Engineering Mathematics-I

About the course

Engineering Mathematics is a branch of science that deals with the mathematical methods and techniques that are typically used in the engineering industry. The subject covers the study of Successive Differentiation, Partial Differentiation and its Applications, Multiple Integration and its Applications, Vector Calculus, etc.

What will you learn?

The complete online syllabus of this course comprises 7 Learning Modules | 150 Topics of Learning | 6 Hours of Learning | 35 Assessments

Module

• Differential Calculus
• Matrices
• Basic of Successive Differentiation
• Curve Tracing and Curvature Of Different Curves
• Multiple Integration
• Application of Multiple Integration
• Vector Calculus

Topics of Learning

• First and Second Order Differentiation
• Application on Simple PD
• Differentiation: keeping variable constant
• Euler’s Theorem
• Numericals on Euler’s Theorem
• Numericals on Euler’s Theorem
• Jacobian
• Application of Jacobian on Implicit Functions
• Errors and Approximation
• Application of Error and Approximation
• Maxima and Minima
• Numerical on Maxima and Minima
• Method of Lagaragninan Multipliers
• Taylor’s Theorem for Function of Two Variable
• McLaurin’s Theorem for Function of Two Variable
• Introduction to Matrices and Determinants
• Minors and Cofactors of Determinant
• Properties of Determinants
• Types of Matrices
• Matrix Algebra
• Some Special Matrices
• Adjoint of a Matrix
• Elementary Row/Column Transformation
• Rank of the Matrix
• Homogeneous & Non Homogeneous Equations
• Inverse of the Matrix
• Gauss Jordan Method
• Partition Method of Finding the Inverse
• Matrix Method(non)
• Cramer’s Rule(homog.)
• Gauss Elimination Method
• Linear Dependence of Vectors
• Consistency of Linear System of Equations
• Characteristic Equation
• Eigen Values and Eigen Vectors
• Properties of Eigen Values
• Caley-Hamilton Theorem
• Normal Form of a Matrix
• Reduction to Diagonal Form
• Complex Matrices
• Continuous Function
• Differentiable Function
• Successive Differentiation
• Leibnitz Theorem
• Curve Tracing: Cartesian Curves
• Curve Tracing: Parametric Curves
• Curve Tracing: Polar Curves
• Double Integration
• Triple Integration
• Change of Order
• Change of Variable
• Application to Area and Volume
• Gamma and Beta Functions
• Dirichlet Integral
• Area of Cartesian Curves
• Area of Parametric Curves
• Area of Polar Curves
• Rectification of standard curves
• Brief Intro of Cylinder, Cone and Conicoids
• Volume of Solids
• Volumes of Revolution
• Surface Area of Revolution
• Vectors
• Vector Function
• Product of Vectors
• Differentiation of Vectors
• Velocity and acceleration
• Point Function
• Normal and Tangent to the curves
• Del Operator
• Gradient of a vector
• Directional Derivatives
• Divergence of a Vector
• Curl of a Vector
• Integration of Vectors
• Line Integral
• Surface Integral
• Green’s Theorem
• Stoke’s Theorem
• Volume Integral
• Gauss Divergence Theorem

For a quick review, please watch our videos here  Online Video-Tutorials For Engineering Mathematics