Unit I Differential Calculus: Rolle’s Theorem, Mean Value Theorems, Taylor's Series and Maclaurin's Series, Expansion of functions using standard expansions, Indeterminate Forms, L' Hospital's Rule, Evaluation of Limits and Applications.
Unit II Fourier Series : Definition, Dirichlet’s conditions, Full range Fourier series, Half range Fourier series, Harmonic analysis, Parseval’s identity and Applications to problems in Engineering.
Unit III Partial Differentiation : Introduction to functions of several variables, Partial Derivatives, Euler's Theorem on Homogeneous functions, Partial derivative of Composite Function, Total Derivative, Change of Independent variables
Unit IV Applications of Partial Differentiation : Jacobian and its applications, Errors and Approximations, Maxima and Minima of functions of two variables, Lagrange's method of undetermined multipliers.
Unit V Linear Algebra-Matrices, System of Linear Equations : Rank of a Matrix, System of Linear Equations, Linear Dependence and Independence, Linear and Orthogonal Transformations, Application to problems in Engineering.
Unit VI Linear Algebra : Eigen Values and Eigen Vectors, Diagonalization Eigen Values and Eigen Vectors, Cayley Hamilton theorem, Diagonalization of a matrix, Reduction of Quadratic forms to Canonical form by Linear and Orthogonal transformations.
Unit I First Order Ordinary differential Equations : Exact differential equations, Equations reducible to exact form. Linear differential equations, Equations reducible to linear form, Bernoulli’s equation.
Unit II Applications of Differential Equations : Applications of Differential Equations to Orthogonal Trajectories, Newton’s Law of Cooling, Kirchhoff’s Law of Electrical Circuits, Rectilinear Motion, Simple Harmonic Motion, One dimensional Conduction of Heat.
Unit III Integral Calculus : Reduction Formulae, Beta and Gamma functions, Differentiation Under Integral Sign and Error functions.
Unit IV Curve Tracing : Tracing of Curves – Cartesian, Polar and Parametric curves, Rectification of curves.
Unit V Solid Geometry : Cartesian, Spherical polar and Cylindrical coordinate systems, Sphere, Cone and Cylinder.
Unit VI Multiple Integrals and their Applications : Double and Triple integrations, Change of order of integration, Applications to find Area, Volume, Mass, Centre of Gravity and Moment of Inertia.
This course is compulsory in third or fourth semester depending on what branch of engineering student have selected. It mainly focuses on higher order differential equations, Transforms(Fourier transforms, Laplace Transform, Z-transform), Vector Calculus(branch specific), Numerical methods, Complex Variables(branch specific), Statistics and probability, applications of partial differential equations, etc.
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Include the official course description from your institution. Include any other relevant information needed for students or others viewing to understand major themes, prerequisites, or if classes are exclusive for specific majors or degree tracks.