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Applied Mathematics-1 - M-1

Course: B.Tech / BEGroup: Mathematics
Applied Mathematics -1
Differential Equations
Complex Variable
Numerical Methods
Transform Theory
Leibniz Rule – 1
Leibniz Rule – 2
Leibniz Rule – 3
Rolle’s Theorem – 1
Rolle’s Theorem – 2
Lagrange’s Mean Value Theorem – 1
Lagrange’s Mean Value Theorem – 2
Cauchy’s Mean Value Theorem
Generalized Mean Value Theorem
Taylor Mclaurin Series – 1
Taylor Mclaurin Series – 2
Taylor Mclaurin Series – 3
Taylor Mclaurin Series – 4
Indeterminate Forms – 1
Indeterminate Forms – 2
Indeterminate Forms – 3
Indeterminate Forms – 4
Derivative of Arc Length
Polar Curves
Derivatives of Area
Limits and Derivatives of Several Variables – 1
Limits and Derivatives of Several Variables – 2
Limits and Derivatives of Several Variables – 3
Limits and Derivatives of Several Variables – 4
Variable Treated as Constant
Total Derivative
Implicit Differentiation
Partial Differentiation – 1
Partial Differentiation – 2
Euler’s Theorem – 1
Euler’s Theorem – 2
Errors and Approximations
Differentiation Under Integral Sign
Taylor’s Theorem Two Variables
Maxima and Minima of Two Variables – 2
Maxima and Minima of Two Variables – 1
Maxima and Minima of Two Variables – 3
Curves in Cartesian Form
Standard Curves in Cartesian Form
Integral Reduction Formula
Improper Integrals – 2
Rectification in Polar and Parametric Forms
Volume of Solid of Revolution
Improper Integrals – 1
Improper Integrals – 2
Double Integrals
Application of Double Integrals
Change of Order of Integration: Double Integral
Change of Variables In a Double Integral
Triple Integral
Change of Variables In a Triple Integral
Applications of Triple Integral
Basic Definitions
First Order First Degree Differential Equations
Separable and Homogeneous Equations
Reducible to Homogenous Form
First Order Linear Differential Equations
Bernoulli Equations
First Order Nonlinear Differential Equations
Clairaut’s and Lagrange Equations
Geometrical Applications
Orthogonal Trajectories
Law of Natural Growth and Decay
Newton’s Law of Cooling and Escape Velocity
Simple Electrical Networks Solution
Method of Undetermined Coefficients
Harmonic Motion and Mass – Spring System
Special Functions – 1 (Gamma)
Special Functions – 2 (Beta)
Special Functions – 4 (Legendre)
Laplace Transform by Properties – 1
Laplace Transform by Properties – 2
Laplace Transform by Properties – 3
Laplace Transform of Periodic Function
General Properties of Inverse Laplace Transform
Table of General Properties of Laplace Transform
Types and Properties of Matrices
Finding Inverse and Rank of Matrix
Rank of Matrix in Row Echelon Form
Rank of Matrix in PAQ and Normal Form
System of Equations and their Consistencies
System of Equation using Gauss Elimination Method
Curve Fitting
Solving Equations by Crout’s Method
Derogatory and Non-Derogatory Matrices
Eigenvalues and Vectors of a Matrix
Cayley Hamilton Theorem
Diagonalization Powers of a Matrix
Canonical Form or Sum of Squares Form
Directional Derivative
Gradient of a Function and Conservative Field
Divergence and Curl of a Vector Field
Using Properties of Divergence and Curl
Surface Integrals
Volume Integrals
Fourier Series Expansions
Fourier Half Range Series
First Order PDE
First Order Linear PDE
First Order Non-Linear PDE
Homogeneous Linear PDE with Constant Coefficient
Non-Homogeneous Linear PDE with Constant Coefficient
Solution of Second Order P.D.E.
Method of Separation of Variables
Solution of 1D Heat Equation
Solution of PDE by Variable Separation Method
Fourier Transform and Convolution
Linear Difference Equations and Z – Transforms
DeMoivre’s Theorem
Expansion of Trigonometric Functions
Logarithm of Complex Numbers
Complex Conjugates
Roots of Complex Numbers
Regions in the Complex Plane
Functions of a Complex Variable
Set Theory of Probability – 1
Set Theory of Probability – 2
Theorem of Total Probability
Baye’s Theorem
Permutations and Combinations
Random Variables
Probability Distributions – 1
Probability Distributions – 2
Mean and Variance of Distribution
Mathematical Expectation
Binomial Distribution
Hypergeometric Distributions
Poisson Distribution
Normal Distribution
Exponential Distribution
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