## Instructor ### Professor

Hemant Kothari

Professor Hemant Kothari teaches from HEART, not just from book. Students love his teaching style and really find it interesting which helps them retain every concept and apply the same in exams. Under his mentorship, students have cleared their engineering exams with flying colors.

## Course curriculum

• 1

### Module 1- Complex Number

• Introduction to Complex Numbers

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• Modulus & Argument

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• Numerical on Modulus

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• Numerical on Argument

• Euler's Formula & De Moiver's Theorem

• Numerical on Euler's Formula & De Moiver's Theorem_1

• Numerical on Euler's Formula & De Moiver's Theorem_2

• Numerical on Euler's Formula & De Moiver's Theorem_3

• Numerical on Euler's Formula & De Moiver's Theorem_4

• Numerical on Euler's Formula & De Moiver's Theorem_5

• Multiple Angles of Sinθ & Cosθ

• Numerical on Multiple Angles of Sinθ & Cosθ_1

• Higher Powers of Sinθ & Cosθ

• Numerical on Higher Powers of Sinθ & Cosθ_1

• Numerical on Higher Powers of Sinθ & Cosθ_2

• Introduction to Roots of Complex Numbers

• Numerical on Roots of Complex Numbers_1

• Numerical on Roots of Complex Numbers_2

• Numerical on Roots of Complex Numbers_3

• Numerical on Roots of Complex Numbers_4

• Numerical on Roots of Complex Numbers_5

• Numerical on Roots of Complex Numbers_6

• Cube roots of Unity

• 2

### Module1- Complex Numbers (Hyperbolic Functions)

• Introduction to Hyperbolic Function

• Numerical on Hyperbolic Identities_1

• Numerical on Hyperbolic Identities_2

• Inverse Hyperbolic Functions

• Numerical on Inverse Hyperbolic Functions

• Numerical on Inverse Hyperbolic Functions

• Relations Between Hyperbolic & Circular Functions

• Compound Angles of tanh h

• Compound Angles of Sin h & Cos h

• Compound Angles of Sin h and Cos h_2

• Series Expansion Separate into Real & Imaginary part

• Series Expansion Separate into Real & Imaginary part_2

• Series Expansion Separate into Real & Imaginary part_3

• 3

### Module 1- Complex Numbers (Log Functions)

• Introduction to log form of Complex Numbers

• Numerical on Complex raised to Complex

• Separate into Real & Imaginary part

• Separate into Real & Imaginary part_2

• 4

### Module2- Partial Differentiation

• Introduction to Partial Differentiation

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• Concept of Symmetry with Numerical

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• Higher Order Differentiation

• Operator Based Numerical

• Implicit Type

• Introduction to Chain Rule

• Numerical on Chain Rule & Free Diagram_1

• Numerical on Chain Rule & Free Diagram_2

• Numerical on Chain Rule & Free Diagram_3

• Numerical on Chain Rule & Free Diagram_4

• Numerical on Chain Rule & Free Diagram_5

• Numerical on Chain Rule & Free Diagram_6

• Implicit & Total derivative using Partial Differentiation_1

• Implicit & Total derivative using Partial Differentiation_2

• Implicit & Total derivative using Partial Differentiation_3

• 5

### Module 2- Partial Differentiation (Homogenous Function)

• Introduction to Homogenous Function

• Proof of Euler's Theorem in 2 Variable

• Proof of Euler's Theorem in 3 Variable

• Numerical on Euler's Theorem_1

• Verify on Euler's Theorem

• Euler's Theorem: Sum of two terms

• Deduction of Euler's if "u" is in homogenous function

• Theorem if f(u) is Homogenous Function

• Deduction if f(u) is Homogenous Function

• Numerical on Euler's and Deduction of Euler's_1

• Numerical on Euler's and Deduction of Euler's_2

• Numerical on Euler's and Deduction of Euler's_3

• Numerical on Euler's and Deduction of Euler's_4

• 6

### Module 3- Successive Differentiation

• Introduction to 1st Formula & Partial Fraction (Type 1)

• Introduction to 2nd formula & Partial Fraction (Type2 )

• Tan Inverse type

• Introduction to Trigonometry type

• Numerical on Defactorization

• Numerical on High Power of Trigonometry

• Introduction to Exponential & Product of Exponential & Trigonometry

• Numerical on Exponential & Trigonometry

• Numerical on Exponential & Trigonometry_2

• Binomial Type

• Introduction to Leibnitz Rule

• Leibnitz Rule Sin Inverse Type

• Leibnitz Rule Sin Inverse Type_2

• Leibnitz Rule Cosh Inverse Type

• Numerical on Leibnitz Rule _1

• Numerical on Leibnitz Rule_2

• Numerical on Leibnitz Rule_3

• 7

### Module 4- Expansion of Functions

• Introduction to Expansions & Formulas

• Numerical on Log_1

• Numerical on Log_2

• Introduction to Maclaurin’s Series

• Numerical on Maclaurin’s Series_1

• Expansion Using Standard Series

• Numerical on Expansion Using Standard Series_1

• Numerical on Expansion Using Standard Series_2

• Numerical on Expansion Using Standard Series_3

• Numerical on Expansion Using Standard Series_4

• Numerical on Expansion Using Standard Series_5

• Numerical on Expansion Using Standard Series_6

• Expansion Using Derivatives & Integration tan Inverse type

• Numerical on Expansion Using Derivatives & Integration tan Inverse type_1

• Numerical on Expansion Using Derivatives & Integration tan Inverse type_2

• Numerical on Expansion Using Derivatives & Integration Sin Inverse type

• Numerical on Expansion Using Derivatives & Integration Sin Inverse type_1

• Powers of (x-a)

• Powers if (x-a)_1

• Using Taylor's Theorem

• Approximate Values

• 8

### Module 5- Matrices

• Types of Matrices

• Properties of Matrices_1

• Properties of Matrices_2

• Properties of Matrices_3

• Examples on Properties of Matrices

• Orthogonal Matrix

• Numericals on Orthogonal Matrix

• Unitary Matrix

• Rank of a Matrix

• Rank of a Matrix by Echelon form

• Rank of a Matrix by Normal form

• Rank of a Matrix by PAQ Normal form

• System of Non Homogenous Equations

• Examples of System of Non-Homogeneous Equations_1

• System of Homogeneous Equations_2

• Examples of System of Homogeneous Equations_3