Submitted By paraaa
Course code: 15MA101 | Engineering Mathematics | L | T | P | C | | | 3 | 1 | - | 4 | Course Objectives | To train the students in basic mathematics essential for modeling and solving engineering problems. | Course Outcomes | 1. An ability to apply knowledge of mathematics, science and engineering. 2. An ability to identify, formulate and solve engineering problems | Differential Calculus:
Review: Functions and graphs, Limits and Continuity, Differentiation, Maxima and minima of a function, Rolle’s Theorem, Mean Value Theorem.
Indeterminate forms and L'Hopital's rule, Infinite sequences and series, Power series, Taylor's and Maclaurin's series, Convergence of Taylor's series, Error Estimates, Polar coordinates and Polar equations.
Functions of two or more real variables, Partial derivatives of second and higher order, Euler’s theorem on homogenous function, Total derivatives, Differentiation of composite and implicit functions, Change of variable, Jacobians, Maxima and minima of functions of two or more variable, Lagrange’s method of undetermined multipliers.
Estimating with finite sums and limits of finite sums, Definite integral, The fundamental theorem of calculus, Trigonometric substitutions, Integration by reduction formula for powers of some trigonometric functions, Improper integrals, Beta and Gamma integrals.
Double integrals, Triple integrals, Change of order of integration in a double integral, Change of variables in double and triple integrals, Area as a double integral, Volume as a triple integral. Differential Equations: Second and higher order linear ODE with constant coefficients, General solution to the…...