresponding eigen vector of a matrix. Applications: Traffic flow. Textbook-1: Chapter-2.7-2.13, 28.5,28.6(1),28.7(2),28.9. Textbook-2: Chapter-7
Textbooks & Resources
- B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 44th Ed., 2021.
- E. Kreyszig, Advanced Engineering Mathematics, John Wiley&Sons,10th Ed.,2018.
- Gilbert Strang, Linear Algebra and its Applications, Cengage Publications,4thEd.,2025.
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Frequently Asked Questions
What is 1BMATE101 (Differential Calculus And Linear Algebra: EEE stream)?
Differential Calculus And Linear Algebra: EEE stream (1BMATE101) is a VTU course covered through module-wise syllabus, notes, and PYQ-driven exam practice available on this page.
How many credits is 1BMATE101?
Credits for 1BMATE101: 04.
Are notes and previous year question papers available for 1BMATE101?
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 1BMATE101 for VTU exams?
Start with module summaries, solve recent PYQs unit-wise, and finish with complete paper practice under time constraints for SEE readiness.
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About Mathematics-I (1BMATE101)
Mathematics-I (1BMATE101) 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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