Engineering Mathematics - I
1001025 modules · 61 topics · 61 with study notes
Module 1Basic Linear Algebra (8hrs)13 topics
- Elementary transformationsNotes
- Rank of MatrixNotes
- Rank by using Echelon and Normal form of MatricesNotes
- Linear dependenceNotes
- independence of vectors in R^n spaceNotes
- Consistency of System of Linear EquationsNotes
- EigenvaluesNotes
- EigenvectorsNotes
- Cayley-Hamilton TheoremNotes
- Similarity of MatricesNotes
- Diagonalization of Square MatricesNotes
- Quadratic FormNotes
- Canonical Form of MatricesNotes
Module 2Differential Calculus: Single Variable (8hrs)12 topics
Module 3Differential Calculus: Several Variables (9hrs)10 topics
- Partial differentiationsNotes
- Euler's theoremsNotes
- LimitNotes
- ContinuityNotes
- differentiability of functions of Several VariablesNotes
- Taylor's theorem with various forms of remaindersNotes
- Maclaurin's theorem and related problemsNotes
- MaximaNotes
- Minima for functions of several variablesNotes
- Lagrange's Multiplier MethodNotes
Module 4Integral Calculus (9hrs)14 topics
- Differentiation under the integral signNotes
- Leibnitz's ruleNotes
- Double integralNotes
- Change the order of integrationNotes
- Evaluation of double integration by changing it into polar co-ordinatesNotes
- Triple IntegralNotes
- Evaluation of Triple integral by changing to Spherical Polar co-ordinatesNotes
- Cylindrical polar co-ordinatesNotes
- BetaNotes
- GammaNotes
- Elliptic integralNotes
- Relation between BetaNotes
- Gamma functionsNotes
- General Properties and related problemsNotes
Module 5Vector Calculus (8hrs)12 topics
- Scalar and vector valued functionsNotes
- Concepts of gradientNotes
- divergenceNotes
- curl and their geometrical and physical significanceNotes
- tangent planeNotes
- directional derivativeNotes
- LineNotes
- surface and volume integralsNotes
- Statement of Green'sNotes
- Stokes'Notes
- Gauss divergence theoremsNotes
- verification and evaluation of vector integrals using themNotes
Theory