Mathematics I

Overview

This course covers topics such as Gauss Divergence Theorem, Stokes Theorem, Surface Integrals, Multiple Integrals, Method of Lagrange Multipliers, Maxima - Minima, Mean Value Theorems, Derivatives, Differentiation, Functions of several variables, Line Integrals, Standard Eigen value problem, special ODEs, Length of a curve, Applications of Riemann integral, Riemann Integrable Functions, Properties of continuous function, Riemann Integral, Power series, Tests of Convergence, Curve sketching, Infinite series, Taylor's theorem, Maxima-Minima, and Mean Value Theorems. The course aims to teach students various mathematical concepts and techniques, including calculus, differential equations, and series. The teaching method involves theoretical explanations, problem-solving, and practical applications. This course is intended for individuals interested in advancing their knowledge and skills in mathematics.

Syllabus

Gauss Divergence Theorem.
Stokes Theorem.
Surface Integrals.
Multiple Integrals.
Method of Lagrange Multipliers.
Maxima - Minima.
Mean Value Theorems.
Derivatives.
Differentiation.
Functions of several variables.
Line Integrals.
Standard Eigen value problem and special ODEs.
Length of a curve.
Applications of Rieman integral.
Riemann Integrable Functions.
Properties of continuous function.
Riemann Integral.
Power series.
Tests of Convergence.
Curve sketching.
Infinite series II.
Infinite series I.
Taylor's theorem.
Maxima-Minima.
Mean Value Theorems.
Differentiable Function.