Mathematics III free videos and free material uploaded by Ramanjaneyulu K .
Syllabus / What will i learn?
Course Objectives:
- The course is designed to equip the students with the necessary mathematical skills and techniques that are essential for an engineering course.
- The skills derived from the course will help the student from a necessary base to develop analytic and design concepts.
- Understand the most basic numerical methods to solve simultaneous linear equations.
Course Outcomes:
At the end of the Course, Student will be able to:
- Determine rank, Eigenvalues and Eigen vectors of a given matrix and solve simultaneous linear equations.
- Solve simultaneous linear equations numerically using various matrix methods.
- Determine double integral over a region and triple integral over a volume.
- Calculate gradient of a scalar function, divergence and curl of a vector function. Determine line, surface and volume integrals. Apply Green, Stokes and Gauss divergence theorems to calculate line, surface and volume integrals.
UNIT I:
Linear systems of equations: Rank-Echelon form-Normal form – Solution of linear systems – Gauss elimination - Gauss Jordon- Gauss Jacobi
and Gauss Seidal methods.Applications: Finding the current in electrical circuits.
UNIT II:
Eigen values - Eigen vectors and Quadratic forms: Eigen values - Eigen vectors– Properties – Cayley-Hamilton theorem - Inverse and powers of a matrix by using Cayley-Hamilton theorem- Diagonalization- Quadratic forms- Reduction of quadratic form to canonical form – Rank - Positive, negative and semi definite - Index – Signature. Applications: Free vibration of a two-mass system.
UNIT III:
Multiple integrals: Curve tracing: Cartesian, Polar and Parametric forms.
Multiple integrals: Double and triple integrals – Change of variables – Change of order of integration. Applications: Finding Areas and Volumes.
UNIT IV:
Special functions: Beta and Gamma functions- Properties - Relation between Beta and Gamma functions- Evaluation of improper
integrals. Applications: Evaluation of integrals.
UNIT V:
Vector Differentiation: Gradient- Divergence- Curl - Laplacian and second order operators -Vector identities. Applications: Equation of continuity, potential surfaces
UNIT VI:
Vector Integration: Line integral – Work done – Potential function – Area- Surface and volume integrals Vector integral theorems: Greens, Stokes and Gauss Divergence theorems (without proof) and related problems.
Applications: Work done, Force.
Curriculum for this course
6 Lessons
00:00:00 Hours
Unit-I
1 Lessons
- Unit -1 Mathematics – III lecture notes
Unit-II
1 Lessons
- Unit -2 Mathematics – III lecture notes
Unit-III
1 Lessons
- Unit -3 Mathematics – III lecture notes
Unit-IV
1 Lessons
- Unit -4 Mathematics – III lecture notes
Unit-V
1 Lessons
- Unit -5 Mathematics – III lecture notes
Unit-VI
1 Lessons
- Unit -6 Mathematics – III lecture notes
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