IIT Madras MfE 1 Lectures: Math for Electronics I
MA110188 lectures12 weeks
Weeks
- Week 17 lecturesIntroduction · Numbers,variables,functions & equations · Visualizing expressions & equations · Functions of one variable · Problems & graphical solutions · Straight lines · Parabolas & quadratic equations
- Week 26 lecturesSystem of linear equations · Solving system of two linear equations · Matrix representation · Solving system of two variables & three linear equations · Solving system of three variables & two linear equations · Solving system of n variables & m linear equations
- Week 38 lecturesProblems related to functions | introduction to calculus · Sequences · Series · Bounded, monotonic, convergent & divergent sequences · Examples of convergent & divergent sequences · Computing limits | part 1 · Computing limits | part 2 · Monotone convergence theorem
- Week 47 lecturesIrrational limit of sequences · Exponential functions · Limit of function & continuity · Computing the limit of function and determining the continuity · Limits & continuity of powers exponentials · One sided limits · Limits at infinity
- Week 57 lecturesDerivative & its applications · Derivative of a function with examples · Differentiation rules · Derivative of power function · Derivative of polynomial and rational functions · Properties & details · Higher order derivatives
- Week 69 lecturesApplications of derivatives · Mean value theorem · Monotonic function & derivatives · LHopital's rule limits & derivatives · Inverse functions & derivatives · Differential & errors · Introduction to taylors theorem · Taylors theorem · Problems & illustration
- Week 79 lecturesPower series introduction · Geometric series · Harmonic series & q-series · Root & Ratio tests · Convergence of power series · Functions defined using power series · Properties of exp(x) · Properties of e^x · Problems related to e^x
- Week 85 lecturesIntroduction to integration · Area under the curve & riemann sums · The definite integral · Fundamental theorem of calculus & anti-derivatives · Integration by substitution
- Week 97 lecturesApplication of integration · Length of arcs · Perimeter/area of a circle, the number pi, improper integral · Computing volumes of solids · Logarithm Function · Applications of logarithm function · Problems on logarithmic functions
- Week 108 lecturesComplex numbers – introduction · Arithmetic with complex numbers · Complex plane, unit circle, angles in radians · Sinusoidal function · Polar coordinates · Derivative of sin & cos · Complex exponential and euler's formula · Trigonometric identities & roots of unity
- Week 118 lecturesFunctions & their characteristics · Rational functions · Trigonometric functions · Problems · Inverse trigonometric functions · Derivatives & integrals of inverse trigonometric functions · Hyperbolic functions · Inverse of hyperbolic functions, derivatives, and integrals
- Week 126 lecturesOrdinary differential equations · Solution to first-order linear ordinary differential equations (ODEs) · Examples of first-order linear ODE · Second-order differential equation · Non-homogeneous second order differential equation · Examples of second-order linear ODE