Calculus

Basic Sets, Real Numbers - Axioms of Real numbers - Euclidean spaces, Sequences, Monotony, Subsequence, Convergence, Numerical Series, Convergence Criteria: Absolute and Relative Convergence, Telescopic Series, Limit, Continuity, Derivative, Basic Theorems of Differential Calculus, Convexity, Taylor Theorem, Taylor Series, Power series, Integral, Beta and Gamma Functions, Applications of Integrals, Differential Equations, Functions of several Variables, Limit and Continuity - Partial Derivative, Extrema, Completion, Multiple Integration, Change of Variables, Fourier Theory, FFT.

Objectives

The learning objective is to familiarize students with the concepts of Basic Theorems of Differential Calculus, multivariate equations and troubleshooting techniques of Calculus and their use in solving problems.

Prerequisites

Non required

Syllabus

Basic Sets, Real Numbers - Axioms of Real numbers - Euclidean spaces, Sequences, Monotony, Subsequence, Convergence, Numerical Series, Convergence Criteria: Absolute and Relative Convergence, Telescopic Series, Limit, Continuity, Derivative, Basic Theorems of Differential Calculus, Convexity, Taylor Theorem, Taylor Series, Power series, Integral, Beta and Gamma Functions, Applications of Integrals, Differential Equations, Functions of several Variables, Limit and Continuity - Partial Derivative, Extrema, Completion, Multiple Integration, Change of Variables, Fourier Theory, FFT.