Mathematics-1

Categories: Semester-1
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Course Content

Calculus:- Unit:- 1
Calculus in engineering mathematics is a branch of mathematics that focuses on the study of rates of change and accumulation. It involves the concepts of differentiation and integration, which are used to analyze and solve problems involving dynamic systems and continuous change. Calculus is fundamental in engineering for modeling and analyzing physical systems, optimizing processes, and designing complex structures. It provides the tools to understand and predict the behavior of variables and functions in various engineering applications, from fluid dynamics and thermodynamics to signal processing and structural analysis.

  • Rolle’s Theorem
    06:15
  • Mean value theorems
    06:37
  • Taylor’s and Maclaurin theorems with remainders
    13:26
  • Indeterminate forms and L’ Hospital’s rule
    52:20
  • Maxima and Minima
    27:26
  • Evaluation of definite and improper integrals
    35:22
  • Beta and Gamma functions and their properties
    18:39
  • Applications of definite integrals to evaluate surface areas and volumes of revolutions
    56:49

Sequences and Series:- Unit :- 2
Sequences are ordered lists of numbers where each number is determined by a specific rule or pattern. Series are the sums of the terms of sequences.

Multivariable Calculus:- Unit:- 3
Multivariable calculus is a branch of mathematics that extends the principles of calculus to functions of multiple variables. It involves the study of how these functions change with respect to changes in their inputs and includes concepts such as partial derivatives, multiple integrals, and vector fields.

Linear Algebra:- Unit :-4
Linear algebra is a branch of mathematics focused on the study of vectors, vector spaces, linear transformations, and systems of linear equations. It deals with concepts such as matrices and determinants to solve problems related to linear relationships and multidimensional spaces.

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